Computer Program for
Calculating and Fitting
Thermodynamic Functions

Bonnie J. McBrideand Sanford Gordon

Nl\SI\--

NASA
Reference
Publication
1271
1992

Computer Program for
Calculating and Fitting
Thermodynamic Functions

Bonnie J. McBride
Lewis Research Center
Cleveland, Ohio
Sanford Gordon
Sanford Gordon and Associates
Cleveland, Ohio

NI\SI\
National Aeronautics andSpace Administration
Office of Management
Scientific and Technical
Information Program

Contents
Page
I

Summary

Introduction. . .. . .. . . .. . . .. . . .. . .. . .. .. . .. . . .. . . .. . . .. . .. . . .. . .. . .. .. . .. .. . . . .. . .. . . .. . . .. . .. . . .. . .. . . .. . . . .. . . .. . . .. ... 1
2
Calculation of Ideal Gas Thermodynamic Functions
Internal Partition Functions for Monatomic Gases
2
Cutoff methods
2
3
Inclusion of predicted levels
Internal Partition Function for Diatomic and Polyatomic Molecules
3
Partition function
3
Internal rotations
4Group Additivity Method
44Empirical Equations For Thermodynamic Functions
Assigned Enthalpy Values
4
Assigned Reference Elements
4
5
Heats of Formation and Equilibrium ConstantsComputer Program................................................................................................... 5
Availability to Other Organizations
5
Input Data Codes................................................................................................... 5
Options
5
Partition functions-monatomic gases
6
Partition functions-diatomic and polyatomic gases
6Internal rotation contributions
6
Estimation by group additivity method
6
Thermodynamic functions from empirical equations
6
6
Least-squares fit
Extrapolation by Wilhoit's method
7
7Heat of formation and loglOK values
Output tables
8
Input
8
Uniform format
8
8Contents of individual records, 8
General Flow of Program
Output9Input data
99Tables of thermodynamic properties
9
Tables of least-squares errors
Intermediate output............................................................................................. 10
EF data
10
Examples. .. . . . . . .. . .. . . .. . . . . .. .. . .. .. . . .. . . .. . . .. . .. .. . .. . . .. .. .. . . .. . . . . .. . .. . . .. . . .. . .. . . .. . .. . . . .. . . .. . . .. . .... 10
Main Routine and Subroutines................................................................................. 10
ATOM
10
DELH
10
DERIV
10
EFTAPE and entry EFLIST.. . .. . .. .. . . .. .. .. . . .. . . .. . . . .. . . .. . . . .. . .. . . .. . . .. . .. . . . . .. .. . . ... 10
EIGEN
10
GROUP
10
HMAT
11
IDENT
11
INPUT
11
INTROT
11
IROTOR
11
LEAST
11

iii

LINKlLOOKPAOEID
POLY
PRINT
PUNCH
QSUM
RECO
TABLESTEMPERWCALCWILHOIBLOCK DATA

11
11
11
11
11
11
11
11
12
12
12
12
12

Appendix A-Symbols

13

Appendix B-Details in Preparing Input
15
Uniform Format
15
Order of Input Records
15
Description of Input Records
16
CTEM record.................................................................................................... 16
Data records
16
Data records for the READIN method
16
Data records for the COEF method
16
Data records for the FIXEDN, ALLN, or TEMPER methods
16
Data records for the RRHO, PANDK, JANAF, NRRAOl, or NRRA02 methods
16
Data records for the ADD method
17
DATE record
17
EFDA and EF data records................................................................................... 17
FINISH record
17
Formula record.................................................................................................. 17
LISTEF record
18
LSTSQS record.................................................................................................. 18
METHOD record
19
NAME record
19
OUTPUT record
19
REFNCE record
20
TEMP record.................................................................................................... 20
Appendix C-Details In Output
Listed Output
Input data
Tables of original thermodynamic properties
Tables of thermodynamic properties from least-squares coefficients
Tables of least-squares errors
EF dataIntermediate data with FILL option for monatomic gases
Intermediate data with INTERM label
Monatomic gases
Diatomic and polyatomic gases
Saved Output
EF data
Least-squares coefficients

IV

21
21
21
21
21
21
21
22
22
22
22
22
23
23

Appendix D~ Examples
24
Example 1 (Ar(g) by Method TEMPER with FILL and LSQS Options)24
Problem
:
24
Input
25
Listed Output
26
Example 2 (C 2H 3(g) by Method ADD with Wilhoit Extrapolation)
30
Problem30
Input
30
Listed Output
31
Example 3 (C4 H4 (g) by Method READIN with Wilhoit Extrapolation)
33
Problem
33
Input
33
Listed Output
34
Example 4 (CSH11(g) by Method RRHO with Internal Rotation)
36
Problem36
Input
36
Listed Output
37
Example 5 (H 20(g) by Method NRRA02 with Intermediate Output)
38
Problem
38
Input
38
Listed Output
39
Example 6 (Mg(cr,f) by Methods READIN and COEF with EFTAPE
and LSQS Options).. . . .. . . .. . . .. . .. . .. . . .. . .. .. . .. . . .. . . . .. . . . .. . . . .. .. . . . . .. .. . . . .. . . . . . .. .. . .. . . .. .. 40
Problem40
Input
41
Listed Output
42
Example 7 (MgO(g) by Method JANAF with LSQS and LOGK Options)45
Problem45
Input
45
Listed Output
46
Example 8 (Na2C03(l,2,f) by Methods READIN and COEF with LSQS
and LOGK Options)50
Problem50
Input
51
Listed Output
52
References

,

,

55

56
Tables I-Fill Procedure Parameters
II-Some Terms In In Q and Their Derivatives
57
III-Terms In In Q~
60
IV- Brief Description of Contents Of Input Records
64
V-Contents of Formula Records
65
VI-Contents of Method Records
65
VII-Contents of Data Records
67
VIII-General Thermodynamic Coefficients Format
70
IX-Group Notation and Structure............................................................................ 71
X-Group Additivity Coefficients
75
XI-Index of Input Record ID'S and Labels
80
Figure 185v

Summary
A computer program is described which (1) calculates
thermodynamic functions (heat capacity, enthalpy, entropy,
and Gibbs energy) for several optional forms of the partition
function, (2) fits these functions to empirical equations bymeans of a least-squares fit, and (3) calculates, as a functionof temperature, heats of formation and equilibrium constants.
The program provides several methods for calculating ideal
gas properties. For monatomic gases, three methods are given
which differ in the technique used for truncating the partition
function. For diatomic and polyatomic molecules, five methods
are given which differ in the corrections to the rigid-rotator
harmonic-oscillator approximation. A method for estimating
thermodynamic functions for some species is also given.

Introduction
The computer program PAC1 (Properties and Coefficients),
documented in reference 1, was initially made available tooutside organizations in 1967. Since that time, PACI has been
continuously revised, updated, and extended. Inasmuch as the
program continues to be widely requested and used, this reportis being published to provide documentation for the current
version, referred to as PAC91.
The two principal purposes for initially preparing PAC 1 arestill valid today, namely, (1) to provide a means for generating
theoretical thermodynamic functions from molecular constantdata and (2) to provide a means of fitting these functions toempirical equations by using a least-squares fit. The coefficientsobtained from the fit may then be used to generate a libraryof thermodynamic data in a uniform and easy-to-use format
for use in other computer codes. Several large compilationsof selected or calculated thermodynamic data currently exist.
(See refs. 2 to 4 for some examples of early compilations andrefs. 5 to 9 for some examples of more recent compilations.)
Nevertheless, in spite of these compilations, there is a continuing need for additional calculations due to (1) discoveryof new species, (2) revision of existing molecular constant dataand structural parameters, (3) need for data at temperaturesother than those already published, (4) availability of new orrevised heats of formation, dissociation, or transition, and (5)revision of fundamental constants or atomic weights. Calculations may also be needed to compare the results of assuming

various possible forms of the partition function. In addition,
as mentioned previously, there is often a preference forthermodynamic data in functional rather than tabular form.
In order to carry out these needs, the PAC91 program has
been prepared to perform any combination of the following:(1) calculate thermodynamic functions (heat capacity, enthalpy,
entropy, and Gibbs energy) for any set of 1 to 202 temperatures, (2) obtain a least-squares fit of the first three of thesefunctions (either individually, two at a time, or all threesimultaneously) for up to eight temperature intervals, and (3)calculate, as a function of temperature, heats of formation andequilibrium constants from assigned reference elements. The
number 202 for temperatures is somewhat arbitrary but was
selected to accommodate a schedule of temperatures from 100
to 20000 K at every 100 K, T = 298.15 K, and one additionaltemperature, if desired, such as T = 273.16 K.
The thermodynamic functions for ideal gases may be
calculated from molecular constant data using one of several
partition function variations provided by the program. For
monatomic gases, (1) one of three partition function cutoff
techniques may be selected and (2) unobserved but predicted
electronic energy levels may be included by the program. For
diatomic and polyatomic gases, (l) one of five partition
functions may be selected which differ in the correction factors
for nonrigid rotation, anharmonicity, and vibration-rotationinteractions and (2) excited electronic states may be included.
Several new capabilities that were added to the program
since the last publication include (l) the estimation ofthermodynamic properties by a group additivity method, (2)the ability to calculate properties for species with internal
rotors, and (3) a method for extrapolating data to hightemperatures.
For the purpose of additional processing, (1) known thermodynamic functions for solids, liquids, or gases may be readin directly or (2) thermodynamic functions may be calculated
from heat capacity equations.
Because of the variety of options provided and the resulting
variety of input data required, an objective was to provide fora relatively simple procedure for reading input data. This was
accomplished by means of a uniform input format.
At the time reference 1 was written (1967) input was readin by means of punched cards. While punched cards are nolonger used, 80-colunm records are still retained for input.
The program and the equations used are described in detail.
Examples of input and output are given for a variety of species.

Calculation of Ideal Gas Thermodynamic
Functions

L

Q=

m

m=l

For gaseous species, the thermodynamic functions may be
calculated from spectroscopic constants. A general discussionof methods of calculation is given in references such as 1 and
8. Many of the equations will be repeated here for convenience.
The properties are expressed as functions of the internal
partition function Q; that is,

H T - Hgd(ln Q)

RT

dT

~--=T

+-5

(2)

2

-ST = T d(ln Q) + In Q + -3 In M + -5 In T + Sc
R

2

dT

_

(3)

2

So
HO
HO
3
G oT - HO0 = -.!.
_ T0 = In Q + _ In M
RT

R

RT

2

5
2

5
(4)
2

+ - In T + S - c

where

(5)

Sc is the Sackur-Tetrode constant. (T] = 1 K. Other symbols
are defined in appendix A.) When Po = 100 000 Pa (1 bar),
Sc = -1.151693. When Po = 101 325 Pa (1 atm), Sc =-1.164856. Thus, values of STIR in units of bars will behigher than corresponding values in units of atm by 0.013163.
The values for Sc and other fundamental constants are
obtained from reference 10. The values of these constants arecontained in BLOCK DATA of the program and are givenin the section BLOCK DATA.
The internal partition function Q in equations (1) to (4) is
given by
L

Q=

E Qm

(6)

m=!

where Qm is the internal partition function for the m th electronic
state and L is the number of electronic states.

Internal Partition Functions for Monatomic Gases
For monatomic molecules, internal energy consists ofelectronic energy only. Equation (6) then becomes2

L

E Q~l= E (21 + 1m=!

L)e-cllllkT =E

gme-c,,/kT

m=!·

(7)
where Q~: 1m , Em' and gm are the electronic energy partition
function, total angular momentum quantum number, electronic
excitation energy, and statistical weight, respectively, for thethm electronic state.
Cutoffmethods.-An infinite number of bound states exist
below the ionization limit for a hypothetical isolated atom
(L = 00 in eq. (7». Inasmuch as the partition function diverges
and approaches infinity as L - 00, the summation must be cut
off. Reviews of various cutoff methods are given in a numberof references such as 1, 8, 11, and 12. The following review
essentially repeats that given in reference 1.
The cutoff methods may be considered to be of the following
types:(1) No dependence on temperature or pressure(2) Dependence on temperature only
(3) Dependence on temperature and pressure (or density)and possibly degree of ionization
In the first of the three types, the summation may include
various numbers oflevels. For example, only the ground stateis used in the Saha equation (see ref. 13) and only valence
states are included in reference 8. The summation of equation(7) may be over a fixed and usually arbitrary number of levels(as, e.g., in ref. 14) or equation (7) may be summed throughall observed levels (as in ref. 15, e.g.).
The second cutoff type is temperature dependent. The
ionization potential is reduced by a quantity referred to as theionization potential lowering, which in this case is a functionof temperature only. The partition function is then permitted
to include only those levels below the lowered ionization
potential. In reference 16 it was suggested that the ionization
potential be lowered by an amount equal to the temperaturefunction kT. This suggested method was used in reference 4.
Other temperature functions are summarized in reference 11.
The first two cutoff types are distinguished by the fact thatthey permit the partition functio.n and related thermodynamic
properties to be calculated as functions of temperature only.
For the third type, it is not possible to calculate the partition
function by specifying temperature only. One cutoff techniqueof this type relates the highest permitted principal quantum
number n to the number of particles per unit volume (number
density) such as suggested by Bethe (see discussion in ref. 11).
Another technique uses the ionization potential lowering
procedure previously described, but in this case the quantity
by which the potential is lowered is a function of electron andionized particle number densities. Several such quantities arc
summarized in reference 11.
This last technique involves mixtures of species andtherefore precludes, for all practical purposes, the possibilityof generating tables for individual species as a function oftemperature only. This is due to the fact that the cutoff criterion
needed to calculate the partition function depends on mixture
composition, while the calculation of mixture composition
depends on the partition function. Thus, an iterative procedure
is required where the partition function at a specified
temperature may be changing from one iteration to the next.
Consequently, since PAC91 calculates thermodynamic properties
only for pure species, just the first two cutoff types are
considered in this report.
Inclusion ofpredicted levels.-In addition to the divergenceproblem, there is the problem of whether to include observed
energy levels only or to also include levels for predicted terms
which, so far, have not been observed. From atomic theory,
as presented in texts such as reference 17, predicted terms canbe derived. Some of these terms are given in tables 10 and
11 in reference 17; in tables 5 to 20 in reference 18; and inreference 19. An examination of the tabulated observed terms
in references 18 and 19 shows that many predicted terms are
missing, especially for the higher quantum numbers.
It has been shown that various series of levels can be
represented by formulas such as the Rydberg or the RydbergRitz formulas (e. g., ref. 20). The constants in these formulas
can be determined from known levels and used to extrapolate
for the unobserved levels. However, the number of observed
levels differ from species to species and, therefore, some
judgment must be exercised in obtaining these constants. An
alternate, but considerably simpler, technique for filling in
unobserved levels, which gives essentially the same results
for the partition function for l1l;any species as does the use of
the Rydberg-Ritz equations, is included in the program. This
alternate technique will now be described.
When the statistical weights gi corresponding to predicted
terms were examined, it was determined that for many
chemical elements the sum of the statistical weights can be
expressed by the following simple function of the principal
quantum number n (except for the ground state n of most
species):(8)

Equation (8) applies only to terms arising from excitationof the emission electron and does not account for other possible
terms. A table in reference 1 contains, for the first 20 chemicalelements, (1) the derived constants b to be used in equation (8)to obtain E gi for any n above the ground state and (2) E gi
values for the ground state. In reference 12, this table was
extended to include all the first 86 elements except for thelanthanide series (elements 58 through 71). Table 5 fromreference 12 (p. 28) appears in this report as table I. The total
quantum number above the ground state is given as a functionof n in equation (8). However, in reference 12 it wasrecommended that, for some elements, the total quantum
number above the ground state should be taken as a constantvalue (called c*) for all values of n. Values of c* are given
in table I for elements 21 through 28, 39 through 46, 57, and72 through 78.
The usefulness of equation (8) arises from the fact that theinclusion of an unobserved level generally makes considerably
more difference in the partition function than does the error
in the estimated energy for this level. Therefore, an option
is provided in the PAC91 program to determine for each n
the difference in statistical weight sums between the observed
levels which have been read in as input and that given byequation (8). The program then adds this difference to the giof the highest observed level for the corresponding n.
This method of filling in predicted, but unobserved, levels
by means of equation (8) was used to calculate the thermodynamic functions of the atomic species in reference 4.

Internal Partition Function for Diatomic and Polyatomic
Molecules
Partition function.-For diatomic and polyatomic molecules,
Qm in equation (6) involves vibrational and rotational as wellas electronic energy. In this report the following factored form
is used to calculate QIlI:orIn QIlI = In Q~'+ In Q'{) + In Q'R + In Q;l+ In Qo' + In Q'iv + In Q~I(9)

A recent review of formula details for these individual
contributions to Q is given in reference 8. Some earlier
references are as follows. The quantities Q~;; Q'O, and Q'R are
the electronic, harmonic-oscillator, and classical-rotation contributions to the partition function, respectively, as given instandard texts (see refs. 21 to 24). The remaining quantities
in equation (9) are the following correction factors: rotational
stretching (centrifugal distortion) Q~l (refs. 24 to 26), lowtemperature rigid rotation Qo1 (refs. 24 and 27), Fermi
resonance Q'w (ref. 28), and both anharmonicity andvibration-rotation interaction Q~' (refs. 29 to 31).
The program provides five methods of cH1culating thepartition function which vary in the inclusion of, and formulasfor, the correction terms (In Q~l, In Q(;', In Q'w, and In Q~II).
This provision is made so that the results of the various
methods may be compared.
Table II contains detailed formulas for all the In QIII terms
and their derivatives except those for In Q~~rwhich are given
in table III. The derivatives of In Q~? are not given directly
as are the derivatives in table II. It was found to be considerably
more convenient to express the derivatives of In Q;~lby meansof general formulas than to obtain the derivatives directly.
These general formulas are given in a footnote to table III.

Internal rotations.-A number of species, such as propyleneoxide or hydrogen peroxide, have internal rotation. Energy
levels for internal rotation may be calculated from potentialfunctions, usually of the form

(10)

where V is the potential, VII an n-fold barrier, n an integer
from 1 to 6, and ¢ the phase angle. These energy levels may
then be used to calculate the internal rotation contribution to
the thermodynamic functions.
A computer program for calculating the energy levels andthermodynamic functions for the equation (10) potential was
written by J. Laane and Associates based on the analysis inreference 32. This program was incorporated into PAC91 withnecessary modifications. In addition, an option was added to
calculate the contribution of a free rotor.
The subroutines which are involved in the hindered rotation
calculation are INTROT, IROTOR, HMAT, EIGEN, and
PRINT. A brief description of these routines is given in thesection Main Routines and Subroutines.

where the exponent qi may be zero or either a positive or
negative whole or fractional number.
Enthalpy and entropy are related thermodynamically to
C1J R as follows:

HOT

bI

JfcodT
p

RT

T

RT

-=-+--~= ", +

1(~;)

(12)

dT

(13)

where b l and b 2 are integration constants.
In equation (12) all terms are divided by Tin order to makethe equation dimensionless. The program uses equations (II)to (13) in two ways: (I) in generating the coefficients ai andbj from a set of thermodynamic data using the least-squares
technique given in reference 40 or (2) conversely in generating
the thermodynamic data from the empirical equations. Some
details of the least-squares method are given in the section
Least-squares fit.

Group Additivity l\1ethod

Assigned Enthalpy Values

Several methods are available for estimating thermodynamic
properties when molecular constant data for calculating partition
functions are not available (e.g., see refs. 33 to 39). One ofthese methods is the group additivity method. S.W. Benson
and coworkers have presented extensive tables of groupproperties for use with this method (refs. 35 and 36). These
group properties permit estimating the heat of formation andentropy at 298.15 K and heat capacities from 300 to 1000 or
1500 K (depending on the group). In reference 37 Steinpresents heat capacity properties to 3000 K for 18 groups
pertaining to hydrocarbons.
Specialized techniques exist for obtaining estimates fromgroup properties which may give more accuracy than that of
Benson's method (e.g., refs. 38 and 39). However, Benson's
method is accepted for PAC91 because of its relative simplicity,
good accuracy, and application to a wide variety of species.

For some applications (see ref. 41) 1t 1S convenient to
combine sensible enthalpy and energies of chemical andphysical changes into one numerical value. An arbitrary base
may be adopted for assigning absolute values to the enthalpyof the various substances, inasmuch as only differences inenthalpy are measurable. For example, the arbitrary baseselected in reference 4 was a value of zero at 298.15 K(H298.15 = 0) for a selected set of elements. This base wasalso selected for PAC91. It makes the assigned value,H298.15, of any substance equal to its heat of formation at
298.15 K from this set of selected elements.

Empirical Equations For Thermodynamic
FunctionsEmpirical equations for thermodynamic functions are often
used for convenience. In dimensionless form, equations forheat capacity are usually of the following type:

E r/,
ai

i=1

4

(ll)

Assigned Reference Elements
The designation of an element in a particular phase to bea reference element is needed in order that values of heats offormation !:J.flr and equilibrium constants loglaK be unambiguously related to specific reactions. Reference 42 gives
thermodynamic functions, phases, transition temperatures, andheats of transition for the following 50 elements plus deuterium
and election gas: Ag, AI, Ar, B, Ba, Be, Br2' C, Ca, Cd,
C1 2 , Co, Cr, Cs, Cu, D 2 , e-, F 2, Fe, Ge, H 2 , He, Hg, 12 ,K, Kr, Li, Mg, Mn, Mo, N 2 , Na, Nb, Ne, Ni, 02, P, Pb,
Rb, S, Si, Sn, Sr, Ta, Th, Ti, U, V, W, Xe, Zn, and Zr.
The enthalpy and free energy values from reference 42 havebeen stored on a file (referred to herein as the EF data file)for the purpose of D.fH and 10gloK calculations.

rHeats of Formation and Equilibrium
Constants

Center) at the following address:
COSMIC382 East Broad Street
Athens, GA 30602
Tel: (404) 542-3265
FAX: (404) 542-4807

In the program described in this report, heats of formationand log 10K for a species are calculated as functions oftemperature for the formation of the species from the elementsin their assigned reference state. The following is an exampleof how these properties are calculated for CO(g) at 1000 K:

11flf.OO) = (H 1000H1000
HfOO)) CO(g) - ()C(graphite) - -21()
02(g)
(14)

A

flO

I...J.J~ [00)

-_

(Go)
[00)

CO(g)

-

(Go)
1000

C(graphile)

-

-1

2

(Go )
loo)

02(g)

The program will generally be sent out on a diskette whichcontains the following four files:
File number

Contents

1
2
3

PAC91 source program
EF data sets for reference elements
Least-squares coefficients for additivity groups
Input data sets for examples

4

(15)

By definition,logl K=o

11 flO- 'J,-,y2.3025851 RT(16)

The preparation of files 2 and 3 is discussed in the section"Saved output" in appendix C. File 4 contains the input for
the eight examples given in appendix D which can serve as
test cases for checking out the program. Files 2, 3, and 4
require approximately 160, 24, and 10.2 kilobytes, respectively.

Input Data Codes

Computer Program
The computer program PAC91 was written in ANSI standard
Fortran 77. PAC91 should work on any system with sufficientstorage. There are about 5500 lines in the· source code whichuses about 300 kilobytes of memory. The compiled program
takes about 390 kilobytes.
Some input and output files are stored in the standard I/Ounits 5 and 6, respectively. Other I/O units are used in conjunction with least-squares coefficients, EF data sets, and group
additivity data (see section "Saved Output" in appendix C).
These nonstandard I/O units are as follows:
I/O unit

Contents or function

10
11
13
14
17
19

Least-squares coefficients
Formatted EF data
Unformatted EF data
Scratch unit for formatted EF data
Scratch unit for unformatted EF data
Group additivity data

No OPEN statements for the I/O units were included in thesource program.

Availability to Other Organizations
The PAC91 program can be obtained for a fee fromCOSMIC (Computer Software Management Information

The input for a particular species is a set of 80-column
records. There are many alphanumeric code words in theserecords. These code words use capital letters and numbers andhave a maximum length of six characters. They either (l)indicate an option; (2) identify a record; or (3) describe theinformation that follows it.
These code words will be used throughout the report. The
input code words in columns 1 to 6 will be referred to as record
IDs. Elsewhere on the record, they will be referred to as labels.
An index of code words is given in table XI which may be
helpful in locating definitions, discussions, and examples. A
complete discussion of input format is given in appendix B.

Options
The program provides a choice of several methods forcalculating the thennodynamic functions Cop' HOy - HO0, HOy- H298.ls, ST, - (GHg), and -(GT - H298.ls), For
ideal gases, these functions may be obtained from one ofseveral assumed forms of the partition function, from empiricalequations, or, for some hydrocarbons, from the group
additivity method. For solids and liquids, the thermodynamic
functions may be calculated only from empirical equations.
In addition, thermodynamic functions for any phase of a
species may be read in directly for additional processing.
The program also has two other capabilities which are
optional: (1) least-squares fitting of the thermodynamic
functions to empirical equations (eqs. (11) to (13») and (2)calculating heats of formation and logloK values for the same
temperature range as the functions.

r-

5

The following is a discussion of these optional features.
Partition functions-monatomic gases. ~The partition
function for monatomic gases is given by equation (7). The
program permits three optional ways of tenninating the numberof energy levels L to be included in calculating this partition
function. These three options, indicated by their input codenames, are: (1) ALLN-inclusion of all electronic levels in
the input data, (2) FIXEDN-inclusion of all levels througha specified principal quantum number n, and (3) TEMPERinclusion of all energy levels that are less than or equal to theionization potential lowered by an amount kT (see section

Cutoff methods).
With any of these three cutoff options, an additional option(FILL) is provided to include predicted but unobserved levels
automatically (see discussion in the section Inclusion ofpredicted levels). All of these options are labels on the
METHOD record (see table VI).
Partition functions-diatomic and polyatomic gases.-For
diatomic and polyatomic gases, the program provides for aselection of five methods of calculating the partition function.
These methods vary in the inclusion of, and formulas for, thecorrection terms (In Qp, In Q(J, In Qw, and In Qc) in equation(9). The formulas for the In Q terms included in each of thefive methods are given in tables II and III. If certain
spectroscopic constants are not available as input, the programautomatically excludes those In Q terms involving them. The
methods (with their METHOD record labels given in parentheses) are as follows:(1) Rigid-Rotator Harmonic-Oscillator (RRHO) approximation~This method excludes all the correction terms inequation (9) (Le., In Qp, In Qo, In Qw, and In Qc)'
(2) Modified Pennington and Kobe (PANDK) method-The
formulas given in table III for In Qc are similar to those given
in reference 29. The method in this report is equivalent to theone described in reference 4 except for the formula for In Q(J(formula 6 in table II). All correction terms in equation (9)are included with the exception of the Fermi resonance In Qw
as indicated in table II.
(3) Joint Army Navy Air Force (JANAF) method-This
method is described and used in reference 6. For diatomic
molecules, it is the same as the PANDK method except forthe definitions of al and XII which are used in formulas 9 and
12, respectively, in table III. For polyatomic molecules, the
JANAF method is the same as the RRHO method.
(4) Nonrigid-Rotator Anharmonic-Oscillator 1 (NRRAOl)In addition to the In Q(J and In Qp terms, all the In Qc terms
given in references 30 and 31 were included which do notcontain a (C2/ T ) 2 or (C2/n 3 factor.
(5) Nonrigid-Rotator Anhannonic-Oscillator 2 (NRRA02)This method includes the same In Qc terms as NRRAO 1 withthe addition of In Qc terms from references 30 and 31 whichcontain (C2/TJ 2 factors.
METHOD record labels are summarized in table VI.
Internal rotation contributions.-As described in the section
Internal rotations, PAC91 includes the capability of calculating6

the contributions of internal rotation, free or hindered. The
contribution of each internal rotor replaces the contributionof a fundamental frequency. Thus the total number of fundamental frequencies (including degeneracies) plus the numberof internal rotors remains 3N-6, where N is the number ofatoms in the molecule.
Estimation by group additivity method. - As mentioned
previously, PAC91 provides an option for estimating thermodynamic properties by a group additivity method. At present,
thermodynamic properties for just 34 groups have been
prepared for use with PAC91 (see section Input). These groupproperties permit estimating properties for some but not allhydrocarbons (e.g., groups for cyclic and fused hydrocarbons
are not included). The group properties are in the form of leastsquares coefficients with C~ represented as a fourth-orderpolynomial. The additivity method requires identifying thevarious groups comprising the species. This is discussed
further in the sections Input and Data records for ADD
method in appendix B and in example 2 in appendix D).
Thennodynamic functions from empirical equations.- The
routine for calculating thermodynamic functions from theempirical equations (eqs. (11) to (13» has the following features:(1) The value of r (number of coefficients a) may be any
number from 1 to 8.
(2) The temperature exponents qi may be zero or any
positive or negative whole or fractional number.
(3) Any number of sets of ai and qi may be read in forvarious temperature intervals for a particular species.
(4) The integration constants b I and b2 may be read in or
calculated by the program from the enthalpy and entropy
values, respectively, for a specific temperature.
(5) When a phase transition occurs, the integration constantsb I and b2 for the second phase may be read in or calculatedby the program from either the enthalpy or entropy oftransition.
(6) There is an option to write the heat capacity coefficientsand the two integration constants for each temperature interval
on I/O unit 10.
.
Least-squares fit.- The least-squares routine fits thethermodynamic functions C~/ R, HT! RT, and Sri R toequations (11), (12), and (13) either individually, any two
simultaneously, or all three simultaneously (the default option).
The selection of the appropriate labels for fitting anyone
function or any two simultaneously is discussed in the section
LSTSQS record(s) in appendix B. The least-squares fit has
the following additional features:(1) The value of r (number of coefficients a;) may be any
number from 1 to 8. (In PACI, r was 1 to 10.)
(2) The temperature exponents qi may be zero or any
positive or negative whole or fractional number.
(3) An option is provided to permit the data to be divided
into any number of specified intervals from 1 to 8. The purposein providing for several intervals is to increase the accuracyof the fit. (In PAC 1, the number of intervals was 1 to 9.)(4) The equations for each temperature interval are usuallyconstrained at an endpoint to fit either the original data or thevalues obtained from fitting an adjacent interval. However,there is an option to remove the constraint by use of the label
NOCNS. The purpose of these constraints is to give equalvalues of the functions at the common point and thus avoid
discontinuities between consecutive intervals. Also, only one
temperature may be specified in the input for which the fitted
equations reproduce the original values. (If no temperatureis specified, the program assigns 298.15 K. In PAC1 thedefault assigned temperature was 1000 K.)(5) For two or more phases, if an enthalpy of transition(labeled DELTAH) or an entropy of transition (labeled
DELTAS) is given, the original data as well as the least= ~t,Hr.
squares fitted data will be constrained so that TJ3.
(6) For each temperature interval, the coefficients ai forheat capacity plus the two integration constants will be written
on I/O unit 10. (In PACl, these data were punched on binary
cards.)(7) If the temperature exponents qi (EXP labels on the
LSTSQS records) are not specified, PAC91 defaults to thefollowing form of equation (11):

t,sr

(17)

and corresponding forms for Hr/RT and STIR (see table VITI).
(8) The equations for C~/ R may be the same or different
for each temperature interval.
(9) At least as many values of C~ (or C~/R) are requiredas the number of exponents in equation (11) or equation (17).
If fewer C~ (or C~/R) values are given in the input than thenumber of exponents requested. PAC91 automatically reduces
the number of exponents to the number of C~ or C~/R values.
It should be noted that the present format for the leastsquares coefficients differs from that of PAC 1. Details of thepresent format are given in table VIII.
Extrapolation by Wilhoit's method.-Occasionally data are
given in the literature to only relatively low temperatures (sayto 1000 or 1500 K) but data may be needed to higher
temperatures for some applications (such as shock tube data
analysis). As has been pointed out (see ref. 5). extrapolationof thermodynamic data with the functional form described in
the previous section may give bad results. An example is theextrapolation of data for iso-octane which are given inreference 7 to 1500 K. The least-squares coefficients which
are generated from these data give an extrapolated value at
3000 K of C~/ R = - 3331. This impossible situation can be
avoided by obtaining extrapolated values from a method forfitting data presented by Wilhoit (ref. 43). Wilhoit gives thefollowing equation for C~:

C;;=C;;(O) + [C;;(OO)-C;(O)]l [1 + (y-l)

IE a;YI](18)

where y = T/ (T + S) (y varying from 0 to I), S a scaling
factor. C~ (0) the low temperature limit for C~, C~ ( (0) thehigh temperature limit for C~, and ai the least-squares
coefficients. C~ (0) includes only rotational and translational
contributions (C~ (0) = 3.5R for linear and 4R for nonlinear
species) while C~ ( (0) also includes the vibrational contributions. The total contributions result in C~ ( (0) = (3N - 1.5) R
for linear and (3N - 2)R for nonlinear species, where N is
the number of atoms in the molecule.
A computer program for this method with n = 3 in equation(18) is given in appendix B of reference 5. This program wassomewhat modified and incorporated into PAC91 as
subroutines WILHOI and WCALC. While the original Wilhoit
method is presented in reference 43 as a method of fitting datarather than extrapolating data, PAC91 uses these subroutines
only for the purpose of extrapolation. The general procedure
involved in PAC91 in using these subroutines is(I) The original input data are fitted to Wilhoit's functional
form and the Wilhoit coefficients are generated.
(2) These coefficients are then used to extrapolate thethermodynamic data to various specified temperatures.
(3) The original data and the extrapolated data are then refitto the PAC91 functional form.
For the example of iso-octane mentioned previously. the useof the Wilhoit fit for extrapolation gives a reasonable valueof C~/R=75.299 at 3000 K. (The classical value is
C~ (oo)/ R = 76.) Additional examples using Wilhoit extrapolation are given for examples 2 and 3 in appendix D.
In addition to the usual input data, the use of the Wilhoit
method for extrapolation requires a WILH label on a
METHOD record. The program also requires knowledge withthis method of whether the species is linear or nonlinear.
Unless specified otherwise, the program assumes the species
is nonlinear. For linear species, the label LINE is required.
Heat of formation and 10gloK values. - The programprovides an option for calculating, as a function oftemperature, heats of formation and log 10K values of a
species formed from its reference elements (see sections
Assigned Reference Elements and Heats of Formation andEquilibrium Constants). These values for a particular species
can be calculated if the necessary enthalpy and free energy
data for the reference elements (referred to as EF data) areavailable. Therefore, the assigned reference elements areprocessed first. For these reference elements there is an option
to save the enthalpy and free energy data in two ways: (I)in an unformatted form on I/O unit 13 replacing any data forthe element already in the library and (2) in a formatted form
appending the data on I/O unit 11. (See appendix C for
additional information on the contents of EF data saved on
7

I/O unit 11.) The data on I/O unit 13 are ready for immediateuse. For backup purposes, the data on I/O unit 11 may betransferred to and included in a file containing EF data informatted and readable form for all reference elements whichhave already been processed. These files replace the set ofpunched binary EF data cards of reference 1.
The data on 110 unit 13 are saved for use with other species
being processed during the same computer run as well as forlater computer runs. The data in the formatted EF data file
discussed previously may be read in as part of the input and,if so, are automatically put on I/O unit 13. The newly read-in
data replace data already on I/O unit 13 for any matchingelements.
If there is a temperature in the data for a particular species
which is not contained in the EF data for the required reference
elements, the reference elements data are interpolated using
three-point Lagrangian interpolation.
Output tables. - There are many options for listed output
tables indicated on an OUTPUT record. The tables vary in
the following ways: in whether they are original data or
calculated from least-squares coefficients; in energy units(dimensionless, joules, or calories); and in whether thefunctions are given to many figures or are rounded and include
columns for tJ.j1T and log 10K.
Input
Input data sets for any number of species may be combined
into one file. The data in each set are read, processed, andcleared before the next set is read. A set of data for a diatomicgas, for example, would contain the chemical formula; theoutput options; the method of calculation, such as PANDK;
molecular data such as We' WeXet Bet and a e ; desired options
such as a least-squares fit or a special temperature schedule;
and, finally, the record ID FINISH to indicate the end of theset of data.
In addition to these input data sets, data contained in two
general files are required for certain applications. The firstof these two files contains enthalpy and free energy data (EFdata) for reference elements which are used to calculate
equilibrium constantslogloK and heats of formation /lilT (seesection Heat of formation and loglOK values). An exampleof the contents of the EF data file for the element Mg is given
in appendix D, example 6. The second general file contains
thermodynamic data (in the form of least-squares coefficients)for various groups that are used to estimate properties of
species (see section Group Additivity Method). These
coefficients for 34 groups are given in table X and have thesame format as that described in table VIn but these use afourth-order polynomial for C~.
The references from which most of the data were taken to
generate these coefficients are given in table IX. In addition,
table IX gives the labels used in PAC91 for these groups,
Benson's notation (ref. 36), the group structure, and the atoms
contained in the group. Of the 34 groups given, thermo8

dynamic data for 18 were taken from reference 36 and 12 fromreference 37. Thermodynamic properties for the remaining
4 groups were calculated by the PAC91 program using datafrom the following references:

Species

References

FormulaName.t!../f298.IS

Spectroscopic
constants

C2H2
C2H
C 2H4
C2H3
C2H3
C6H6
C6Hs

Acetylene
Ethynyl radical
Ethylene
Vinyl radical
Stabilized vinyl radical
BenzenePhenyl radical

7
44
7
44
a44,48
7
7

8
45
46,47
8
b8
49

49

aAjfli9B.15 is taken to be the same as that for the vinyl radical pillS an estimated resonancestabilization energy of 8 kcal/mole taken from reference 48.
bAssumed to be the same as for the vinyl radical.

Uniform format. - Many types of input are used in PAC91.
To facilitate the preparation of this input, a uniform format
was devised for the original version of this program (ref. 1)
for most input data. This format is retained for the present
program as well. While in the original version, input was readin from 80 column punched cards, in the present program input
is in the form of 80 column records. Details of the uniform
format are given in appendix B.
Contents ofindividual records. - A brief description of thecontents of the individual records is given in table N. (Detailed
descriptions are given in appendix B.) The right-hand column
indicates which records are optional. The word in columns
1 to 6 on all records except the formula record will be referred
to as the record ID. Words in other columns will generally bereferred to as labels. While the record ID may contain up to
six characters the PAC91 program will use only the first fourcharacters of the code to identify the record. The code isintended to be a mnemonic device. Thus, for example, the
LSTSQS record contains information for the least-squares fitof the thermodynamic data. Since the program uses only the
first four characters, the word LSTS is required for this record,
while characters in columns 5 and 6 are optional.
As shown in table IV, the record ID does one or more of
the following:(1) Indicates what information is in the record (e.g.,
NAME, REFN, OUTPUT, TEMP, LSTSQS, or CTEM).
(2) Identifies the data on the records which follow it (e.g.,
METHOD and EFDA).
(3) Calls for some intermediate output (i.e., LISTEF).
(4) Indicates the end of a set of data (i.e., FINISH).

General Flow of Program(1) Each record (except for the EF data) is read and listed.
The flow is directed according to the record ID.

(2) The input data (including options) are cleared at the
beginning of the program and after each FINISH record ID.
(3) There may be any number of sets of data-each having
any combination of options and each ending with a FINISH
code.
(4) The records NAME, formula, LSTSQS, OUTPUT,
DATE, and REFNCE should come ahead of the METHOD
record but their order is immaterial.
(5) Any record ID ahead of the METHOD record ID which
is not recognized by PAC9I will be assumed to be a chemical
formula record.
(6) From the chemical formula, the following items are
determined by the program:(a) molecular weight(b) phase of the species(c) number of atoms (Le., whether species is monatomic,
diatomic, or polyatomic)(7) The Hg value may be calculated from an assigned
enthalpy value at any temperature or a heat of formation (seechemical formula record in appendix B and table V). (The HS
value is used in calculating dIRT and log I oK and the integration
constant hI (eq. (12».
(8) The temperature schedule (TEMP record), if not thestandard 100(100)6000 K, must be read before each METHOD
record giving the calculation method. However, it should be
noted that TEMP records are not used with method READIN
inasmuch as temperatures for the READIN method are givenon the data records.
(9) The data records must follow the METHOD record.
(10) Thermodynamic functions are calculated immediately
after PAC91 reads a record ID different from the one it was
reading in the data records.
(11) After the FINISH code is read, a check is made forthe LSQS and LOGK options from the OUTPUT record. Also,
tables of thermodynamic functions are listed (from original
data and, if the CTAB label is on the OUTPUT record, fromleast-squares coefficients).
(12) With an EFTAPE label on an OUTPUT record for areference element, the EF data for that element will be written
on 110 units 11 and 13. The data on I/O unit 13 will beavailable for use with any succeeding calculations.
(13) Any number of sets of METHOD record and corresponding data records may be read for a set of input data. Thisis useful for species with more than one phase in thetemperature range of interest. For example, the thermodynamic functions for the solid may be read in directly while
the liquid data may be obtained from empirical equations. The
data for both phases will appear in the same listed tables of
the thermodynamic properties.
(14) Contributions of excited electronic states may be
included in the calculation of the thermodynamic functions for
diatomic and polyatomic gases. There may be any number ofstates, each having its own set of molecular constants. Thisis accomplished by grouping the data records for each state
together with a code number in columns 79 and 80. The valuesof QII!, T dQm IdT, and T2 d 2Qm IdT2 are calculated after thedata records for each state are read. These values are summed
as they are calculated.

OutputMost of the output are tables of thermodynamic data. These
data may be original data calculated by PAC9I according to
one of the methods specified by a METHOD record or thedata may be calculated from least-squares coefficients
generated by PAC9I with the LSQS option. Original datatables have the word ORIGINAL on the first line of the tableand on the last line of each page. Tables with data from leastsquares coefficients have the word COEFFICIENTS on thefirst line of the table and on the last line of each page.
Other possible types of output include input data, the leastsquares errors table, EF data, and intermediate output. A brief
description of output data is given in this section. Additional
details are given in appendix C.
Input data.- The contents of all input records in the uniform
format are always listed in the output. Some additional
information calculated by PAC91 such as molecular weightand Wilhoit parameters are interspersed with the record images.
Tables of thermodynamic properties.- There may be ten
possible tables of functions printed for the temperatureschedules. The tables vary according to the labels on the
OUTPUT records. Five are for original data. With a CTAB
label, a corresponding five possibilities are for thermodynamic
functions calculated from the least-squares coefficients. With
the MFIG label, three of the five possible tables are given to
many figures (usually from 6 or 7 to 10 or 11). With the LOGK
label, the remaining two tables are rounded to the same numberof figures as in the JANAF tables (ref. 6) and also may containvalues of dtH} and log 10K. The three many-figured tables
and the two rounded tables vary in the energy units which mustbe specified with label options. The JOULES label is required
for energy units injoules and the CAL label for energy units
in calories. Only the many-figured tables have an option for
dimensionless units (label DMLESS). The temperature schedule
for the original data is either the default schedule, temperatures read in with data, or a schedule set by the TEMP
records. The coefficients data will have the same schedule
unless a special schedule is given with CTEM records.
Table ofleast-squares errors.- These tables are listed with
the LSQS option. They provide information concerning theaccuracy of the fit. The word "error" in the output refers to
the difference between the original and fitted data. In addition
to listing the least-squares coefficients for each temperatureinterval, the following information is listed: (1) the thermodynamic functions (both the original and those obtained fromthe least-squares fit for each temperature, (2) the errors between
the original and the fitted data for each temperature, and (3)average, maximum, and least-squares errors and relative errors
for C~;IR, (HT- H3)IRT, STIR, and -(G T - H3)/RT.
9

Intermediate output. - With an INTERM label on the
OUTPUT record, additional intermediate data are listed as
detailed in appendix C. These intermediate data are often usefulfor debugging purposes.
EF data.-EF data for a reference element contain the enthalpy
and Gibbs energy data for that reference element. These data
are required for 10glaK and jj,fHt calculations for compounds
containing that element. See sections Listed Output and Saved
Output in appendix C for additional discussion of EF data.

ExamplesEight sample problems were selected to illustrate a numberof the methods and options of PAC91. The input data files,
listed output and some discussion of these examples are given
in appendix D.

Main Routine and Subroutines
The previous program (PAC1) consists of a main routine
and 17 subroutines. The present program (PAC9l) consistsof a main routine, 24 subroutines, and BLOCK DATA. One
function, KD, was dropped from the previous program andeight new subroutines and BLOCK DATA were added. Of
these eight new subroutines, five are for internal rotation(EIGEN, HMAT, INTROT, IROTOR, and PRINT); two arefor extrapolation by the Wilhoit method (WCALC and WILHOI);
and one is for the group additivity method (GROUP). The
remaining 16 subroutines from PACI were extensively revised
to accommodate more modern computers.
A short description of each subroutine follows.
ATOM.-This routine calculates thermodynamic functions
for monatomic gases.
The routine calls INPUT to read all data records plus thenext record. The J; or gi values (eq. (7», which are read withan alphanumeric format, are changed to floating point numbers
and stored.
Energy levels are sorted in order of increasing energy
values. The number of levels included in the calculations isdetermined by the cutoff method (ALLN, FIXEDN, or
TEMPER) given on -the METHOD record. Predicted but
unobserved levels will be included with the FILL option.
DELH. - This routine has several functions. It calculates
the H o value from information given on the formula card(either heat of formation at 298.15 K (HF298), heat of formation
at any temperature (jj,fHt) and the corresponding temperature
T, or an assigned enthalpy Ht and the corresponding temperature 7). If a LSQS label has been included on the OUTPUT
record, subroutine LEAST is called to perform a least-squares
fit. Subroutine PUNCH is called to write least-squares
coefficients on 110 units 6 and 10. The coefficients may also
have been read' in with method COEF if a TCOEF label is
included on the data records.
Subroutine DELH is called from the main program after
the FINISH card has been read. However, it will also be called
10from RECO for phase transition points. In this latter case, any
processing (the Hg calculation, the least-squares fit, or thewriting of coefficients) will be for the species phase coming
ahead of the transition point in the input. For example, fora species with input data for the solid followed by the liquid,
DELH will process the solid when it has been called from
RECO. The liquid will be processed when DELH is calledfrom the main program.
DERIV.- This subroutine calculates the first and second
derivatives of the logarithm of Q~n (the anharmonicity andvibration-rotation interaction contribution to the total partition
function QIn). It uses the special method given in footnote eof table III. The routine is called from a number of places in
LINKI. The values of the variables in the call vector ofDERlV
are calculated in LINK1.
EFTAPE and entry EFLIST.-Subroutine EFTAPE andentry EFLIST are concerned with preparing, reading, andwriting the enthalpy and free energy data records of reference
elements (EF data). These EF data are used in conjunction
with the option of calculating tables of 10giaK and jj,;Ht forany species. Subroutine EFTAPE is called under two circumstances: (1) if an EFTAPE label is included on an OUTPUT
record of a reference element and (2) if an EFDA record isread. Entry EFLIST is called when a LISTEF record is read.
In the first case of subroutine EFTAPE being called (by an
EFTAPE label on the OUTPUT record), the formatted EF
data set for the reference element being processed is written
on I/O units 6 and 11 and the unformatted data set is written
on I/O unit 13.
An EF data set for the reference element currently being
processed may already exist on I/O unit 13 from a previous
run or from being read in from a special file (see section Saved
output). In this event, the EF data set for the current run
replaces the existing EF data set for this reference element
on I/O unit 13. Otherwise, the current EF data set is written
at the end of all other EF data sets on I/O unit 13.
In the second case (EFDA record is read), subroutine
EFTAPE is called to read data created in the first case andpreviously written on I/O unit 11. These data are usually
backup data or data that come with the program. The subroutine merges the data with the unformatted form of the dataon I/O unit 13.
Entry EFLIST writes the contents of I/O unit 13 into I/Ounit 6 in order to obtain a legible listing of the EF data for
all reference elements currently in the I/O unit 13 file.
EIGEN.- This is one of the five subroutines associated withthe calculation of the contribution of internal rotation tothermodynamic functions. It is called by HMAT and solves
for the eigenvalues of the Hamiltonian matrix which are thenused to obtain the energy levels of the rotor(s).
GROUP.-Subroutine GROUP is called from the Main
Program when the label ADD is included on the METHOD
record. Subroutine GROUP locates and adds together thecontributions of various groups specified in the input. The
group contributions are in the form of least-squares coefficients(see table X) and, when added together, produce the leastsquares coefficients for the desired species. Occasionally, fora special configuration such as gauche, a constant correction
is required for HTI R. For this case, the correction may be
included in the input with the label HRCO.
HMAT.- This is one of the five subroutines associated withthe calculation of the contribution of internal rotation to thermodynamic functions. It calculates the elements HINT (I,J) fora Hamiltonian matrix. It is called by IROTOR. HMAT, inturn, calls EIGEN to solve the matrix for the energy levelsof the rotor.
IDENT.- This routine analyzes the chemical formula oneither the formula record or the EFDA record. It separates andstores each chemical symbol and corresponding number ofatoms in the chemical formula. The chemical symbols arematched with the SYMBOL array stored from BLOCK DATA.
Corresponding indexes are stored. When analyzing a chemical
formula from a formula record the molecular weight is calculated.
INPUT.- This routine is called from the main program. It
reads and lists all standard input from I/O unit 5 except thethermodynamic data following the EFDA record and unformatted
data. I/O unit 14 is used as a scratch unit for reading in data.
INTROT.- This is one of the five subroutines involved withinternal rotation. It calculates the contribution of the internal
rotor(s) to the partition function and its first and second
derivatives. It uses the energy levels which are generated insubroutines HMAT and EIGEN. It is called from LINKl.
IROTOR.- This is one of the five subroutines involved withinternal rotation. It is called from POLY if the label INTROT
appears in the input data set. IROTOR calls INPUT to obtainthe necessary input for internal rotation calculations (hinderedor free). The potential function is then calculated and stored
for optional printout (see subroutine PRINT). IROTOR thencalls HMAT to set up a Hamiltonian matrix which is thensolved in EIGEN to obtain the energy levels for the rotor. For
each rotor present, IROTOR then calculates the relative valueof the energy levels of the rotor above the lowest energy forthat rotor. A maximum of four unique rotors is permitted.
LEAST.- This routine is called from DELH only if the
LSQS label was included on the OUTPUT record. It calculates
the least-squares coefficients and lists certain informationcomparing original thermodynamic functions with those
calculated from the coefficients. See Tables of least-squares
errors and Least-squares coefficients in appendix C.
LINKl. - This routine calculates the partition function for
diatomic and polyatomic gases. The formulas given in tables
II and III are evaluated according to the method specified.
The routine is called from subroutine POLY. LINKI in turncalls two subroutines, DERIV to calculate the derivatives ofthe partition function and QSUM to keep a running total ofthe various contributions to the partition function.
LOGK. ~ This routine is called from the main program only
if a LOGK label has been included on the OUTPUT record.
It calculates 6.fl7fRT, 6.flr, -IlP7fRT, and 10glOK for theformation of the species from the assigned reference elements.

The required enthalpy and free-energy data for these reference
elements have been previously stored in the file on I/O unit
13 by the EFTAPE subroutine.
The LOGK routine lists the two tables of rounded properties
as detailed in appendix C. If any required data for the reference
elements of the species being processed are not on I/O unit
13, the appropriate columns in these two tables are left blank.
PAGEID.- This routine is called from a number of places
and lists three items of information at the bottom of a pagein the output listing and skips to a new page. The three items
are (1) the name in columns 7-22 on the NAME records; (2)the word COEFFICIENTS if the page contains thermodynamic
properties from least-squares coefficients or ORIGINAL ifotherwise; and (3) either BAR or ATM to designate thestandard reference unit of pressure as being either one bar or
one atmosphere. PAGEID allows approximately 55 lines tobe printed on a page. Up to six names from NAME records
are saved and printed.
POLY.- This routine calculates thermodynamic functions
for diatomic and polyatomic gases. It is called from the main
program.
Subroutine INPUT is called from POLY to read the data
records plus the next record. Subroutine LINK! is called to
calculate the partition function according to the method specified(RRHO, PANDK, JANAF, NRRAOI, or NRRA02).
If more than one electronic state is present, the various states
are identified by a code in columns 79 to 80 of the data records.
In this case, data records for only one state at a time are readin and stored. The partition function for each state is calculated
prior to processing data records for the next state.
PRINT.- This is one of five subroutines involved withinternal rotation. This subroutine prints the number of energy
levels and values of the potential function specified by NOUT
(a label in a data record). It is called from IROTOR as an
option only if NOUT is greater than zero.
PUNCH. - This routine writes on I/O units 6 and 10 thecoefficients obtained either from a least-squares fit or from thedata records associated with method COEF. PUNCH is calledfrom subroutine DELH. See output details in appendix C.
QSUM.-This routine keeps a running total of all, except
translational, contributions to the partition function and its
derivative for each electronic state. These contributions arelisted if an INTERM label has been included on the OUTPUT
record. QSUM is called from a number of places in LINK!.
RECO.- The routine is called from the main program after
reading a METHOD record which contains either a COEF
or READIN label. The RECO routine calls INPUT to readthe data records plus the next record.
For READIN, the temperature and the thermodynamic
functions on each record are simply stored. For COEF, thethermodynamic functions are calculated for the temperatureson the temperature schedule and stored.
The RECO routine is also used to relate the enthalpy of twophases of the same species by means of an enthalpy or entropyof transition. One of these transition values is given on the
11

METHOD record of the second phase (DELTAH or DELTAS
labels, see table VI) and used to calculate the enthalpy of thesecond phase at the transition temperature. The Gibbs energy
value of the second phase is taken to be equal to the Gibbs
energy value of the first phase at the transition temperature.
If a transition is present, the routine calls DELH (discussed
in the section "DELH") to check for the options of leastsquares fit or storing coefficients for the first phase.
TABLES.-This routine is called from the main programfor printing the many-figured tables (MFIG on the OUTPUT
record). It lists tables of thermodynamic functions for threesets of energy units for either original or coefficients data as
discussed in appendix C. The format varies depending on theavailability of the following values: (1) the H~98.l5 - H3 value
which is required in obtaining H T- H~98.15 and -(GT- H~98.15)' and (2) the HS value which is required in
obtaining H Tand - Gr.
TEMPER. - This routine ,stores the temperature schedules
as given on TEMP or CTEM records. The TEMP records arefor original data and CTEM for coefficients data. The routine
is called from the main program after a TEMP record has beenread and just before the coefficients tables are processed.
WCALC. - This is one of the two subroutines pertaining to
the Wilhoit method of fitting thermodynamic data. It is calledby subroutine WILHOI to calculate thermodynamic functions
from Wilhoit coefficients.
WILHOI.- This is one of the two subroutines pertaining
to the Wilhoit method of fitting thermodynamic data. It is usedin PAC91 only for the purpose of extrapolation. WILHOI is

12called in the main program if the label WILH has been included
on a METHOD record. It generates the Wilhoit coefficientsused in WCALC to extrapolate data. The desired temperatureschedule for extrapolation is specified with TEMP input
records.
BLOCK DATA.-BLOCK DATA contains the fundamental
constants and information concerning chemical elements fromhydrogen (atomic number 1) through californium (atomic number'
98) and also electron gas and deuterium. These data consistof the following information for each element:(1) Chemical symbol(2) Atomic weight(3) Constant b in equation (8) or c* for FILL option (seesection Inclusion of predicted levels, and table I)(4) Sum of statistical weights for ground state (for FILL
option)(5) Phase(6) Atomic number(7) Number of atoms in most abundant form of the element
at room temperature
The atomic weights were taken from reference 50. The
fundamental constants were taken from reference 10. The
Sackur-Tetrode constant is given in equation (5). Other
constants are as follows:
R = 8.31451 kJ/kg-mol-K
C2= (hc/k) = 1.438769 cm-K

Appendix A-Symbols
rotational constants corresponding toequilibrium separation of atoms

enthalpy of formation (heat of formation)of a substance at temperature T from its
reference elements in their standard state

rotational constants for lowest vibrationalstateenthalpy of transition between two phasesof a substance at temperature T

temperature coefficients in eq. (11)constant defined in eq. (8)integration constant defined by eq. (12)integration constant defined by eq. (13)heat capacity at constant pressure forstandard stateC~(O)heat capacity at constant pressure at 0 K

C~(oo)

heat capacity at constant pressure at infinite
temperatureevelocity of light

cr
e*

k

Boltzmann constantLtotal number of electronic energy states

crystal phase of chemical substanceeliquid phase of chemical substancesecond radiation constant, he/ kMmolecular weight

constant representing total quantum weight
for each principal quantum number nabove ground state n for some elements(see table I)

mIL

atomic mass constantNnumber of atoms in moleculennumber of unique frequencies, number ofphase angles, or principal quantum numberPoQ

standard state pressure in eq. (5)Qminternal partition function for m th electronic
state

Q

correction factor to the partition function foranharmonicity and vibration-rotation interaction for m th electronic stateQeelectronic partition function for m thelectronic state

Gibbs energy at temperature T relative toenthalpy at 298.15 K for standard state

Q'R

classical rotation partition function for m lh
electronic state

Gibbs energy of formation of a substanceat temperature T from its reference elementsin their standard state

Q'J}

harmonic-oscillator partition function form lh electronic state

QIW

Fermi resonance correction factor topartition function for m th electronic statedegeneracy associated with Vi

HZ98.15principal moments of inertia
total angular momentum quantum number
equilibrium constantrotational stretching constants for lowest
vibrational state

OT -Planck constantK

spectroscopic constants for rotational
stretching

OT-Hoentropy of transition between two phasesof a substance at temperature T

either (G T- H o) + H o or (G T- H298.15)+ HZ98.15
Gibbs energy at temperature T relative toenthalpy at 0 K for standard stateelectronic statistical weightinternal partition function

/Il

C

IIl

anharmonicity constant for doubly
degenerate vibrations in linear moleculesHSchemical energy at 0 K for standard state

H298.15

assigned enthalpy at 298.15 K for standard
state (equal to .t1f!z98.15)

HTeither (HT- H o) + Hg or (HT- H 298 . 15)

HT-Ho

sensible enthalpy at temperature T relative
to 0 K for standard state

H T- H298.15

sensible enthalpy at temperature T relative
to 298.15 K for standard state

low temperature rigid rotational correction
factor to partition function for m th electronic
state
Q~I

rotational-stretching-correction factor topartition function for m th electronic state
temperature exponents in eq. (11)+ H298.15

universal gas constantrnumber of coefficients Gi in eq. (11)constant defined by eq. (5)entropy at temperature T for standard state

13

T

To

temperature, K
electronic excitation energy between lowest
vibrational states (v = 0) of ground andexcited state for diatomic and polyatomic
gases

ABC

ai,ai,a;,aij

vibration-rotation interaction constants forpolyatomic molecules/3;

rotational-stretching-vibration interaction
constant

temperature, 1 K

Emenergy of m th electronic stateUi

c2 vJTVi

observed fundamental frequencyv

potentialprotational-stretching spectroscopic constantv"

n- fold barrier
vibrational quantum number
Fermi resonance constantanharmonicity constants for polyatomic
molecules
vibration-rotation interaction constants for
diatomic and linear polyatomic molecules

14

(J

We

symmetry number
zero-order vibrational frequency for
diatomic molecule

weXe,weYe,weze anharmonicity constants for diatomic
molecules

Appendix B-Details in Preparing Input
Uniform Format

do not need to be left-adjusted. (See section Data records inthis appendix and example I in appendix D.)(2) All blank labels are ignored by the program.
(3) Each numerical value must be immediately preceded byits label. However, the order of values is usually immaterial.
Exceptions are noted in the details for the individual records.
(4) The numerical values may be the following:(a) A right-adjusted integer(b) A floating-point number without exponent (e.g.,With a few exceptions, all input records are read in withan 80-column uniform format, namely A6, 4(A6, DI2.0), 12.
The exceptions are the formula, NAME and REFNCE records
discussed in the section Description of Input Records.
Another exception is EF data; however, EF data records areprepared by the program and not the user (see section EFDA
and EF data records). The record columns for the uniform
format are as follows:

RecordID

Label
I

Numerical
value

Label

2

Numerical
value

Label

3

2

1

Numerical
value

Label

4

3

Numerical
value

4

Recordcolumns

1-6

7-12

13-24

25-30

31-42

43-48

49-60

61-66

67-78

79-80

Format

A6

A6

D12.0

A6

D12.0

A6

D12.0

A6

D12.0

12

The labels (label I, label 2, ... ) are codes on all types of
input records except one. (The exception, described in thesection Data records for the FIXEDN, ALLN, or TEMPER
methods, is the record containing spectroscopic data foratoms.) These codes serve two purposes. One purpose is tospecify an option in the program. For example, the label
RRHO specifies a method of calculation. The second purpose
is to identify the number which follows it. For example, thelabel STATWT precedes the numerical value of the statisticalweight.
The last two columns (79 and 80) are used for several
purposes:(1) For atomic gases, the principal quantum numbers are
put in these columns, right- adjusted, for methods FIXEDN
and TEMPER. (See example I in appendix D.)(2) For diatomic and polyatomic gases, the electronic level
identification is put in these columns if excited states areincluded.
(3) For polyatomic gases with molecular data and internal
rotors, the integers in these columns indicate the rotor to which
the data belong.
(4) On the LSTSQS record, if different equations are used
for different temperature intervals, the integer in column 80
indicates the interval associated with the information on theremainder of the record. Integers range from I to 8, with I
assigned to the lowest temperature interval. (See example I
in appendix D.)
Some general rules in preparing the input are as follows:(1) With one exception, record ID's (columns I to 6) andlabels are alphanumeric and must be left-adjusted. The
exception is that the labels on the data records which containspectroscopic constants for monatomic gases are numbers and

0.00021), anywhere in the field(c) A right-adjusted floating-point number with exponent
indicating decimal place (e.g., 2.1-4 is 2.1XIO- 4 )(5) The last two columns (79 and 80) are right-adjusted
integers.
Order of Input Records
Some discussion on the order of the input records is givenin the section General Flow of the Program. Specificinstructions for placement of the individual records are givenin the details for preparing the records.
For a single computer run, there may be any number of
species processed where each species requires its own set of
input data. The set of input data records for each species should
generally be in the following order:(1) NAME record. While this record is optional, it is usuallyconvenient to be first. Part of the contents of this record
appears with least-squares coefficients output and also on thebottom of output listings. When there are multiple phases(indicated by two temperatures in the temperature schedulebeing adjacent and equal), there should be a corresponding
NAME record for each phase. See example 8 in appendix D.
(2) Formula record (must be the first nonoptional recordin the set)(3) Miscellaneous records in any order containing options
and information (namely, DATE, REFNCE, OUTPUT or
CTEM)(4) TEMP record(s), if any] There may be more than(5) METHOD record
one set of these records for a(6) Data record(s)a single species. (See exam(7) FINISH record
ples 6 and 8, appendix D.)

15

There are two kinds of input records not directly related to
input data sets, namely the LISTEF record and the EF data
records.

Description of Input Records
Examples of the individual records discussed in this section. are given in appendix D. All input records except the formula
record are identified by a record ID (columns 1 to 6).
However, PAC91 reads only the first four of the first six
columns of the record ID. Six columns were reserved in orderto provide a little more assistance in identifying the record.
For example, the term METHOD is more descriptive than
METH. However, either METH in columns 1 to 4 or
METHOD in columns 1 to 6 is equally acceptable.
CTEM record. -The purpose of these records is to provide
a temperature schedule for output tables generated from leastsquares coefficients. However, the tables from coefficients will
be printed only if the label CTAB is on the OUTPUT record.
If no CTEM records are included in the input data set, theprogram will default to the temperature schedule of the originaldata. The labels associated with CTEM (T and I) and theircorresponding numerical values have the same definitions as
those used with the TEMP record. (See TEMP record.)
Data records.- These records follow the METHOD recordand contain the input data required by the method. Except forthe spectroscopic data of monatomic gases (see example 1,
appendix D), the labels are codes identifying the numericalvalues that follow them. Table VII is a summary of the labels
and numerical values to be used on data records for the various
methods given in table VI. The data records may optionallycontain identifying information in columns 1 to 6. For
example, in the sample problems of appendix D, the species
C4H4 (example 3) has the identifying word C4H4 in columns
1 to 6 of its data records. By contrast, columns 1 to 6 are blankfor the species Na2C03(s) (example 8). However, whatever
appears in columns 1 to 6 on the first data record, blank orotherwise, must also appear in columns I to 6 on all theremaining data records in the input data set. No data records
are associated with METHOD WILH. A further descriptionof the data records for various methods follows:
Data records for the READIN method: Generally, eachrecord contains four labels with the four corresponding
numerical values as indicated in table VII. The four labels
correspond to temperature, heat capacity, enthalpy, and either
entropy or Gibbs energy. Temperature, which must always
be given, has the label T; however, for the other threeproperties there are several options of labels as given in table
VII depending on the data to which they correspond. If
enthalpy and Gibbs energy are referred to H~98.15 rather thanH8, the H298_15 - H3 value must be included on the
METHOD record (label H298HO) if H T- Hg values aredesired in the final tables. (See examples 6 and 8, appendix D.)
Sometimes one or two of the three properties are omitted
in the data records or ignored by the PAC91 program. This16

occurs when there are LSTSQS records that include one or
two of the NOCP, NOH, or NOS labels. See LSTSQS .
records.
Data records for the COEF method: The coefficient andexponent values for each set of empirical equations (eqs. (11)to (13» must be preceded by the values of the temperature
limits (T labels in table VII) for which the equation applies(see examples 6 and 8, appendix D). The lower T value must
be the first numerical value.
Occasionally the coefficients aj (i = 1, r) are available
while the integration constants for enthalpy and entropy h]and b 2 are not. For this case, hI and b 2 values may be
calculated by the program in one of the following ways:(1) Reading in an enthalpy and an entropy or Gibbs energy
value with the corresponding temperature on the first record.
The labels and values should be the same as for the data records
for the READIN method except that C~ or C~/R may beomitted.
(2) Using the value of enthalpy or entropy of transition(DELTAH or DELTAS on the METHOD record (see table VI).
This method may be used only when the two phases relatedby the transition value are being processed in the same run.
The reason is that the transition value is combined with theenthalpy or entropy value for the last temperature of thepreceding phase. (See examples 6 and 8, appendix D.)
With the COEF method the TCOEF label provides an option
to write these coefficients on I/O unit 10 in the same format
as least-squares coefficients. (See table VIII.) For each set of
coefficients, the temperature intervals may be specified in two
different ways:(1) If only the TCOEF label is given with no additional
information on the record concerning temperature intervals,
the temperature intervals will be taken from the T values
accompanying the coefficient data (see Mg(e), example 6, andNaZC0 3(f), example 8, appendix D).
(2) Any temperature intervals may be specified by TCOEF
labels and corresponding values which give the endpoints of
the intervals. These values mayor may not be the same as
the T values for the set.
Data records for the FIXEDN, ALLN, or TEMPER methods:
In contrast to all other types of records using the uniform
format, these records use the label columns as well as thenumerical columns for numbers. The labels contain either the
total angular momentum quantum number 1m or the electronic
statistical weight gm (eq. (7», and the numerical values containthe excitation energy En/he (eq. (7» in centimeters -1. If gm
values are used, the label GLABEL must be included on the
METHOD record. For either the FILL option or the FIXEDN
method, the principal quantum numbers must be included incolumns 79 to 80, right~adjusted. The data on the remaining
portion of the record must correspond to that principal quantum
number. (See example 1, appendix D, for the TEMPER method
and FILL option.)
Data records for the RRHO, PANDK. JANAF, NRRAOl,
or NRRA02 methods: The equations for the partition function

of the various methods are given in tables I and II. The input
data must always contain at least the following quantities foreach electronic state:(1) The fundamental vibrational frequencies of the molecule(we or vi)(2) Either the rotational constant(s) (Eo for linear; Ao, Bo,
and Co for nonlinear molecules) or the moment(s) ofinertia (Is for linear; lA' I B , and Ie for nonlinear
molecules)(3) The symmetry number(4) The statistical weight
Other spectroscopic constants such as anharmonicity or
rotation-vibration interaction constants are optional. If these
optional constants are not included, correction terms involving
them are automatically excluded from the partition function.
(See example 4 (RRHO), example 7 (JANAF), and example
5 (NRRA02) in appendix D.)
When excited electronic states are involved, the data for eachstate are read and processed separately. Therefore, the data
records must be grouped together with an identifying number
in columns 79 to 80. For example, the data for the 15 electronic
states included in example 7, appendix D, are distinguishedby the integers 1 to 15 in columns 79 and 80.
Data records for the ADD method: The label and quantity
for each of the appropriate groups forming the desired species
must appear on these records. Example 2 in appendix D
illustrates the ADD method. Table IX facilitates the preparationof the records inasmuch as it contains the PAC91 label
notation, the Benson notation, the structure, the elements
contained in the group, and the references for the selected
thermodynamic data. The following two examples, for npentane and i-pentane (2-methyl butane), are given to further
illustrate the use of this method:(1) n-pentane(a) Structure:(b) Groups:

H

H

I

I

I

C-

C-CH 3

H 3C-C -

H

[

I

I

H

H

H

(d) PAC91 record:

2C-(H)3(C) + 3C-(H)ZCC)2(labelnumber label

CH3C

2.

H3C

H

CH2C2

(2) i-pentane(a) Structure:I

H 3 C-C -I

HI
C-CH 3I

H

3CH3 , lCH z, and lCH(c) Benson notation:

3C-(H)3CC) + C-(H)2(C)2+ C-(H)(C)3Cd) PAC91 record:(label number label number label number)
CH3C
3. CH2C21.
CHC31.
HRCO 402.6

The label HRCO on the second record is a correction term
for the heat of formation due to the gauche interaction in ipentane. Its value is obtained by dividing the value of 0.8
kcallmole given in reference 36 by R = 1.987216 cal/mol-K.
Other terms used in the ADD method are given in table VII.
DATE record.- The purpose of the DATE record is toinclude a date and/or reference code with the least-squares
coefficient output. The record should contain only one label
which will be included in the second record of the least-squares
coefficient output for each species. (See examples I to 4 and
6 to 8, appendix D.)
EFDA and EF data records.- The data on these records
are used in conjunction with the LOGK option to obtain 10giaK
and .byH values. These records are prepared automaticallyby the program when an EFTAPE label is included on the
OUTPUT record of a reference element. For each reference
element which has been processed in this manner one EFDA
record and a varying number of EF data records are prepareddepending on the amount of thermodynamic data available foreach reference element. The combination of the one EFDA
record and EF data records which follow it will be referred
to as EF data. The contents of an EFDA record consists ofthe chemical formula of the EF data reference element, thedate code, the Hoi R value, the melting point, if any, and thenumber of temperatures for which there are enthalpy and Gibbs
energy values following the EFDA record. Each EF data
record consists of a temperature (K), an enthalpy (HH3) IRTvalue, and a Gibbs energy -(GHg)IRTvalue followed
by a second temperature, enthalpy, and Gibbs energy. A listingof typical EF data for an element is shown in the output for
Mg(s,t), example 6, appendix D.
Additional discussion of EF data sets is given in the section
Saved Output in appendix C.
FINISH record. -This required record is the last record in
the input set for each species. It contains only the code FINISH
in columns I to 6.
Formula record. - This is the first nonoptional record in the
input data set for each species and is reserved for two pieces
of information. First, the species formula, as detailed below,
is always required. Second, either an assigned enthalpy or aheat of reaction value with the corresponding units andtemperature is required only if the assigned enthalpy column(H~;' or H'TIR) is desired in the output tables, or when callingrr-

2CH3 and 3CHz(c) Benson notation:(b) Groups:

number)3.

r-17

for either of the following two options:(1) LoglOK and Afi'T calculations (also requires a LOGK
label on an OUTPUT record), or(2) Least-squares fit of the thermodynamic functions (alsorequires a LSQS label on an OUTPUT record)
All the examples in appendix D, with the exception of CzH 3(example 2), have either an assigned enthalpy ASINDH or aheat of formation HF298. CzH 3 uses METHOD ADD whichcalculates the heat of formation.
The first 12 columns are reserved for the formula of thespecies. The formula should be left-adjusted and contain noblanks. It should be prepared in the following order:(1) Each atomic symbol followed by the number of atoms
even if the number is 1; these atomic symbols should
all be in capital letters and correspond to the symbols
in BLOCK DATA.
(2) For ionic species, the proper number of pluses or minuses(3) For condensed species, a left parenthesis(4) For condensed species other than reference elements,
any character except G (e.g., an L for a liquid, an
S for solid, or C for crystal)(5) For condensed species to be used as reference elements,
the character must be S for solid or L for liquid (in orderto match the formula in BLOCK DATA).
(6) For condensed species, a right parenthesis
The following are some examples, primarily for ionizedspecies:Species

Columns 1 to 12

CaC03 (s)
FN+
0++
0;

CAICI03(S)
FlNl+
01++
02-

The remainder of the record is reserved for a heat of formation,
the energy units, and the temperature of the reaction. There
are three forms in which the heat of formation may be
expressed and six choices of units. These are summarized intable V.
LISTEF record.- This option is used to obtain a listing of
the EF data stored on I/O unit 13.
LSTSQS record.-No least-squares calculations will bemade without a LSQS label on the OUTPUT record. By
contrast, the LSTSQS record is required only for specifying
any of the nonstandard (or non-default) options pertaining to
the least-squares fit of the functions cg/ R, H'TI RT, and SriR
to equations (11) through (13). The options are summarizedin table IV.
With a LSQ~ label and no LSTSQS record, the program
will attempt the default options. They include the following:(1) Fitting the three functions simultaneously(2) Setting the qi values in equation (11) to be -2, -I,
0, 1, 2, 3, and 4
18(3) Setting two temperature intervals, 200 to 1000 and 1000
to 6000 K(4) Constraining the fit to fit the three functIons exactly at
298.15 K(5) Constraining the fItted functions to match at 1000 K (Thecoefficients for the higher temperature interval areconstrained to reproduce the fitted results of the lower
temperature interval at 1000 K.)
If an OLD label is listed on the LSTSQS record, the default
qj values in equation (11) change to 0, 1,2, 3, and 4, to matchthe old polynomial form used for cg in reference 41.
If a NOCNS label is given, the fit is not constrained to fit
any values of the functions. The fit may be constrained to fit
the functions exactly at a specified temperature provided thetemperature is in the temperature schedule of the data. Thistemperature value follows a TCONST label. In this case any
common points between any succeeding intervals will be
constrained to match.
The temperature intervals may be changed by using T labels,
each followed by one value (namely, the first temperature,
the breakpoints, and the final temperature, all in kelvin). The
program will order these values from the lowest to the highest.
Allowance is made for up to 8 intervals (9 values).
The qi values in equation (11) may be set with EXP labels.
These exponent values may be positive, negative, zero, or
fractional. As always, the integers following a label must
include a decimal point. The program orders these values fromthe lowest to the highest. The limit on the number of exponents(r in eq.(II» is 8. Different sets of EXP values may be used
for different temperature intervals by giving the appropriate
temperature interval number in column 80 (with 1 referringto the lowest interval). If a set of EXP values is given without
specifying an interval (i.e., column 80 is blank), this set will
be used for all unspecified intervals. If there is no EXP set
given with column 80 blank, the default set will be used forthe unspecified intervals.
For fitting one function only or some combination of two
functions the labels NOCP (no c~), NOH (no H
and NOS(no S]-), are provided. The labels are used as follows:r),

Functions to be
fit simultaneously

Label on
LSTSQS record

q/R only
H'f/RTonly
S'f/R only
Rand H'j-/ RT
Cpt Rand S'j-/R
H'f/ RT and S'j-/R

NOH and NOS
NOCP and NOS
NOCP and NOH
NOS
NOH
NOCP

q/

With NOS and NOH combinations, an enthalpy value isrequired to obtain the b l integration constant and an entropy
value is required to obtain the bz constant. In this case, a
TPROP label with its corresponding temperature is requiredon the record. PAC91 then expects to find the requiredproperties at this temperature in the data obtained from the
METHOD and data records. When NOCP, NOH, or NOS
orforlabels are used, it is assumed these data (C~,the remaining temperatures are either missing or wrong.
PAC91 will fill these data with the values it gets from the leastsquares fit, even for the original tables. These simultaneous
fit combinations may vary between temperature intervals using
the same method described above for the functional form. The
temperature interval number is put in column 80 on the
LSTSQS records with the appropriate parameters.
METHOD record.- This record follows the option records
and must be included for any calculations to take place. It
specifies the technique for obtaining the thermodynamic
functions (see section Options) and immediately precedes thedata required by the method (data records). The record has
the code word METHOD in columns 1 to 6. The possible
codes in the label and numerical value columns are summarizedin table VI. The functions may be (1) calculated from molecular constants for ideal gases (labels FIXEDN, ALLN, or
TEMPER for monatomic molecules and labels RRHO,PANDK, JANAF, NRRAOl, or NRRA02 for diatomic andpolyatomic molecules) (see examples 1,4,5, and 7, appendixD); (2) calculated from coefficients and exponents using
equations (11) to (13) (label COEF), (see examples 6 and 8,
appendix D); (3) read in directly (label READIN) (seeexamples 3, 6, and 8, appendix D); (4) estimated by a group
addivity method (label ADD) (see example 2, appendix D);or (5) extrapolated functions using the Wilhoit method (label
WILH, see examples 2 and 3, appendix D). The calculation
techniques listed in (1) are discussed in the section Calculationof Ideal Gas Thermodynamic Functions.
In conjunction with these method labels, the METHOD
record may contain some additional labels and information as
indicated in table VI.
Occasionally, a single method may not apply to the entire
desired temperature range for a species. In this case thefollowing records must be included for each temperature interval,in order: (1) TEMP record(s) for the desired temperatureinterval (if the method is not READIN), (2) a METHOD
record for this temperature interval, and (3) the associated data
records. The sets should be in order of increasing temperature.
(See examples 2, 3, 6 and 8, appendix D.)
The WILH method always follows another method andrequires no data records to follow it. This method generates
Wilhoit-fit coefficients in order to extrapolate thermodynamic
data obtained from the previous method to higher temperatures. The temperature schedule for the extrapolation mustbe specified with TEMP records immediately preceding theWILH method record. If the species is linear, the label LINE
must be specified (otherwise the default is to nonlinear).
NAME record.-This record contains a name and comments.
PAC91 allows for up to six NAME records in a data set fora species. For least-squares coefficients, one name and associatedcomments are transferred to the output for each set ofHr, Sr )coefficients. Columns 7-24 are used for the name and columns
25-80 are used for comments (see table VIII).
Multiple NAME records are useful in identifying multiple
phase or lambda transitions for condensed species. When
PAC91 encounters the same temperature in two adjacent slots
in the temperature schedule, it assumes there will be a new
set of coefficients using the name and comments from the next
NAME record, if there is one. If there is not, it uses the nameand comments from the previous NAME record (see examples
6 and 8, appendix D).
OUTPUT record.- The OUTPUT records contain options
for output. There are 10 possible labels for this purpose andno numerical values. These labels (options) are now summarized:
ATM label. Calls for pressure to be in units of atmospheresin the entropy and Gibbs energy values appearing in the output
tables. The default units are bars.
CAL label. Calls for tables with calories as the energy units.
The label must be combined with either MAG or LOGK or both.
CTAB label. Calls for tables of functions calculated fromcoefficients to be printed. The label must be combined witheither MFIG or LOGK or both.
DMLESS label. Calls for many-figured tables in dimensionless units.
EFTAPE label. Used with an assigned reference element
whose data are needed for b.fir and 10glOK calculations.
H3)
Inclusion of the label causes the H3 value and the (H/ RT and - (GH3) / RT data for this species to be mergedwith the EF data on I/O unit 13 in unformatted form. These
functions are also written on I/O unit 11 in formatted form.
See example 6, appendix D.
INTERM label. Calls for intermediate output to be printed
when thermodynamic functions are being calculated frommolecular constants. (See section Intermediate data with
INTERM label, appendix C and example 5, appendix D.)
JOULES label. Calls for tables with joules as the energy
units. The label must be combined with MFIG or LOGK or
both.
LOGK label. Causes rounded tables of thermodynamic
properties including b.fIrand log 10K to be listed. If no units
label is specified, JOULES will be assumed. If the appropriate
EF data are not available on I/O unit 13, the b.fIr and 10giaK
columns will be left blank. If there is no matching temperaturein the assigned reference element data, the data that are there
will be interpolated by three-point Lagrangian interpolation.
(See example 8, appendix D.)
LSQS label. Calls for a least-squares fit of the functions toequations (11) to (13). Unless otherwise specified on the
LSTSQS record, the qi values assigned will be -2, -1, 0,
1, 2, 3, and 4. If no T's are given, the temperature intervals
assigned will be 200 to 1000 K and 1000 to 6000 K. For
condensed species, transition points are automatically inserted.
MFIG label. Causes many-figured (unrounded) tables offunctions to be printed. If no energy unit label is given,
JOULES will be assumed.

r-

r-

19

REFNCE record.- The only purpose of this record is forcomments such as identifying sources of input data. All theinformation in columns 7-80 in this record is alphanumeric.
The usual labels and numerical values are ignored. (Seeexamples 1, 3, 4, and 6, appendix D.)
TEMP record. - These records give a temperature schedule
for which thermodynamic functions are to be calculated. The
program allows for a maximum of 202 temperatures per
species.
Each temperature in the desired temperature schedule may
be specified individually with a T label. (See table IV.) However,if there are several temperatures incremented by a fixedamount, this part of the temperature schedule may be specified
by giving, in order, the lowest temperature labeled T, theincrement labeled I, and the highest temperature labeled T.
For example, the temperature schedule, 100, 200, 298.15,
300,400,500,600,688.2,700,750,800,850,900,962.3,
and 1000, could be designated as follows:

The temperature 298.15 K is always inserted in the.
temperature schedule automatically by PAC91 when there aretemperature values below and above 298.15 K. (See examples
1 and 4, appendix D.)
If there are no TEMP records in a set of data where thethermodynamic functions are to be calculated, the programassumes the standard temperature schedule used in reference
4-namely, every 100 K from 100 to 6000 K with 298.15 K
inserted between 200 and 300 K. (See example 7, appendix D.)
TEMP records should not precede METHOD records withREADIN. For this option, the temperatures are read in on thedata records together with the thermodynamic functions to which
they correspond. (See examples 3, 6, and 8, appendix D.)

RecordID

Label
1

Numerical
value 1

Label
2

Numerical
value 2Label
3

Numerical
value 3Label
4

Numerical
value 4

TEMP
TEMP
TEMP

T

100.
700.
1000.

I
I

100.
50.

T
T

600.
900.

T

688.2
962.3

20

T

T

T

Appendix C-Details in Output
Listed Output
Input data in the uniform format as well as some intermediate
data are listed for each set of input. Other tables and data will
be listed according to the options on the OUTPUT record.
Input data.-All input data in the uniform format are listed
immediately after they are read in the same format. Numericalvalues which are zero may be left blank. (See examples inappendix D.)
Tables of original thermodynamic properties.-(See section
Output for discussion of original data and data from leastsquares coefficients.) There are 10 possible tables printed
according to the labels on the OUTPUT record, five for original
data and a corresponding five for data calculated from leastsquares coefficients. In each set of five tables, there are threepossible many-figured tables (label MFIG) and two possible
rounded tables with AfHy.and log 10K columns (label LOGK).
These tables vary with units: (I) dimensionless with DMLESS
label (for many-figured tables only); (2) SI units with a
JOULES label; and (3) energy units in calories with the CAL
label. The properties in these tables are the following:(1) In dimensionless form-

T, C~/R, (Hy. - H3) IRT, (HT- H298.15) IRT (if T =298.15 K is in T range), STIR, - (Gy. - H3)/RT,- (G T - H~98.15)IRT (ifT= 298.15 K is in Trange),
and HTI RTand - GTIRT (if an H8 value is available)(2) In dimensioned, many-figured form-

T, C~, Hy. - Hg, H T - H~98.15 (if T = 298.15 K is in
T range), Sr, - (G r - H8), - (G T- H298.15) (if T= 298.15 K is in T range), and Hyand - GylRT (if an
Hg value is available)

format as the original tables described in the previous section
for the same labels on the OUTPUT records. They may bedifferentiated from the tables of original data by the word
COEFFICIENTS on the bottom of each page. The temperatureschedule for these tables may be changed from the input
temperature schedule by the use of CTEM records.
Tables of least-squares errors.-A least-squares fit of thefunctions C~/R, (R T- H3)/RT, and SrlR results when a
LSQS label is included on the OUTPUT record. (See examples
1, 6, 7, and 8 in appendix D.)
For each temperature interval, the following information islisted:(1) For each T within the interval,(a) C~/R, (RT - H3)/RT, STIR, and -(G r - Hg)IRT(b) Functions in (la) above as calculated from leastsquares coefficients and equations (11) to (13)(c) Differences in (Ia) and (lb); these values are referred
to as errors hereinafter(d) Values in (Ic) divided by original values in (1a);these values are referred to as relative errors
hereinafter(2) For errors in entire interval for each function in (la):(a) Maximum relative error (MAX REL ERR) andcorresponding temperature-see (1d)(b) Average relative error (AVER REL ERR)-see (Id)(c) Root mean square of relative errors (REL LST SQ
ERR)-see (1 d)(d) Maximum error (MAX ERR) and corresponding
temperature-see (Ic)(e) Average error (AVER ERR)-see (Ic)(£) Root mean square of errors (LST SQ ERR)-see (Ie)(g) C~I R equation (see eq. (11» for coefficients ai(h) Integration constants in equations (12) and (13) as
follows:(H - HO)/R CONSTANT = b l ~ H31R

(3) In dimensioned, rounded figure formT, C~, H T - H298.15 (if T = 298.15 K is in Trange),

ST' - (Gy. - H298.15) (if T= 298.15 K is in Trange),Hy, and AfHT and log 10K for formation from assigned
reference elements
These tables will have an asterisk and a footnote indicatingwhere a phase transition has occurred in an assigned reference
element. (See example 8, appendix D.)
All five of the tables containing original data have the word
ORIGINAL on the bottom of each page.

Tables of thermodynamic properties from least-squares
coefficients.-If a CTAB label is included on an OUTPUT
record, tables of properties calculated from least-squares
coefficients will be listed. These tables will have the same

H/R CONSTANT = b l
SiR CONSTANT = b1
Finally, the contents of the least-squares coefficient records
are listed on I/O unit 10 as well as on I/O unit 6. See the section
Output and table VIII.
EF data.- These data, which contain the enthalpy and Gibbs
energy data for reference elements, will be listed for two
situations. First, they will be listed when a reference element
is being processed and there is an EFTAPE label on the
OUTPUT record. The data, in dimensionless form, are written
on I/O unit 11 as well as on I/O unit 6 (see example 6,
Appendix D for a listing of EF data for a reference element).
The data are also merged in the library of unformatted dataon 1/0 unit 13 (see Saved Output). Secondly, a LISTEF record
will cause all unformatted data on I/O unit 13 to be listed.

21

Intermediate data with FILL option for monatomic gases.Unobserved but predicted energy levels for monatomic gases
will be included in the partition function (eq. (7» if the FILL
code is included in the METHOD record. See the section
Inclusion of predicted levels for the method of predicting thelevels.
In argon (example 1, appendix D), the following data arelisted in columns from left to right (refer to eq. (8) and table I):(1) b value(2) Principal quantum number n(3) bn z or c* [predicted E (Vi + 1)](4) E (2Ji + 1) from input data
(5) Column (3) minus column (4)(6) Highest energy level for principal quantum number(7) Sum of column (5) and 2Ji + 1 for level of column (6)Intermediate data with INTERM label. - Intermediate data
are listed for ideal gas calculations if an INTERM label is
included on the OUTPUT record for a particular species.
Monatomic gases: For monatomic gases several items arelisted. The input data are listed in order of increasing energy
level values. The data include, from left to right, values forthe principal quantum number n, Ii. 2li + 1, and the energy
level.
For each temperature, three lines of data are listed as follows:(1) A statement indicating where the energy levels were cut
off; five possible statements are the following:(a) NOT ALL LEVELS WERE USED. X IS GREATER
THAN 85. - This statement indicates that not all atomic energy
levels were used because E/kT> 85 in equation (7).
(b) ALL LEVELS USED THROUGH N = (FIXEDN
value)-This statement indicates all atomic levels were usedthrough a fixed principal quantum number (method FIXEDN).
(c) ALL ASSIGNED LEVELS HAVE BEEN USEDThis statement indicates all atomic levels in input were used(method ALLN).
(d) NOT ALL ASSIGNED LEVELS WERE USED,Q AND DERIVATIVES ARE TOO SMALL-This statement
indicates not all atomic levels were used because the following
conditions occurred:(3) Values of €/kT. Q, T dQ/dT, TZ dZQ/dTz + 2T dQ/dT
Diatomic and polyatomic gases: Intermediate results are listed.
when an INTERM record is included in the input data set fora diatomic or polyatomic gas and the method of calculation is
RRHO, JANAF, PANDK, NRRAOI, or NRRA02. These
results include values for the formulas and variables defmed intables IT and m. Although the molecular constants are always
listed as they appear in the data records, with an INTERM record
many of them are listed again.
The following data are listed (see tables II and ill for definitionsand HzO(g) in example 5, appendix D):(1) ail a~where i = 1 to the number of uniquefrequencies(2) It 0z, 03(3) A o• Bo. Co. par, af°(4) Yijk(5) Xi"(6) LEVEL = (value in record columns 79 to 80 which is used
to identify the electronic levels)(7) Vi' di • gii(8) T(9) Ui' Ti. Sit i(10) As required by the method of calculation, values for theformulas in tables II and ill are listed for Q. In Q. T d(ln Q) / dT,
and TZ d 2(ln Q) /dT2 + 2T d(In Q) /dT. The latter three values
are additive contributions to -(GHg) /RT, (HHg) I RT,
and C~/ R, respectively, when only the ground electronic stateis considered. These values are identified in the listing by codes
which correspond to the formula numbers as follows:r-

Code onlisting
ELEC
H.O.
R.R.
RHO
THTA
FERM
ALFA
XU

. Qlll :::5 1 X 10- 10

YUK
G+AG
WEZE
AXU
XU2
XY
G2GX
AX2

and

when Em/kT> 2.
(e) ALL LEVELS HAVE BEEN USED TO THE
THERMAL BINDING ENERGY-This statement gives thelowered ionization potential value (i. e., ionization potentialkT/ hc) where energy levels with higher values have been cut
off.
(2) Values of T. C~/R. (HT- H3)/RT, and -(Grr - H3)

IRT

22

r-

Fommla numbers intables IT and ill
1

2

3 or 45
6
7
8 to 1112 or 14
13
16
15
17
18 and 19
20 and 21
22 and 23
24 to 27

Saved Output
As previously mentioned (see section Computer Program),some of the options require I/O units 10, 11, 13, 14, 17, and
19 in addition to the standard I/O units 5 and 6. I/O
units 14 and 17 are scratch formatted and unformatted output
units respectively for EF data processing. The other I/O unitscontain data that may be saved for various purposes as summarized in the following table. More details are given in thefollowing sections.
I/O
uniP

OptionRecordContents

Format

I/O
type

Coefficients(Groupsand Species)
Coefficients(Group)EF data b
EF databEF databEF databFormatted(table VIII)

OutputFormatted(table VIII)
Unformatted
Formatted
Unformatted
Formatted

Input

Label

ID
10

OUTPUT

LSQS

19METHODADD

13
11

OUTPUTOUTPUTOUTPUTEFDA

EFTAPEEFTAPE
LOGK(element)

135

OutputOutput
Input
Input

aNote that some of the input data (I/O units 19. 13. and 5) used by PAC9J were also produced by
PAC91 (I/O units 10. 13. and II)
bReference elements.

The coefficients for a group written on I/O unit 10 have to
be moved to the file associated with I/O unit 19 for future use.
On the other hand, when an EFTAPE label is included on the
OUTPUT record for a reference element, the EF data areautomatically inserted in the unformatted data on I/O unit 13
for immediate use. The data are also written in formatted formon unit 11 which may be moved to a file as a backup. This file

may be read in on I/O unit 5 and the program will put the dataon 1/0 unit 13. The LISTEF record simply lists the data from
I/O unit 13 so that they may be checked if so desired.
EF dnta.-For every reference element processed by PAC91
which includes an EFTAPE label on the OUTPUT record, theEF data which are generated are stored in I/O unit 11 in formatted
form and in I/O unit 13 in unformatted fonn. (See example 6,
appendix D, for a typical EF data set.) I/O unit 11 is used tostore these data for just the reference elements currently being
processed. I/O unit 13, by contrast, is used to include these datawith EF data for all reference elements previously processed.
If the current element has the same name as an element previously
stored on I/O unit 13, the previously stored data for that element
will be replaced by the current data. The formatted data on I/O
unit 11 may be moved to another file and saved if desired. There
are three reasons for doing this: (1) the data are legible, (2) they
can serve as a backup since PAC91 can read in the data on 110
unit 5 and write it out on I/O unit 13, and (3) they are moreeasily transported to other computer systems.
Least-squares coefficients.- The least-squares coefficients are
written in the file associated with 110 unit 10. The fonnat is
described in table VIII. Generally these data will be for use inother computer programs (e.g., ref. 41). These coefficients may
also be for a group and used by PAC91 for the group additivity
method (METHOD ADD). For this latter case, the coefficients
must be transferred from I/O unit IOta the file of data associatedwith 110 unit 19.

23

Appendix D-Examples
Eight sample problems were selected to illustrate a numberof the methods, features, and options of PAC91. Both input
and output are given in these examples. To conserve space,the output has been deliberately kept short by using shorter
temperature schedules than would normally be used. For
example, only one temperature, T = 5000 K, is given for
H 20 due to the large amount of intermediate output.
In addition to the H 20 intermediate output several othertypes of intermediate output are also illustrated. These will
be discussed for the appropriate examples.
The following methods are illustrated for the species shown:

MethodSpecies

Examplenumbers

ADD
COEF
JANAF
NRRA02READINRRHOTEMPER
WILH

C2H 3
Mg(e), Na2C03(f}MgO
H 2O
C 4 H4 , Mg(s), Na2C03(l,2)
C SH 11Ar
C 2H 3, C 4 H4

2
6,8

7
5
3,6,8
4
I

2,3

The required records-namely, the formula, OUTPUT,
METHOD, data and FINISH records-appear in eachexample. The optional NAME, DATE, REFNCE, TEMP, and
CTEM records as well as a number of other records and labels
are also illustrated in the following examples.
Example 1. Ar(g) from Method TEMPER with FILL and
LSQS Options
Problem. -Calculate and print thermodynamic functions to
20 000 K for Ar using method TEMPER with FILL option
and obtain a least-squares fit of the calculated data. Print tablesof functions, both original data and data from least-squares
coefficients, in the three options of energy units and the manyfigured form.
The standard I/O unit 5 input and the standard I/O unit 6
output are listed below.
For the input, the record names were all limited to fourcharacters except the FINISH record. The number of andnames of these records are, in order: 1 NAME, 1 formula,
1 DATE, 1 REFN, 2 TEMP, 5 LSTS, 2 OUTP, 1 METH,
35 data, and 1 FINISH. The NAME record gives the nameof the species and, for the comments portion, the data reference24

and method of calculation. The formula record gives the.
species formula in capital letters for the alphabetic part, thestoichiometric coefficient of 1, and the assigned enthalpy ofa at 298.15 K (HF298). The DATE record contains a codechosen to stand for Lewis, June 1988-namely, L 6/88. The
REFN record gives more information regarding the reference
for the spectroscopic data. The TEMP records give thetemperature schedule-namely, 100 and 500 and 1000 to
20 000 K in 1000 K increments. The first LSTS record gives
the temperature interval endpoints for the least-squares fitnamely, 298.15,1000,6000, and 20 000 K. The second andthird LSTS records give just one EXP = 0 value (qi in eq.
(11)) for temperatures intervals 1 and 2 (given in column 80).
This is because C~/ R is a constant in these temperature
ranges. The last two LSTS records give seven exponent values
for the third interval (6000 to 20 000 K).
No least-squares fitting will take place and no tables printed
unless these options are listed on the OUTP records. In thiscase, the options include many-figured tables (MFIO) in threesets of energy units (DMLESS, JOULES, and CAL), a leastsquares fit (LSQS), and tables from the least-squares
coefficients (CTAB). Specified energy units apply to bothoriginal and least-squares tables.
The METH record indicates the temperature cutoff method(TEMPER) with the missing levels filled in (FILL). The data
records, which are identified by AR in columns 1 and 2,
contain energy levels and corresponding 1m values. The principal quantum numbers 3 through 14 to which these energy
levels belong are required by FILL and are given in columns
79 and 80. The Jill values are found in the label portions of
the records. Note that these values may be anywhere in thelabel columns and integers do not require decimal points. The
last data record contains the ionization· potential (IP) needed
for the temperature cutoff method.
The first part of the listed output is simply a copy of the
input records except for the atomic weight which is inserted
after the METH record. The seven columns of information
following the FINISH record are related to the FILL option.
These are described in appendix C under Intermediate datawith FILL option for monatomic gases. Similarly, the leastsquares output is detailed in the section Tables of least-squares
errors. The remaining tables result from the remaining labelson the OUTP record-namely, DMLESS, JOULES, CAL,
MFIG, and CTAB. Again refer to the appendix C sections
Tables of original thermodynamic properties and Tables ofthermodynamic properties from least-squares coefficients.

Input. - The input data set for Ar, example 1, is as follows:

Rec. ILabel
ID
1
1-6
7-12

a ~AME~Rl

Numerical
value 1
13-24

Argon

DATE

abel
2

25-30

Numerical
value 2
31-42

Label
3

43-48

~

label
4

~1-66

Numerical
value 467-78

NSRDS- NBS 35, 1971 . Temp erature cuto rt=f & F~LL.
HF298
O.

l 6/88MOORE, ATOMIC ENER GY LEV ELS, NSRDS-N BS 35,
100.
500.
rr
rr
rr
!20000.
298.15
1000.
T
If
EX?
O.
EX?
O.
EX?
1.
O.
EXP
EXP
EXP
EX?
-1.
EX?
4.
r>1FIG
lo~1LESSJOUl ESLSQS~TAB
trEMPERFILL
0o.
0111667.87
IAR
tAR
1111818.09 4112750.22 3
1114147.75 2
IAR113426.05 3
3114831.99 2
lAR
114805.18 1
IAR93143.8
1~1IAR95399.87 1
104102.144 3
1
IAR106087.305 ~
106237.597 0
2
IAR
107289.747 1
107496.463 00IAR118512.17 1
118651.447 4lAR
2118906.665 1
119847.81 2lAR
2120619.076 3
120753.52 2
1120188.34 2
lAR
120188.66 5
3~R
120229.81 2120230.07 7.5
AR2113468.55 1113643.26 0AR1
116660.054 3116942.815 2AR2117183.654 0117563.020 1AR1118459.662 0
118870.981 0
AR
10122090.
122514.29 5.5
1
AR123372.987 1
123815.53 27.5~...
~R
119683.113 1
119760.22 0AR
11.5121205.
5.5122633.
19.5
AR
27.5
124050.
13.5125483.
AR$.5122455.
1.5
123880.
11.5
AR
19.5
124652.
9.5126069.
27.5
AR
11.5
124400. 5.5125800.
19.5
AR~.5123920.
1.5125340.
AR~.5124780.
1.5126210.
11.5
AR
19.5
125650.
3.5
127130.
27.5
AR~.5125330.
11.5125540. 19.5
AR~.5125712.
1.5
127130.
5.5
AR3.5127610.
AR
tl.5
126000.
19.5126300.
3.5
AR126200.
1.5
15.5
127610.
19.5
AR3.5126330.
1.5127600.
19.5
ARIP127109.9
FINISHa REFN
h"EMP
lrEMP
LSTS
lSTS
LSTS
LSTS
LSTS
OUTP
IoUTP
METH

Numerical
value 3
49-60

1971, PP 21 1-215.
1000.
I
6000.
2.
-2.

1000.
20000.

EX?

3.

tAL

105462.80~

112138.98
114641.04

1
2
3
3

3
3

3
3

2

107054.319 1
108722.668
119023.6993
119444.88 3120600.944 1
120207.32 4120250.15 13.5
114861.67 1
116999.389 1
118407.494 2
121794.158 1
122310.
5.5122700.
13.5121096.67 1
123741.
9.594553.707
105617.315
107131.755

4
4
4119212.93
119566.11
121011.979
120207.77
121654.
114975.07
117151.387
118469.117
121932.908
123535.
124137.
121161.356
125140.

4
4123230.
124863.
125280.

5.5
13.5
27.5

124660.
126295.
125390.

125100.
125754.
125940.
125860.

1.5126524.2

3.5
19.5

127410.
126155.

3.5
3.5

127880.
127970.

127760.
126430.
126520.

-80

Expl . 1

If113020.39 2113716.61 2115366.993750.639 0

179

4

4

4
4
5
5
5
5
5

5
6

6
6
7
7
8
8
9
9
10
11
11
12
13
14

a All alphanumeric characters.

25

Listed output. - The listed output for Ar, example 1, IS as follows:
tlllMEI1SRDS-llBS 35. 1971. rempera"ture cutoff & Fill.

Argon

AR1
DATE

L 6/88REFH

MOORE, ATOMIC EllERGY LE\lELS, lISRDS-llllS 35. 1971. PI' 211-215.

TEr1p

100.

TEMt'

20000.

lST5
l5TS

500.

1000.

1000.

29iL 15

EXP

6000.

LSTS

EXP

O.

EXP

O.

EXp

l.

EXP

lSTS

EXP

4.

EX?

-1.

EXP

OUll'

Hf-lG
LSQS

METH

TEMPERZOOO\} .

2.

3.

EXP

CAL
CTAB

Fill
39.94800

ATD/1Ie t'IEIGHT

AR

111667.37

\).

foR

111818.09

112750.22113020.39

112138.98

AR1141',7.75

113426.05

113716.61

114641.04

fiR

114831. 99

114805.111

115366.9

ARAR95399.117

95143.3

93750.639 094553.707

104102.144

105462.804

105617.315
107131. 755

AR106087.305

106237.5')7

107054.319

Ar.

107289.747

107496.463 0108722.663

I>.f118512.17

11&651.447

119023,6995

AR

118906.665

119847.81

119444.88

119566.11

120619.076

120753.52

120600.944

121011.979

1l'l212.95"'R120188.34

1211lBll. 66

AR120229.81

120250.07

AR113463.55

113643.26

114861.67

114975.07

AR

116660.054

116942.815

116999.389

117151.387

AR117183.654 0117563.020

118407.494

118469.117

AR118459.662 0

118870.9111

121794.158 1

121932.'108

1211207 .32
7.5120250.15

1211207.17

U.S

122090.

122514.29

5.5

122310.

5 . .,

AR

123372.987

123815.53

27.5122700.

13.5

AR119683.113

119760.22

AR

10

AR

11.5

121205.

5.5122633.

AR

27.5

124050.

13.5125483.

121096 .67
19.5

123741.

121654.

123535.
124137.
121161.356

9.5125140.

AR.L';122455.

1.5

123880 .

11.5

123230.

5 . .,

124660.

AR

19.,.

124652.

9.5126069.

27 . 5124863.

13.5

126295.

AR

11.5

5.5

125800.

19.5125280.

27.5125390.

AR

3.5123920.

1.5125540.
1.5126524.2

124400.

AR

3.5124780.

1.5126210.

11.5

1251UO.

AR

19.5

125650.

3.5

127130.

27 .512575 1"AR

3.5125330.

11.5125')40.

3.5127410.

10

AR

3.5

125712.

1.5127150.

5.5

125860.

19.5126155.

11

AR

3.5

127610.

AR

7.5126000.

19.5126311U.

3.5

127760.

AR

5.5126200.

1.5127610.

19.5

AR

3.5

126330.

1.5127600.

19.5

AR

II'

127109.9125540.19.5

11

FIllISH

8
12.0
12.0
12.0
12.0
12.0
12.0
12.0
12.0
12.0
12.0

II

t
5
6

7
8

9
10
11
12

12.0

U

12.0

14

PRED. SUM(2J+l)
61. 0
192.0
300.0
432.0
588.0
768.0
972.0
1200.0J 452.01128.02021\.02352.0ACT.

SUM( 2J+ 1)
61.0
192.0
192.0
1?2.0

In.o

144.0
144.0
80.0
72 .0

64.0
6" .Il

60. a

BAR

26

1000.

O.

LSTS

OUTP

Exp1. 1

O.

HF298

Ar\lon126430.
126520.

DIFF

0.0
0.0
103.0
2,,0.0

3'16 . a

624.0
820.0
1120. a1380.0J664.0
1%".0

un.O

12
:$.5

12788013

3.5127970.

14

MAX LEVEL

115366.9000
121654.0000
124137.0000
125483.0000
126295.0000
125800.0000
127130.0000
127410.0000
127610.0000
127760.0000
12n30.000U

127970. 0000

2Jt 1. MAX LEVEL
3.0
28.0
136.0
268.0
424.0
631•. 0836.0
11 za. n1383.01672.01972.02300.0LEAST SQUARESCP/R INPUT
HH/RT INPUT
HH/RT CALC
CP/R CALCSiR ItWUT
SIR CALCINPUT-CALC
ItlPUT-CALC
FRACTIONINPUT-CALC
FRACTIONFRACTION
2.5000000
2.5000000
2.5000000
2.5000000
18.6236667
18.6236667
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
500.002.5000000
2.5000000
2.5000000
2.5000000
19.9161952
19.9161952
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
1000.00
2.5000000
2.5000000
2.5000000
2.5000000
21.6490631
21.6490631
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
MAX REL ERR CP/R
0.000000TEMP
1000,AVER REL ERR CP/R
0.000000
REL LST
f,AX REL ERR HH/RT
0.000000
298,
TEMP
AVER REL ERR HH/RT
0.000000
REL LST~lAX REl ERR SIR
0.000000
TEr-1P500.
AVER REL ERR SiR
0.000000
REL LST
MAX REL ERR GH/RT
0.000000TEMP
500.
AVER REL ERR GH/RT
0.000000
REL LSTMAX ERR CP/R
0.000000
TEMP.
1000.
AVER ERR CP/R
0.000000lST~IAX ERR HH/RT
O.OOOUOO
298.
AVER ERR HH/RT
TEt1P
0.000000
L5T~lAX ERR S/R
0.000000TEMP
500.
AVER ERR SIR
0.000000LSTMAX ERR GH/RT
0.000000
TEr1P
500.
AVER ERR GH/RT
0.000000
LST
CP/R
2.5000000e+OOT~~ 0.0(H-HO)/R CONSTANT-0.11368&84e-12. H/R CONSTAllT =-0.74537500e+03. SIR COI1STAIH
0.4379674ge+Ol
298.15=-GH/RT ItIPUT
I1IPUT-CALC
16.1236667
0.0000000
17.4161952
0.0000000
19.1490631

o.oaaOooa-GH/RT CALCFRACTION
16.1236667
O. 0000000
17 .4161952
0.0000000
19.1490631

o.aoooooo

SQ ERR CP/R
SQ ERR HH/RT
SO ERR SIRSQ ERR GH/RT
SQ ERR CP/R
50 ERR HH/ RT
SQ ERR SI R
SO ERR GH/RT

0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000-GH/RT ItIPUT
WPUT-CALC
19.1490631
0.0000000
20.8819311
0.0000000
21.8955938
0.0000000
22.6147990
0.0000000
23.1726579
0.0000000
23.62S{j6130.0000000
SQ ERR CP/R
SQ ERR HH/RT
SQ ERR SIRSQ ERR GH/RT
SO ERR CP/R
SQ ERR HH/RT
SQ ERR SIRSQ ERR GH/RT-GH/RT CUC
FRACTIOII
19.1490631
0.0000000
20.8819311
0.0000000
21.395593il
0.0000000
22.6147993
0.0000003
23.172657J
0.0000000
23.62a4613
0.0000000
0.000000
0.000000
0.000000
0.000000
0.000001
0.000000
0.000000
0.000000=

CP/R ItWUT
CP/R CALC
HH/RT IUPUT
HH/RT CALCSIR INPUTSiR CALCINPUT-CALC
rtWUT -CA LC
FRACTIOrl
FRACTION
ItIPUT-CALC
FRACTION
1000.00
2.5000000
2.5000000
2.5000000
2.5000000
21.6490631
21.6490631
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
2000.00
2.5000000
2.5COnaaa
2.5000000
2.5000000
23.3819311
23.3819311
0.0000000
0.0000000
O.OOOUOOO
0.0000000
0.0000000
0.0000000
3000.00
2.5000000
2.5000000
2.5000000
2.5000000
24.3955933
24.3955933
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
4000.00
2.5000000
2.5000000
2.5000000
2.5000000
25.11479%
25.1147990
O.OOOOGOO
0.0000000
O.OOQQOOO
0.0000000
0.0000000
0.0000000
5000.00
2.5000000
2.5000000
2.5000000
2.5000000
25.6726579
25.6726579
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
6000.00
2.5000014
2.5000000
2.5000001
2.5000000
26.1284613
26.1284618
0.0000014
0.0000006
0.0000001
0.0000000
0.0000001
0.0000000
MAX REL ERR CP/R
0.000001
TEMP
6000.
AVER REL ERR CP/R
0.000000
REL LSTrolAX REL ERR HH/RT
0.000000
TE~IP
6000.
AVER REL ERR HH/RT
0.000000
REL LST
MAX REL ERR SIR
0.000000
TEMP
6000.
AVER REL ERR SIR
0.000000
REL l5T
MAX REL ERR GH/RT
0.000000
TEMP
6000.
AVER REL ERR GH/RT
0.000000
REL lST~lAX ERR CP/R
0.000001
TEt-1P.
6000.
AVER ERR CP/R
0.000000lST
MAX ERR HH/RT
0.000000
TEMP
6000.
AVER ERR HH/RT
0.000000LSTMAX ERR SIR
0.000000
TE~lP
6000.
AVER ERR SiR
0.000000LSTMAX ERR GH/RT
0.000000
TEMP
6000.
LS,
AVER ERR GH/RT
0.000000
CPIR
2.5000aOOe+OOT** 0.0
U;-HO )/R CONSTANT = -0.34106051e-12. HlR CONSTANT =-0.74537500e+03. SIR CONSTANT = 0.4379674ge+Ol
T

CP/R IHPUT
CP/R CALC
HHI RT ItlPUT
HH/RT CALCSiR INPUTSIR CALC-GH/RT ItlPUT-GH/RT CALCINPUT-CALC
FRACTION
IUPUT-CALC
fRACTlotl
Ir~PUr~CALC
fRACTIOll
WPUT-CALCFRACTION
2.5000014
2.5000000
2.5000001
2.5000000
26.1284618
26.1234613
25.6284618
23.628461~
0.0000014
0.0000006
0.0000001
0.0000000
0.0000001
0.0000000
0.0000000
O.OOOOOQO
7000.00
2.5000300
2.4949369
2.5000015
2.5005617
26.5138400
26.5142450
24.0133386
24.013333:;
0.0050931
0.0020372-0.0003602-0.0001441-0.0004050-0.0000153-0.0000448-0.000001'1
8000.00
2.5003059
2.4836759
2.5000167
2.4987464
26.8476846
26.8464133
24.3476679
24.3476661
0.0166300
0.0066512
0.0012704
0.0005081
0.0012713
0.0000474
0.0000009
0.0000000
9000.00
2.5018654
2.4912337
2.5001131
2.4973733
27. FI22446
27.1392646
24.6421:>15
24.6413853
0.0106317
0.0042495
0.0027343
0.0010937
0.0029801
0.0001098
0.0002457
0.000010:J
10000.00
2.5074146
2.5047161
2.5004979
2.4974261
27.4060574
27.4024269
24.9055595
24.9050009
0.0026985
0.0010762
0.0030718
0.0012285
0.0036305
0.0001325
0.0005537
0.000022.
11000.00
2.5234699
2.5210257
2.5017210
2.4987833
27.6456495
27.6418679
25.1439285
25.ltt30845
0.0024441
a.000%&6
0.a029377
0.0011743
0.0037817
0.0001368
0.0000439
0.0000356
12000.00
2.5583346
2.5512414
2.5046980
2.5017379
27.8664056
27.8623567
25.3617076
25.3606187
0.0075932
0.0029674
0.0029601
O. 0011818
0.0040439
0.0001453
0.0010888
o.
000042')13000.00
2.6274245
2.6146798
2.5077049
2.5110032
28.0733960
28.06e7779
25.5623928
25.5610730
0.0127447
0.0043506
0.0032982
0.0013135
0.0046131
0.0001645
0.0013198
0.0000516
14000.00
2.7520110
2.7316496
2.5233415
2.5191514
28.2722222
28.2664413
25.7438807
25.7472899
0.0203613
0.0073987
0.0041901
0.0016605
0.0057309
0.0002045
0.0015908
0.0000618
15000.00
2.9194142
2.9171869
2.5418264
2.5390956
28.4652037
28.4603115
25.9233774
25.9217159
0.002227 ;)0.0007629
0.0027308
0.0010743
0.0043923
0.0001543
0.0016615
0.0000641
16000.00
3.1811838
3.1761285
2.5725349
2.5704448
28.6608111
23.6569628
26.0832763
26.0365180
0.0050553
0.0015891
0.0020901
0.0008125
0.0038434
0.0001343
0.0017583
0.0000674
17000.00
3.5296303
3.4993640
2.6169087
2.6153123
28.3622713
23.8589572
26.2453625
26.2436249
lL0302663\).0085749
O. \)015964
0.00\)610\)
I) .IHJ33341
0.001)1155
0.0\)17376
O.OaOO66Z
18000.110
3.8183774
3.8610143
2.6607190
2.6743812
29.0552237
29.0690987
26.3945047
26.3947176-0.0426374-0.0111664-0. 0136621-0. 0051.348-0.0133751-0.0004775-0. 0002129-0.0000081
19000.00
4.2690023
4.2163096
2.7297792
2.7463394
29.2695115
29.2875293
26.5397323
26.5411899
0.0526927
0.0123431-0. 0165602-0.0060665-0.0180178-0.0006156-0.0014576-0.0000549
20000.00
4.{,S35984
4,4999787
2.7773394
2.8273923
29.4538747
29.5114350
26.6765353
26.6840921-0.0113803-0.0025354-0.0500529-0.0180219-0.0576103-0.0019559-0.0075573-0.0002833
MAX REL ERR CP/R
0.012343
TEMP
19000.
AVER REL ERR CP/R
0.004478
REL LST SO ERR CP/R
0.005864
I1AX REL ERR HH/RT
0.018022
TEMP
20000.
AVER REL ERR HH/RT
0.002668
REL LST SQ ERR HHiRT
0.005166
MAX REl ERR SiR
0.001956
TEMP
20000,
AVER REL ERR SiR
0.000294
REL LST SQ ERR SIR
0.000555
MAX REL ERR GH/RT
0.000283
TEMP
20000.
AVER REL ERR GH/RT
0.000051
REL LST SQ ERR GH/RT
0.000084
MAX ERR CP/R
0.052693
TEMP. ~ 19000.
AVER ERR CP/R
0.014830
LST $Q ERR CP/R
0.021188~lAX ERR HH/RT
0.050053
TEMP
20000.
AVER ERR HH/RT
0.007168
lST SQ ERR HH/RT
0.014243~lAX ERR S/R
0.057610
THIP = 20000,
AVER ERR SIR
0.003506
LST SQ ERR 51 R
0.016311
MAX ERR GH/RT
0.007557
TEMP = 2000U.
AVER ERR GH/RT
0.001339
LST SQ ERR GHiRT
0.002232
CP/R-1.2955921e+09T**-2.0
8.220145ge+05T**-1.0 -2.0865673e+02T** 0.0
2.8064385e-02T** 1.0 -2.0298347e-06T** 2.0
7.5268416e-l1T** 3.0-1.1012887e~15T*~ 4.0
CH-HO)/R CONSTANT = -0.64818047e+07. H/R CONSTANT =-0.64825501e+07. S/R COil STANT = o .13234371et04
6000.00=

THERMODYNAMIC DATA COEFFICIENTS. RECORD IMAGES Argon
NSRDS-NBS 35. 1971. Temperature cutoff & FILL.
Expl. 13 L 6/88 AR 1.00
0.00
0.00
0.00
0.00 039.94800
0.000
298.150
1000.000 1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
6197.423
2.50000000d+OQ
O.OOOOOOOOd+OO
O.OOOOOOOOd+OO
O.OOOOOOOOd+OO O.OOOOOOOOdtOO
O.OOOOOOOOd+OO
O.OOOOOOOOd+OO
O.OOOOOOOOd+OO -7.45375000dt02 4.37967491d+00
1000.000 6000.000 1 0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
6197.423
2.50000000d+00
O.OOOOOOOOd+OO
O.ODOOOOOOd+OO
O.OOOOOOOOd+OO O.OOOOOOOOdtOO
O.OOOOOOOOd+OO
O.OuOOOOOOd+OO
O.OOOOOOOOd+OO -7.45375000d+02 4.37967491d+OO
6000.000 20000.000 7 -2.0 -1.0
0.0 1.0 2.0
3.0 4.0
0.06197.428-1.29559206d+09 a.22014586d+05 -2.08656731d+02
2.80643S48d-02 -2.02983469d-06
7.S26341S7d-ll -1.10128867d-15
O.OOOOOOOOd+OO -6.48255009d+06
1.82343707d+03

ORIGIrIAL

liAR

Argon

27

ORIOINAl

Argon

ASSIGlIED H/R AT

oK-745 ..315 K

T

CP/R

(H-HOI/RT

CH-HZ98)/RT

S/R-(G-HO)/RT-CO-H298)/RT

H/Rf-O/I.H

2.50000
2.50000
2.50000
2.50000
2.50000
2.50000
2.50000
2.50000
2.50000
2.500032.500312.50187
2.507412.525'17
2.55883
2.627422.75201
2.919413.18118
3.52963.L81838
4.26900
4.ci8860

2.5000000
2.5000000
2.5000000
2.5000000
2.5000000
2.5000000
2.5000000
2.5000000
2.5000001
2.5000015
2.5000167
2.5001131
2.5004'179
2.5017210
2.50ci6980
2.511 0032
2.5233415
2. 5'1ll!2~4
2.5725349
2.6169087
2.6607190
2.7297792
2.7773394-4.9537500
0.0000000
1.0092500
1.75'4"250
2.1273125
2.2515"172.3136562
2.3509250
2.3757109
2.3935193
2.4068449
2.4172937
2.4259604
2.4339597
2.4425834
2.4536666
2.4701004
2.4921347
2.5259490
2.5730632
2.6193093
2.6905489
2.7400706

15.8926004
18.6236667
19.9161952
21.6'190631
23.3819.311
24.3955938
25.1147990
25.6726579
26.1284618
26.5138400
26.8476846
27 .1422446
27.4060574
27.6456495
27.8664056
28.0733960
28.2722222
28.4652037
28.6608111
28.8622713
29.0552237
29.26'15115
29.4538747

13.3926004
16.1236667
17.4161952
19.1490631
20.8819311
21.8955938
22.61'17990
23.1726579
23.6284618
24.0138386
24.3476679
24.6421315
24.9055595
25.1439285
25.3617076
25.562.5928
25.7488807
25.9235774
26.0882763
26.2453625
26. 39{,504 7
26.5397523
26.67653B

20.8463504
18.6236667
18.9069452
19.89"',381
21.25',6186
22. FI',0522
22.8011428
23.3217329
23.7526910
24.1203207
24. ',408398
24.7249509
24.9800970
25.2116898
25.4238222
25.6197293
25.8021218
25.9730691
26.1348622
26.2892081
26.4359144
26.5789626
26.7138041-4.9537500
0.0000000
1.0092500
1 . 7546250
2.1273125
2.2515417
2.3136562
2.3507250
2.3757709
2.3935193
2.40684,,92.4172937
2.4259604
2.4.>39597
2.4425834
2.4536666
2.4701004
2.',921347
2.5259490
2.5730632
2.6193093
2.6905489
2.7400706

20.8463504
18.62366,,718.9069"52
19.89,,4331
21.25',6186
22.1440522
22.8011428
23.3217329
23.7526910
24.1203207
24. ',408398
24.72"9509
24.9800970
25.2116818
25.4238222
25.61972')3
25.8021218
25.9730691
26.1348622
26.2892081
26.43591 .. 426.5789626
26.7138041

S-(O-HO)
J/MOl-CG-H298 )
J/MOl

J/MOl

J/MOl

11135.291
39970.105
72403.564
159215.077
347246.049
546153.',02965346.479
1178754.491
1397643.106
1619511.425
1843985.237
2070775.239
2299653.893
2530(,42.054
2763004.017
2997250.569
3233102.708
3',70579.741
3709694.597
3950232.712
4192632.525
4li360',6.393

17332.719
46167.533
78600.992
165412.505
35344S .',71552350.829
758321.318
969543.907
118'.951.919
1403840.5.B
1625708.853
1850182.665
2076972.667
2305851.321
2536639.482
2769201.445
30034"7.996
3239300.136
3476777.169
3715892.025
3956430.140
4198829.953
4442243.821-4118.800
0.000
4195.710
14588.847
35375.122
56161.397
76947.672
977.53.947
118520.225
139306.582
160093.886
180H7.514
201706.720
222609.002
243706.612
265213.465
287527.442
310813.182
336032.445
363693.909
392008.920
425041.321
455646.895 .

17332.719
46167.553
78600.992
165412.505
353'.43.477
552350.829
758321.318
969543.907
1184951.919
1',03840.533
1625708.853
1850182.6(,52076972.667
2305851.321
2536639.432
2769201.4"53003447.996
3239300.136
3476771.169
3715892.025
3956430.140
4198829.953
4',42243.821

100.00298.15500.001000.00
2000.00
3000.00
4000.00
5000.00
6000.00
7000.00
8000.00
9000.00
10000.00
11000.00
12000.00
BOOG.OO
14000.00
15000.00
16000.00
17000.00
18000.00
19000.00
20000.00
ORIGIIIAl

Argon

ASSIOtJED H AT

K :;

T
DEO-K

CI'
J/MOL-K

100.00298.15500.001000.00
2000.00
3000.00
4000.00
5000.00
6000.00
7000.00
8000.00
9000.00
10000.00
11000.00
120(10.00
13000.00
14000.00
15000.00
16000.00
17000.00
18000.00
19000.00
20000.00

20.78627
20.78627
20.78627
20.78627
20.78627
20.78627
20.78628
20.78628
20.78629
20.78652
20.78882
20.80179
20.84792
20.98142
21.27546
21.84575
22.88162
24.27350
26.44998
29.34715
31. 74794
35.49466
37.32050

ORIGIrlAl

Argon

ASSIGIIED H AT

K =

CP

H-HO

H-H29S
J/MOl

J/110l2078.627
6197.428
10393.137
20786.275
41572.550
62358.825
83145.100
10.5931.375
124717 .653](,5504.010
166291.314
187084.942
207904.1(,8228806.429
2{,9904.040
271410.89.5
293724.870
317010.610
342229.873
369891.337
398206.348
431238.1fI8

46184".323

J/MOl-K-4111L800
0.000
4195.710
14588.847
35375.122
56161.397
769(,7.672
97133.9',7118520.225
139306.582
160095.886
180887.514
201706.720
222609.002
2,..3106.612
265213.465
287527.442
310813.182.336032.445.363693.909
392008.920
425041.321
455646.895

132.139185
154.846663
165.593404
180.001352
194.409300
202.837{,09208.817248
213.455571
217.245357
220.4"9588
223.225342
225.6744(,4227.867939
229.860029
231.695508
233.416532
235,069674
236.674221
238.300601
239.975643
241.579948
2',3.361646
244.894536

752123.1190

H-G-1481.221 CAl/MOlE

T
DEG-K

CAl/MOl-K

H-HO
CAl/HOl

H-H296
CAl/MOL

CAl/MOl-K

S-(G-HO)
CAl/MOL-CO-H298 )CAl/MOL

H
CAl/MOL-G
CAl/MOL

100.00298.15500.001000.00
2000.00
3000.00
4000.00
5000.00
6000.00
7000.00
8000.00
9000.00
10000.00
11000.00
12000.00
13000.00
14000.00
15000.00
16000.00
17000.00
18000.00
19000.00
20000.00

4.96804
4.96804
4.96804
4.96804
4.96804
4.96804
4.96804
4.96804
4.96804
4.968104.96865".97175
4.98277
5.01468
5.084965.221265.468845.80151
6.32170
7.01414
7.58794
8.483438.91981496.804
1481.2212484.019
4968.059
9936.078
14904.117
19872.156
248{,0.195
29808.254
34776.293
39744.578
4'1714.374
49690.284
54686.049
59728.499
64868.760
70201.929
75767.354
81794.903
88406.151
95175.601
103068.535
110383.4(,2-984.417
0.000
1002.799
3486.818
8454.857
13422.896
18390.935
23358.974
28327.014
33295.072
38263.357
43233.153(,8209.063
53204.828
58247.278
63387.540
68720.708
74286.133
80313.682
86924.930
93692.381
101587.314
108902.222

31.582023
37.009241
39.577713
45.021356
46.464938
48.479304
49.908520
51.017106
51.922887
52.688716
53.352137
53.937491
54.4617('4
54.937866
55.376555
55.787890
56.183001
56 566496
56.955211
57.355555
57.738993
58.164829
58.531199

2661.393
9553.084
17304.867
38053.317
82993.798
130533.796
179761.924
2302"5.334
281729.085
33404'4.719
387072.520
440723.049
494927.160
5"9630.472
604790.166
660373.809
716360.079
172730.093
829488.'166
886638.288
944128.277
1002063.223
1060240.534

4142.619
11034.305
18786.088
39534.537
84475.018
132015.017
181243.145
231726.555
283210.306
335525.940
388553.741
442204.270
496408.381
551111.692
606271.387
661855.030
7178't}.299
774211.314
830lJ69.687
888119.509
945609.498
1003544.444
1061721.755-984.417
0.000
1002.799
3486.818
8454.857
13',22.896
18390.935
23358.974
28327.014
33295.072
38263.357
43233.153
48209.063
53204.828
58247.278
63387.540
68720.708
74286.133
80313.682
86924.930
93692.381
101587.314
108902.222

4142.619
llG34.305
18786.0-38
39534.537
84475.018
132015.017
181243.1 .. 5231726.555
283210.506
335525.9',0388553.741
442204.270
496408.381

OR I GlIlAl

28-6197.428 J/MOU'

lIAR

Argon

551111.6n606271.337
661855.030
7178',1.2?9]7"211.314
830969.637
8881l9.51J9
945609.498
1003544.444
1061721.755

CO[TFICI [tiTS
ASSIGtIED H/R AT

298.15500.001000.00
2000.00
3000.00{IOOO.OO

5000.00
6000.00
7000.00
8000.00
9000.00
10000.00
11000.00
1200C.00
13000.00
14000.00
15000.00
16000.00
17000.00
18000.00
19000.00
20000.00.... rgonoK-71\5.375 K

CP/R(H-HO)/RT(H-H298 )/RTSIR-(G-HO)/RT-(G-H298)/RT

tURT

-GIRT

2.50000
2.50000
2.50000
2.50000
2.50000
2.50000
2.50000
2.50000
2.49'194
2JI8368
2 ... 9125
2.50472
2.52105
2.55124
2.61468
2.73165
2.917193.17615
3.49936
3.86101
4.216314.49998

2.5000000
2.5000000
2.5000000
2.5000000
2.5000000
2.5000000
2.5000000
2.5000000
2.5003617
2. (,987(,642.4973788
2.4974261
2.4987853
2.5017379
2.507701\97..5191514
2.5390956
2.5704448
2.6153123
2.6743812
2.7463394
2.8273923

0.0000000
1.0092500
1.7546250
2.1273125
2.2515417
2.3136562
2.3509250
2.3757708
2.3938796
2.4055745
2.4145594
2.4228886
2.4310219
2.4396233
2.4503684
2.4659105

18.6236667
19.9161952
21.6490631
23.3819311
24.3955938
25.1147990
25.6726579
26.1284618
26.5142"50
26.846"13321.1392646
27.4024269
27.6418679
27.8623567
23.0687779
28.2664413
28.4608115
28.6569628
28.8589372
29.0690987
29.2875293
29.5114850

16.1236667
17.4161952
19.1490631
20.8819311
21.8955938
22.61'17990
23.1726579
23.6284618
24.0138833
24.3(,76669
24.6418858
24.9050009
25.143081\525.3606187
25.5610730
25.7472899
25.9217159
26.0865180
26.2436249
26.3947176
2.6.5411899
26.6840927

18.6236667
18.906?452
19.8944381
21.2546186
22.1440522
22.8011428
23.3217329
23.7526909
24.1203655
24.4408388
24.7247052
24.9795384
25.2108459
25.4227333
25.6184095
25.8005310
25.9714075
26.1331039
26.2874705
26.4361273
26.5804202
26.7213614

0.0000000
1.0092500
1.7546250
2.1273125
2.2515(,172.3136562
2.3509250
2.3757708
2.3938796
2.1\055745
2.4145594
2.4228886
2.4310219
2.4396233
2.4503684
2,"659103
2.4894039
2.5238589
2.5714667
2.6329714
2.7071091
2.7901236

18.623661)7
18.9069452
19.89('4381
21.2546136
22.14(,0522
22.8011428
23.3217329
23.7526909
24.1203655
24.4408388
24.7247052
24.9795384
25.2108459
25.4227333
25.6184095
25.8005310
25.9714075
26.1331039
26.2874705
26.4361273
26.5804202
26.7213614

COEFFIcIEtns

Argon

ASSIGtlED H AT

K"~.4894039

2.5238589
2.5714667
2.6329714
2.7071091
2.7901236-6197.428 J/MOLET
DEG-I(CP
J/MOl-K

H-HO

H-H298S-(G-HO)-(G-H298 )

H

J/MOl

J/MOl

J/MOl-K

J/HOl

J//10L

J/HOl

298.15500.001000.00
2000.00
3000.00
4000.00
5000.00
6000.00
7000.00
8000.00
9000.00
10000.00
11000.00
120&0.00
13000.00
14000.00
15000.00
16000.UO
17000.00
18000.00
19000.00
20000.00

20.78627
20.78627
20.78627
20.78627
20.78627
20.78627
20.78627
20.78627
20.74418
20.65055
20.71339
20.82549
20.9610921.21232
21. 73978
22.71233
24.25498
26.40795
29.09550
32.10245
35.05655
37.41512

6197.428
10393.1.)]
20786.275
41572.550
62358.825
8311'5.100103931.375
124717.650
1 (,5524 . 977
1662lJ6.813
186880.330
207648.739
228537.747
249608.700
271054.390
293237.128
316670.037
341951.827
369665.689(,00251.040
433&54.863
470167.636

154.846663
165.59340('
180.001352
194.409300
202.837(,09
208.817248
215.455571
217.245357
220.452956
223.214772
225.649687
227.8517 53
229.828587
231.661843
2B.378U5
235.021609
236.637701
238.268604
2H.9"i7922
241.695312
2',3.511455
245.373537

39970.105
72403.564
159215.017
347246.049
5('6153.402
752123.890
963346.479]178754.491
1397645.713
1619511.362
1843966.850
2070728.790
2299576.707
2550333.416
2762861.359
2997 06 5.396
3232895."i853470345.830
370'J448.987
3950264.576
4192862.790
4437303.106

46167.533
78600.992
165412.505
353443.477
552350.829
758321.318
969543.907
1184951.919
1 (,03843 .141
1625708.790
1850164.278
2016926.218
2305774.155
2536530.84'1
2769058.7tH
3003262.823
3239092.913
3476543.258
3715646.414
3956 .. 62.004
4199060.218
4443500.534

0.000
4195.710
14588.847
35375.122
56161.397
76947.672
97733.947
118520.222
139327.5('9160009.385
180682.902
201451.311
2223'10.319
243411 .212
264856.962
287039.701
310472.609
335754.399
363468.261
394053.612
427657.435
463970.208

S
CAL/HOl-K-(G-HO)-(G-H298)

CAl/IWL

CAl/MOLH
CAL/MOL

CIll/MOl

9553.084
17304.867
38053.317
82993.798
130533.796
179761.92"
2302"i5.334
281729.085
334045.342
387072.505
440718.654
494916.059
5(l9612.024
604764.201
660339.113
716315.821
772680.565
829432.560
886579.586
9(,4135.893
1002118.258
10605(,0.8?511034.305
18786.088
39554.537
84475.018
132015.017
1812(,3.1"5231726.555
283210.306
335526.563
388553.726
442199.875
496397.280
551093.244
606245 ... 22661820.934
717797.042
774161.786
830913.781
888060.807
945617.114
1003599.479
1062022.116

0.000
1002.799
3486.818
8454.857
13"i22.896
18390.935
2B58.974
28327.013
33300.083
38243.161
43184.250
48148.019
53140.612
58176.6':10
63302.333
68604.135
74204.734
80247.227
86870.999
94181.074
102212.580
110891. 541

11034.305
18786.0:)839534.531
84475.018
132015.017
181243.1'1;231726.555
283210.306
335526.563
388553.726
442199.875
496397.250
551093.244
6062(,5.422
661820.934
H7797.0'<2774161.7,%
830913.731
888060.807
945617.114
1003599.479
1062022.116

COEFFlCI EHTSASSIGtlED H AT
T
DEG-K

298 .15500.001000.00
2000.00
3000.00
4000.00
5000.00
6000.00
7000.00
8000.00
9000.00
10000.00
11000.00
12000.00
13000.00
14000.00
15000.00
16000.00
17000.00
18000.00
19000.00
20000.00

0.000
4195.HO
14588.847
35375.122
56161.397
769(,7.672
97755.947
118520.222
139327.5(.9160009.385
180682.902
201451.311
222340.319
2<i3411.272
264856.962
287039.71)1
310472.609
335754.399
363'.68.261
394053.612
427657.435
463970.208-G
J/~10l46167.553
78600.9n
165(,12.505
353443.417
552?50.829
758321.318
969543.907
1184951.919
1403843.1'11
1625708.790
1850164.278
2076926.218
2305774.135
2536530.8(,42769058. n7300321)2.82S
32H092.91?
3"i76543.258
3715646.414.3956462.004
4199060.218
4443500.5~4

Argon

0 K =

-1481.221 CAl/MOLE

CP
CAlI~lOl-K

H-HO

H-H298

CAL/HOL

CIIL/I·IOL

4.96804
4.96804
4.96804
4.96804
4.96804
4.96804
4.96804
4.96804
4.95798
4.93560
4.950624.977415.00982
5.06987
5.195935.42838
5.79708
6.31165
6.95399
7.672678.37872
8.94243

1481.2212484.019
4968.039
9936.078
1(,904.117
19872.156
24840.195
29808.234
34781.304
39724.382
44665.471
49629.140
54621.832
59657 .911
64783.554
70085.356
75685.955
81728.448
88352.220
95662.295
103693.801
112372.762

0.000
1002.799
3486.818
8454.857
13422.896
18390.935
23358.974
28327.013
3HOO.083
38Z43.161
4?184.250
48148.019
53140.612
58176.690
63302.333
68604.135
74204.75480247.227
86870.999
94181.074
102212.580
110891.541

COEFFICIENTS

BAR

37.009241
39.577773
43.021356
46.464938
48.479304
49.908520
51.017106
51.922886
52.689521
53.349611
53.931569
54.454530
54.930351
55.368509
55.778713
56 171513
56.557768
56.947563
57.348930
57.766566
5&.200635
58.645683

-G

Argon

29

Example 2 (C 2H 3 (g) by Method ADD with Wilhoit
Extrapolation)

Problem. -Estimate thermodynamic properties for theC2 H3 radical by adding group properties using method ADD
and then extrapolate these properties to higher temperaturesby means of the Wilhoit fit. Finally, obtain a least-squares fitof the previously generated data. C2H3 can be represented as

CDH2

(H-b

being formed from twogroups=) with ahydrogen atom removed by subtracting an HVIN group (Seetable IX). Inasmuch as the group data extend to only 3000 K,
extrapolation to higher temperatures, e.g., to 5000 K, can beaccomplished by means of the Wilhoit fit.
The input data set for example 2 consists of 12 records. The
first is a NAME record giving the species name and comments.
The second is a formula record. It gives a formula only. Withmethod ADD, the heat of formation comes from the group
additivity calculation and any value on the formula record isignored. The DATE record gives a code (03/91) to representGroup additivity, March 1991. The OUTP record calls fora many-figured table (MFIG) in SI units (JOULES) and leastsquares coefficients (LSQS). There are also two LSTS records
giving five EXP values (qi in eq. (l1» for the first temperature interval (l in column 80), namely the default interval
298.15 to 1000 K. These are the same exponents as in theequation representing the group data (see table X). Since no
information is given for the second interval, it will be thedefault interval of 1000 to 6000 K and the default equation
for C~ with qi values in equation (17).
There are two METH records each preceded by a set ofcorresponding TEMP records. For METH ADD, the temperature schedule is 298.15 K and 300 to 3000 K in 100-degreeincrements. For METH WILH, the schedule is 3500 to 6000
Kin 500-degree increments. METH ADD is followed by one
data record and METH WILH is the only method with no data
records. The data record following the METH ADD record
has a blank record ID. The labels on this record contain thegroup names, left-adjusted, followed by the number of times
the group should be added or subtracted as well as thesymmetry number (SYMNO) and statistical weight (STATWT)of the species formed. In this case all the numerical values
are integers which should always be followed by a decimal.
Numerical values should never encroach on the label spaces.
The last record is the required FINISH record.
The first part of the output consists of input record images
and some additional intermediate information. The molecularweight is inserted after the METH ADD record and the Wilhoit
coefficients and integration constants are inserted after the
METH WILH record image. The least-squares output is detailed
in the section Tables of least-squares errors. The output tablein SI units is described in appendix C in the section Tablesof original thermodynamic properties. The columns for HHO and - (G-HO) are blank because no H~98. 15 - Hg value(H298HO) was available.

Input. - The input data set for C 2H3 , example 2, is as follows:

Rec. Label
ID
1
1-6
7-12
a NAME

C2H3
DATE
TE~1P

OUTP
lSTS
LSTS
METH

TEMP
METH

FINIS~

Numerical
value 1
13-24

C2H3 RlADICAL
G 3/91
T
298.15
MFIG
EXP
O.
EXP
4.
ADD
CDH2
2.
T
3500.
~~I lH

Label
2
25-30

Label
3
43-48

Numerical
value 3
49-60

Label
4
61-66

Numerical
value 4
67-78

300.
T
JOULES
EXP
1.

I

HVIN
I

SYMNO
T

-1.
500.

LSQS
EXP

179
-

lao

Expl. 2

GROUP lADDITION WI1H WILH pIT EXTRAPOl ATION.

a All alphanumeric characters.

30

Numerical
value 2
31-42

100.

T

3000.

2.

EX?

3.

1.
6000.

STATWT

2.

1
1

Listed output. - The listed output for C2 H3 , example 2, is as follows:
NAME

C2H3 RADICAl

GROUP ADDlTIOIl WITH WILHOIT EXTRAPOlA·TIOtl.

Expl. 2

C2H3
DATE

G 3/91

OUTP

MFIG

l3T3

EXP

O.

LSTS

EXP

4.

TEMP

J OUl ES

lSQS

EXP

EX?

298.15

METH

2.

300.

EXP

100.

3.

3000.

ADD

MOlECUlAR tH.=
CDil2

27.04582
2.000000HVIN

TEMP

3500.

METH

-1.000000SYMtW

1.000000STAHIT

500.

2.000000

6000.

HILH

IHLHOIT COEFFICIENTSACO) =

a .924838250e+02

Itn EGRA TI ON COIlS TAlITS:
B =

150.0

CPO/R

=

A(1) = -0.367443984e+03

0.498539437e+03

A( 2)

H/R

0.78800460ge+05

S"-R =-0.172647715e+OZ

4.0000

CPUR =IIOli-l WEAR

13.0000

AC 3)-0.225971567e+03

110. ATOMS

FItllsH

lEAST SQUARESCP/R !tiPUT
CP..-R CALCItlPUT-CALC
FRACTION
5.1354587
5.1334587
0.0000000
0.0000000
300.005.1531178
5.1551178
0.0000000
0.0000000
400.006.1157304
6.1157304
0.0000000
0.0000000
500.006.9177637
6.9177687
0.0000000
0.0000000
600.007.6026413
7.6026413
O. 0000000
0.0000000
700.008.2006088
3.2006088
0.0000000
O. 0000000
800.008.7287346
8.7237846
0.0000000
0.0000000
900.009.1911343
9.1911.543
0.0000000
0.0000000
1000.00
9.5784758
9.5184758
O. 0000000
0.0000000~lAX REL ERR CP/R
TEMP
0.000000MAX REL ERR HH/RT
0.000000
TE~'P~lAX REl ERR S/R
0.000000
TE~1P
t1AX REl ERR GH/RT
Tn,p0.000000MAX ERR CP/R
0.000000TEMP.
MAX ERR HH/RT
0.000000HMPMAX ERR S/R
O. 000000
TE~lP
MAX ERR GH/RT
TEMP
0.000000
CP/R
6.7053736e-01TlO! 0.0
2.05200
298.15

HH/RT INPUT
ItIPUT-CALC
0.0000000
0.0000000
0.0317170
0.0000000
1.4562780
0.0000000
2.4546466
0.0000000
3.2569567
0.0000000
3.9213848
0.0000000
4.4899800
0.0000000
4.9872741
0.0000000
5.4277252
0.0000000
400.
400.
500.
700.
900.
500.
500.
700.
8e-02T~~ 1.0

CH-HO )/R COtlSTllliT = -0.93794084e+03, H/R COI1ST MiT

1000.00
EOO.OO
1200.00
1300.00
1400.00
1500.00
1600.00
1700.00
1800.00
1900.00
2000. DO
2100.00
2200.00
2300.00
2400.00
2500.00
2600.00
2700.00
2300.00
2900.00
5000.00

CP/R It/PUT
ItlPUT-CALC
9.5784758
0.0000000
9.9445347-0.0031261
10.2624975-0.0032441
10.5390577-0.0011634
10.7792387
0.0014425
10.9878845
0.0034784
11.1691592
0.0043931
11.3270"74
0.0040681
11. 4651042
0.0026928
11 .5865047
o. 0006474
11.6940448-0.0015973
11.7901404-0.0035633
11.3768279-0.0048367
11.9557641-0.0051185
12.0232262-0.0042756
12.0951116-0.0023753
12.1569382
0.0002843
12.2138442
0,0031490
12.2655882
0.0053883
12.3115491
0.0058806
12 3507263
0.00.01944
ORIGINAL

CP/R CALCFRACTION
9.5734758
0.0000000
9.9476603-0.0003144
10.2657416-0.0005161
10.5402211-0.0001104
10.7778462
0.0001338
10.9844061
0.000316611.16(17661
0.0003933
11.3229793
0.0003592
11.4624113
o .0002349
11.5858573
0.0000559
11.6956421-0.0001366
11.7937042-0.0003023
11.3816646-0.0004072
11.9608826-0.0004281
12. 0325018-0.0003555
12.0974869-0.0001964
12.1566540
0.0000234
12.2106952
0.0002578
12.2601994
0.0004393
12.3056685
0.0004777
12.3(,7531'1
0.0002586
BAR

HH/RT CALC
S/R INPUT
S..-R CALC
-GH..-RT !tIPUT-GH/RT C~LC
FRACTI 011!tIPU T-CA LC
FRACTIOt/
FRACTIOtJ
ItIPUT-CALC
0.0000000
23.1551124
28.1531124
28.1531124
28.153112 /1
0.0000000
0.0000000
0.0000000
o. 0000000
O.ooooooa
0.0317170
28.1849275
28.1849275
28.1532105
28.1532105
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
1.4362780
29.80361144
29.8036844
23.3674064
28.3674064
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
2.4546466
31.2570661
31.2570661
28.8024195
28.3024195
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
J.2569567
32.5803752
32.5803752
29.3234185
29.32341115
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
3.9213848
33.7982078
35.7932078
29.3768230
29.87611230
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
4.4899800
34.9284533
34.9234533.30.4384733
30.43&4733
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
4.9872741
35.9839172
35.9839172
30.9966431
30.9966431
0.0000000
0.0000000
0.0000000
0.0000000
O. 0000000
5.4277252
36.9730&16
36.9730816
31.5453565
31.5453565
0.0000000
0.0000000
o. 0000000
0.0000000
0.0000000
AVER REl ERR CP/R
0.000000
REl lST SO ERR CP/R
0.000000
AVER REL ERR HH/RT
0.000000
REL LST SO ERR HH/RT
0.000000
AVER REl ERR S/R
0.000000
REl LST SO ERR $/ R
0.000000
AVER REl ERR GH/RT
0.000000
REl L5 T SO ERR GH/RT
0.000000
AVER ERR CP/R
0.000000
LST sO ERR CP/R
0.000000
AVER ERR HH/RT
0.000000
0.000000
LST SO ERR HHI RT
AVER ERR S/R
0.000000SQLSTERR S/R
0.000000
AVER ERR GH/RT
0.000000
0.000000
LST SO ERR GH/RT-2.32294 02e-051~)( 2.
1.7095426e-08Tl<l( 3.0 -5.4781628e-12TH 4.0= 0.80540633e'05,

HH"RT ItlP UT
I tlPUT -CAL C
5.4277 252
0.0000000
5.8221381-0.0001256
6. I 792256-0.0004027
6.5042090-0.0005493
6.8011941-0.0004994
7.0735169-0. 0002968
7.3239614-0.0000258
7.5548939
O. 0002304
7.7683818
0.0004095
7.9662075
0.0004778
8.1499633
0.0004300
8.3210581
0.0002846
8.4807461
0.0000775
8.6301433-0.0001463
8.7702412-0.0003398
8.9019158-0.0004624
9.0259358-0.0004865
9.1429680-0.0004045
9.2535822-0.0002342
9.3582548-0.0000249
9.4573714
0.0001335

HH/RT CALCFRACTIml
5.4277252
0.0000000
5.8222637-0.0000216
6.1796233-0.0000652
6.5047584-0.0000845
6.8016934-0.0000734
7.0738158-0.0000420
7.3259872-0.0000035
7.5546635
O. 0000305
7.7679722
0.0000527
7.9657297
0.0000600
3.1495333
0.0000528
8.32077 35
0.0000342
8.4806686
0,0000091
8,6302896-0.0000169
8.7705810-0.0000387
3.9023782-0.on00519
9.0264;,>23-0. 0000539
9.1433724-0.0000442
9.2538164-0.0000253
9.3582797-0.0000027
9.4572332
0.0000146

S/R Cot/STAin= o.19106863e+02

S..-R IIlPUTrIIPUT-CAlC
36.9730316
0.0000000
37.9036300-0.0001285
38.73286911-0.0004237
39.6154873-0.0006147
40.4055165-0.0006 047
41.1564927-0.0004304
41.3715572-0.0001700
42.55352'17
0.0000926
43.2049603
0.0002904
43.8281674
0.0003332
44.4252656
0.0003591
44.9981873
0.0002316
45.5486985
0.0000331
46. 0784120-0.0001922
46.5887969-0.0003962
47.01\11868-0.0005355
47.5567863-0.0005786
48.0166759-0.0005136
43.4618162-0.0003552
48.8930517-0.0001505
49.311Jl36
0.0000149

S/R CAlC
FRACTION
36.9730316
0.0000000
57.9037535-0.0000034
38.7832985-0. 0000111
39.6161020-0.0000155
40.4061212-0.0000150
41.1569231-0.0000105
41.8717272-0.0000041
42.5534371
O. 0000022
43.2046699
0.0000067
43. &277842
0.0000087
44.4249065
0.0000031
44.9979557
O. 0000051
45.5486655
0.0000007
46.0786042-0.00000"2
46.5391931-0.0000035
47.0817223-0. 000011(.
47.5573649-0.0000122
48.0171395-0.0000107
48.4621714-0.0000073
48.8932022-0.0000031
49.3110937
0.0000003-GH/RT !tIPU T
IHpUT-CAlC
31.5453565
0.0000000
32.0814'H9-0.0000029
32.6036442-0.0000260
33.1112732-0.0000653
33.6043224-0.0001054
34.0829758-0.0001.B6
34,5475953-0.0001442
34.9936308-0.0001378
35.43657115-0.0001191
35.8619599-0.0000946
36.2753024-0.0000708
36.677 1292
-0.0000530
37.0679524-0.0000444
37.4482686-0.0000459
37.8185557-0.0000564
38.1792710-0.0000751
38.5308506-0. 0000921
38.8737079-0.0001092
39.2082340-0.0001Z10
39.5347970-0.0001256
39.8537422-0.0001234-GH"RT CALCFRACTIOH
51.5453565
O.OOOOOOJ
32.0814943-O.OOOOOOl
32.6036702-0.0000003
33.1113430-0. 0000020
53.6044273-0.0000031
3£1.0331093-0.0000039
54.5477400-0.0000042
34.9987636-0.0000039
35. (,36697';-0.000003.
35.8620545-0.0000026
36.275373Z-0.000002:'>36.6771822-0.0000014
37.0679969-0.0000012
37.448314.,-0.0000012
37.8186121-O.OOOOOlS
38.1793441-0.0000019
38.530942"-0.000002'.
38.8738171-0.0000023
39.2083550-0.0000031
39.5349226-0.0000032
39.1I53865,j-0.000003l

C2H3 RADICAL

31

35UO.00

12.5136171
12.5139980-0.0003809-0.000030"
12.6258090
12.6286924-0.0028834~0.OO02284
4500.00
12.705721&
12.7082897-0.0025681-0.0002021
5000.00
12.7644316
12.7638239
0.0006078
0.0000476
5500.00
12.8086825
12.8053269
0.0033555
0.0002620
6000.00
12.8427587
12.8442720-0.0015133-0.0001178
MAX REl ERR Cf'/R
0.000478
TEMP
MAX REl ERR HH/RT
0.000084
TEMP
MAX REl ERR SIR
0.00(}016
1El-1PNAX REL ERR Gli/RT
0.000004
TEI1P
MAX ERR CP/R
0.005881
TEIIP.
~1AX ERR HH/RT
0.0005{.9
TEMP
HAX ERR SIR
O.00Q615
TEI1P
l·fAX ERR GH/RT
0.000150
TENP
4000.00

q .8830643
0.0002836
10.2193107
0.00002{,210.4913770-0.0003127
10.7158907-0.0003952
10.904223')-0.0001544
11.0644080
0.0000223
2900.
1300.
1300.
1600.
2900.
1300.
1300.
6000.

9.882/11U6
51.2279'162
41.3",,9520
51.2271975
0.0000287
0.0001987
0.0000039-0.0000849
10.2192865
52.9067248
52.9067615
42.6874141
0.0000024-0.0000368-0.0000007-0.0000609
10.4916897
54.3986970
54. 39'H1884'13.9013201-0.0000298-0.0003914-0.0000072-0.0000787
10.7162859
55.7ft05685
55.7410827
45.02ft6778-0.0000369-0.0005142-0.0000092-0,0001190
10.9043782
56.9593193
56.9596208
46.0550954-0.0000142-0.0003015-0.0000053-0.0001',72
11.0643857
58.0753434
58.0754710
47.0109354
0.0000020-0.0001276-0.0000022-0.0001499
AVER REt ERR CP/R
0.000237
REL LST SO ERR CP/R
AVER REt ERR Hl-11RT
o.oooonREl lST SQ ERR HH/RT
IWER REl ERR SIR
0.000007
REl lSl SO ERR SIR
AVER REL ERR GH/RT
0.000002
REL LST SO ERR. GH/RT
AVER ERR CP/R
0.002786
LST SO ERR CP/R
AVER ERR HH/RT
0.000268
1ST SQ ERR HH/RT
AVER. ERR SIR
o .000299
lST SQ ERR SIR
AVER ERR GH/RT
0.000088
LST SQ ERR GH/RT

2 0575702e+06T*~-2.0 -9.4600005et03T~~-1.0
1.B762547e+OlTX~ 0.0-2.2520423e-031x. 1.0-6.7520919a-11Tv,x 3.0
3.43~72S5e-151v~ 4.0
CH-HO)/R CONSTANT = 0.55034170e+05, H/R CO"STA~T = O.13651275et06, SIR CONSTANT =-0.99058768e+02

CP/R =

41.5450169-0.0000021
42.687'i750-0.0000014
43.9075987-0.0000018
45.02(,7963-0.0000026
46.0552426-0.0000032
47.0110853-0.0000032
0.000274
O.OOOMO
0.000008
0.000003
0.003226
0.000318
0.000354
0.000098

5.3448381e-07TXX 2.0

THERNODYNAMIC DATA COEFFICIEIHS. RECORD IMAGES C2H5 RADICALGROUP AODITIOU WITH WILHOIT EXTRAPOlATIOU.
E'lCP1. 2
2 G 3/91 C
2.00H
3.00
0.00
0.00
0.00 027.04582
677454.462
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0 0.0 0.0 0.0
0.000
6.70537360d-Ol 2.05200777d-02 -2.3229402Id-05 1.70954257d-08 -5.47816280d-12
O.OOOOOOOOd~OO O.QDOOOOOOd+OO
O.OOOOOOOOd+OO 8.05406384dt04 1.91068625dtOI
1000.000 6000.000 7 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0
0.000
2.05757019dt06 -9.46000054d+03 1.87625468dtOI -2.25204228d-03 5.3448381Id-07-6.75209185d-l1 3.43872846d-15 O.OOOOOOOOdtOO 1.36512749d+05 -9.90587681dtOl

ORIGINAL

C2H3 RADICALASSIGNED H AT 298 K =677454.462 J/MOlE

T
DEO-K

CP
J/MOl-K

298.1542.68219
42.1'.4565
50.84930
57.51786
63.21224
6& .13 r,04
72.57557
76.4197879.64033
82.68393
85.32764
87.62710
89.62450
91.35888
92.86609
94.17885
95.32672
96.33611
97.23025
98.029Z4
98.75000
99.40632
100.00881
100.56493
101.07898
101.55213
101.98236
102.36450
102.69024
104.04459
104.97742
105.64185
106.12999
106.49792
106.7&125

300. {H)400.00500.00600.00700.00800.00900.001000.00
IHO.OO
1200.00
BOO.OO
1400.00
1500.UO
1600.00
1700.00
1800.00
1900.00
2000.00
2100.00
2200.00
2300.00
2400.00
2500.00
2600.00
2700.00
2800.00
2900.00
3000.00
3500.00
4000.00
4500.00
5000.00
5500.00
6000.00

ORIOIl~AL

32

H-tiO
J/MOL

H-H298
J/I'fOl
0.000
19.1154776.779
10204.592
16247.999
22823.1>75
29865.587
37320.066
45128.875
53249.048
61652.679
70303.105
79168.034
88219.241
97432.241
106785.980
116262.518
125846.712
135525.902
145289.59{,
155129.146
1650J7 .450
175008.619
185037.670
195120.206
205252.106215429.205
2256tj6.978235900.228
28760(,.928
339874.244
392537.964
445486.902
498648.031
551970.787

8AR

C2H3 RADICALS

J/MOL-K
234.079335
234.343862
247.803032
259.887189
270.889856
281.015536
290.412974
299.188639
307.413057
315.150111
322. {,60558
329.383565
335.957071
342.196070
348.141481
353.811748
359.228074
364.409736
369.374315
374.137878
378.715109
383.119417
387.363017
391.456999
395.411375
399.235132
402.936255
406.521767
409.997747(,25.935687
439.893492
452.298511
463.455514
473.588830
4&2.8681124-CO-HO)

JIMOL-CO-H298 )J/MOl
69790.754
7022'• . 045
9431i4.43',
119739.002
146285.914
17 3587. 801
202464.793
231949.709
262284.182
293416.074
325299.991
357895.270
391164.865
425074.864
459594.129
494693.992
530348.016
566531.786
603222.729
640399.950
6780{.4.095
716137.209
754662.623
793604.827
832949.370
872682.749
912792.310
953266.147
994093.013
1<'03169.977
1419699.725
1642805.334
1871790,669
2106090.531
2345237.356

H

-0

J/MOl

J/MOl

677454.462
677533.575
682231.241
687659.054
693702.461
700277 . 537
707320.0ft9714774.528
722583.337
730703.510
739107.141
747757.566
756622.496
765675.703
774886.703
784240.442-61>7665.708-607250.417-583110.028-557715.459-531168.5·j8-5Q3566.661-474"189.6oS9-445S04.753-415170.230-38,,038.338-352154.471-319559.192-286289.517

795716.

no803301.174
812980.364
822744.056
832583.608
842491. 912
852463.081
862492.132
872574.668
882706.568
892883.667
903101.440
913354.690
965059.390
1017328.7U61069992,426
1122941.364
1176102.493
1229425.249-252379.5'n-217860.:s:n-182760.470-IG7106.4r.6-110922.676-74231.733-37054.512
589.633
38682.748
77208.161
116150.365
155{.94.9lJ&
195228.237
235337.8"i8275811.636
316638.551
525715.515
742245.263
965350.872
1194336.208
1423636.070
1667782.874

Example 3 (C 4 H 4 (g) by Method READIN with Wilhoit
Extrapolation)
Problem.-Use method READIN to process thermodynamic
data obtained from the literature. Inasmuch as the data to beprocessed are available to only 1500 K, use the Wilhoit fit
to extrapolate to higher temperatures.
The input follows the same pattern as in the first two
examples. The NAME record gives the name and reference
for the species. The second record, the required formula
record, gives the formula and heat of formation at 298.15 K(HF298)-namely, 435 000 J/mol. This is followed by a
DATE record where XlO/85 was chosen to represent the Texas
TRC Thermodynamic Tables along with the date of theparticular table. The two REFN records give more informationon the reference. The first label ATM on the OUTP record
specifies that the pressure unit in the output entropy and Gibbs
energy functions be in atmospheres rather than the default unit
which is bars. The remaining OUTP record labels call formany figures tables (MFIG), in both dimensionless (DMLESS)
and joules (JOULES) energy units.
There are two METH records. The first is a READIN
method with no preceding TEMP records since the temper-

atures for the data come from the data records. The METH WILH record is for Wilhoit extrapolation and the TEMP
record which precedes it gives the extrapolation schedule. The
KJOULE label on the METH READIN record specifies thatthe input enthalpy values are in units of kllmo!. However,C~ and 81 values are in llmol-K whether the label is KJOULE
or JOULES. The BAR label specifies that the standard statepressure in the entropy values on the data records is one bar.
The 19 data records have the optional record ID of C4H4.
The METH WILH record has no other labels since themolecule is nonlinear, the default structure. Linear molecules
require a LINE label. Since this method has no data records,
it is followed by the final FINISH record.
The listed output consists of the input record images, theWilhoit coefficients and integration constants, and the twotables requested on the OUTP record. It should be notedthat the OUTP record specifies one atmosphere (ATM) for
the output standard state entropy pressure while the METH
record indicates the standard state pressure is one bar (BAR)
for the input entropy. Thus, at T =: 298.15 K, Sr = 251.67
J/mol-K in the input and 51 = 251.56 J/mol-K in the output.

Input. - The input data set for C 4 H4 , example 3, is as follows:

Rec. Label
ID
1
1-6
7-12

a NAMEC4H4OATE
a REFNa REFN
OUTP
~1ETH

C4H4
C4H4
C4H4
C4H4
C4H4
C4H4
C4H4
C4H4
C4H4
C4H4
C4H4
C4H4
C4H4
C4H4
C4H4
C4H4
C4H4
C4H4
C4H4
TEMP
~1ETH

FINISH

Numerical
value 1
13-24

CYCLOE UTAOIENE

label
2
25-30

Numerical
value 2
31-42

label
3

~3-48

Numerical
value 3
49-60

Label
4
~1-66

TRC TAIBLES T,U,V,~ '-2920 , OCT 31, 198 5.
HF298
435000.
JOULES

Numerical
value 4
67-78

17c;

-

~(

Exp1. ~

XI0/85
TRC TH ERMODYNAMIC TABLES - HYOROCAR~ ONS. trhe Texas A8. M UnivIersity Syste ~,CoIl ege Station, TX 77 ~43-3111.
abIes ft,u,v,w-2920 , Oct. ~L1985.
ATM
OMLESSMFIGJOULE5READltIKJOULE
BAR
T
50.000 CP
33.2600 H-HO 0.1663000 015
182.78000
T
100.000 CP
33.6300 H-HO 0.3330000 015
205.88000
T
150.000 CP
36.6100 H-HO 0.5071000 015
219.96000
T
200.000 CP
43.0200 H-HO 0.705000D 015
231.30000
T
273.160 CP
55.9800 H-HO 0.106550D 025
246.56000
T
298.150 CP
60.7500 H-HO 0.121140D 02S
251.67000
T
300.000 CP
61.1000 H-HO 0.1222700 025
252.04000T
400.000 CP
79.3000 H-HO 0.1926700 025
272.17000
T
500.000 CP
94.4500 H-HO 0.2798300 025
291.56000
T
600.000 CP
106.5000 H-HO 0.3805300 02S
309.88000
T
700.000 CP
116.1700 H-HO 0.4920400 025
327.05000T
800.000 CP
124.1200 H-HO 0.6123100 02S
343.10000
T
900.000 CP
130.8100 H-HO 0.7399000 025
358.12000
T
1000.000 CP
136.5000 H-HO 0.873600D 025
372.20000
T
1100.000 CP
141.5000 H-HO 0.101260D 035
385.50000
T
1200.000 CP
145.7000 H-HO 0.1156300 O~S
398.00000
T
1300.000 CP
149.4000 H-HO 0.130390D 0..; 5409.80000
T
1400.000 CP
152.7000 H-HO 0.1455000 03 S
421.00000
T
1500.000 CP
155.5000 H-HO 0.1609200 03 S
431.60000
T
1600.
I
200.
T
5000.
WIlH

a All alphanumeric characters.

:nListed output. - The listed output for C4H4' example 3, is as follows:
NAME

CYClOBUTADIENE

C4H4

TRC TABLES T,U,V,W-2920, OCT 31, 1985.
HF298

Dt,TE

XIO/85REFN

TRC THERMODYNAMIC TABLES - HYDROCARBONS.

REfN

Expl. 3

JOULES

435000.

College Station, TX 77843-3111.

The Texas A&M University System,

Tables t,u,v,w-2920, Oet.31,1985.

OUr?

AIM

DMlESSMFIGMETHREADINKJOULE

BAR

C4-14

T

50.000CP

33.2600

H-HO

0.166300D 015

182.78000

Cl,H4

T

100.000CP

33.6300

H-HO

0.3330000 015

205.88000

C4H4

T

150.000

CP

36.6100

H-HO

0.507100D 015

219.96000

C4H4

T

200.000CP

43.0200

H-HO

0.7050000 01S

231.30000

C4H4T

273.160CP

55.9800

H-HO

0.1065500 02S

246.56000

JOULES

C4H4

T

298.150CP

60.7500

H-HO

0.1211400 025

251.67000

C4H4

T

300.000CP

61.1000

H-HO

0.1222700 025

252.04000

C4H4

T

400.000CP

79.3000

H-HO

0.1926700 025

272.17000

C4H4

T

500.000CP

94.4500

H-HO

0.2798300 025

291.56000

C4H4

T

600.000CP

106.5000

H-HO

0.3305300 OZ5309.3BOOO

C4H4

T

700.000CP

116.1700

H-HO

0.4920400 025

327.05000

C4H4

T

800.000

cp

124.1200H-HO

0.612310D 025

343.10000

C4H4T

900.000CP

130.8100H-HO0.739900D 025

358.12000

C4H4

T

1000.000CP

136.5000

H-HO

0.8736000 023

372.20000

H-HO

0.1012600 035

385.50000
398.00000

C4ti4

T

1100.000CP

141.5000

C4H4

T

1200.000CP

145.7000H-HO

o .115630D 03S

C4H4

T

1300.000CP

149.4000

H-HO

0.130390D 035

409. BOOOO

C4H4

T

1400.000CP

152.7000

H-HO

0.145500D 035

421.00000

C4H4T

1500.000CP

155.5000

H-HO

0.1609200 03S

431.60000

ATM

TEMP

T

~lETH

W! LH

CYCLOBUTADIEtlE

5000.

T

200.

1600.

WILHOIT COEFFICIEtlTS
ACO);

INTEGRATION COtl5TANTS;
B::

200.0

ACl)::

0.415261964e+00

CPO/R ::

0.540942637e+Ol

H/R

S/R :-0.890756216e+02

4.0000CPI/R:

NON-LINEAR

22.0000

FINISHORIGIIIAL

34-O.61054644ge+OlA(2}0.103765248e t 05

ATM

CYCLOBUTADIEIIE

NO. ATOMS

8A(3)-0.117525765e+OlI)IHGIflAL

CYClOIlUTADlEUEASSIGIIED H/R AT

o K

T

Cr/R

(H-HO)/RT(H-H298)/RT

SIR-(G-HO)/RT-(G-H298)/RT

H/RT

50.00
100.00150.00200.00273.16298.15300.00400.00500.00600.00100.00llOO.OO
900.001000.00
1100.00
1200.00
1300.00
1400.00
1500.00
1600.00
1800.00
2000.00
2200.00
2400.00
2600.00
2800.00
3000.00
3200.00
3400.00
3600.00
3800.00
4000.00
4200.00
4400.00
4600.00<i800.00
5000.00

4.00024
4.04474
4.40315
5.174096.732817.30650
7.3(,860
9.53754
11.35966
12.80895
13.97196
14.92812
15.73274
16.41708
17.01844
17.52558
17.96859
18.36548
18.70224
18.89517
19.33589
19.68191
1"9.95893
20.18447
20.37080
20.52673
20.65870
20.77154
20.86888
20.95353
21.02769
21.09308
21.1510921.20284
21.24923
21.2910221.32882

4.0002357
4.0050466
4.0659842
4.2395764
4.691.:s700
4.8867047
4.9018723
5.7931856
6.7311243
7.6213297
8.4540675
9.2054433
9.8876676
10.5069331
11.0715539
11.5891776
12.0632485
12.4996628
12.9027447
13.2691069
13.9197380
14.4793212
14.9653234
15.3911641
15.7672659
16.1018181
16.4013296
16.6710308
16.9151685
17.1372236
17.3400752
17.5261239
17.6973&70
17.8555715
18.0021314
18.1383128
18.26S1S<16-25.1391844-10.5646635-5.6471558-3.0452787-0.6423941
0.0000000
0.0453025
2.1507581
3.8171823

21.9700928
24.7483683
26.4'117935
27.8056742
29.6410199
30.2556081
30.3001086
32.7211773
35.0532450

17.9698570
20.7433217
22.3758092
23.5660978
24.9496498
25.3689034
25.3982363
26.9279917
28.3221207
29.6ZIH'12Z
50.8616191
52.0466036
33.1708597
54.2450194
35.2800118
36.2657839
37.2109188
38.1215(,71
38.9933',49
39.8.379256
41.4393608
42.9356282
44.3389736
45.6597799
46.9068838
48.0878422
49.2091514
50.2764264
51.2945"67
52.2677745
53.1998517
54.0940793
54.9533822
55.7803635
56.5773(,9057.3464250
58.0894691

47.1092772
35.3130318
32.0889493
30.8509529
30.2834139
30.2556081
30.2548063
30.5704192
31.2360628
32.0570773
32.9490062
H.867817{t34.7897164
35.70199\}436.6045309
37.4799264
58.5316657
39.1622407
39.96(,6569
40.7485525
42.2<i87691
43.6641137
45.0012332
46.2668512
47.4672573
48.6081890
49.6948084
50.7317299
51.7230676
52.6724887
53.5852651
54.'i583220
55.3002801
56.111"933
56.8940819
57.6499606
58.3808633

1021.2243415
512.6170995
343.1406862
258.5456028
190.8870257
175.4760231
17(,.43922B
132.9('61989
108.4535348
92.5965052
lH.1129322
72.7819499
66.4001179
61.368B84
57.3090152
53.9755154
51.1872525
48.8290952
46.8102149
45.0573602
42.1759632
39.9099238
38.0840530
36.5833330
35.3292680
34.2665345
33.3550647
32.5651575
31.8743465
31.2653362
30.7246029
30.2(114252
29.8071978
29.4149364
29.0589152
28.7343973
28.4374306

S
JI'MOL-K-(G-HO)-(G-H29a)
J/MOl

H
J/MOL

-0
J/MOl

182.670556
205.770556
219.850556
231.190556
246 .... 50556
251.560556
251.930556
272.060556
291.450556
309.770556
326.940556
342.990556
358.010556
372.090556
385.390556
397.890556
409.690556
420.890556
431.490556<'<'1.558953
460.283781
477 .377171
493.086170
507.608685
521.104845
533.705572
545.519000
556.635303
567.130359
577.068551
586.504928
595.486896
604.055547
612.246718
620.091836
627 .618607
634.851573

7(,70.528
17247.056
27906.583
39188.111
56665.43"62888.780
63352.167
89557.222
117742.278
1"7809.334
179654.389
213161.4'15
2('8219.500
284730.556
322669.612
361838.667
402207.723
443746.779
486315.834
529972.529
620186.563
713977.420
8110',5.047
911132.872
1014020.162
1119515.165
1227449.944
1337676.322
1450062.674
1564(,91.362
1680856.657
1799063.053
1919023.872
2040660.116
2163899. (,98
2288675.634
2(.14927.359

19584.528
29361.056<i0020.583
51302.111
68779.434
75002.780
75466.167
101671.222
129856.278
159923 . .334
191768.389
225275.445
260333.500
296844.556
334783.612
373952.667
414321.723
455860.779
498429.834
542086.5Z9632300.363
726091.420
823159.047
923246.872
1026134.162
1131629.165
1239563.944
1349790.322
1462176.674
1576605 _362
1692970.657
1811177.053
1931137.872
2052774.116
2176013.498
2300789.654
2427041.359

424549.000
426216.000
427957.000
429936.000,,33541.000
435000.000
435113.000
442153.000
450869.000
460939.000
472090.000
484117.000
496876.000
510246.000
524146.000
538516.000
553276.000
568386.000
583806.000
599'\07.795
631210.442
663662.921
696650.528-415415.4 1 2-{, 0 56 38.9',(,-39"979.417-383697.839-366220.566-359997.220-35953.L833-333328.778-3051U. 722-275076.6(,6-243231.611-209724.555

730013.971<'88246.872
591134.1,,2696629.165
80('563.914
914790.322
1027176.674
1141605.362
1257970.657
1376177.053
1496137.872
1617774.116
1741015.4'J8
1865789.654
1992041.359

50861.205

ArM

ORIG1I1AL

ORIGIUAL
A~·StGUEO

I(

5.1995{~476.3726803
7.3842295
8.2688109
9.0499621
9.74703 .. 810.3750351
10.9425015
11.4S89bn
11. 9.S14507
12.3585000
15.1103097
13.7508357
14.3030638
14.7840929
15.2068925
J 5.5814713
15.9156726
16.2157274
16.4866476
16.7325095
16.9566618
17.1618812
17.350(,8'12
17.5244'tl7

17.6853n6

17.8347772
17.9137954

37.2566ZZ0

59.3216866
41.2520469
43.0585275
44.7519524
46.5515656
47.8549615
49.2741672
50.6212099
51.8960896
53.1070525
55.3590988
57 .... 149494
59.3042970
61.0509441
62.6741498
64.1896603
65.6104809
66.9474573
68.2097152
69.4049981
70.5399269
71.6202032
72.6507692
73.6359350
74.5791\80575.4llfe7378

76.~546S87-GIRT-999.2542438-487.8687312-316.6988n7-230.7399236-161.2(,60058-1"5.2204150-144.1391147-100.2250215-73.4002898-55.1~9118~2-41.7912456-31.5299030-23.3~15906-16.6161859-10.9574476-6.1185539-1.9130853
1.7921148
5.0858747
8.0496723
13.1831356
17.5050256
21.22024~0

24.4676111
27.3'148818
29.9231260
32.2554163
34.3822998
36.3353637
38.1396619
39.8153240
41.3787780
42.8435714
44.2209936
45.5205653
46.7503405
47.91722"'1

CYCI.OnUTADIEUECYClOBUTAOI£UE

K = 422886.000 J/MOLE

H AT

0

DEG-K

T

CP
J/MOl-1(

H-HO
J/t10L

50.00
100.00150.00200.0027.3 . 16
298 .15500.00400.00500.00600.00700.00800.00900.001000.00
1100.00
1200.00
1500.00
1400.00
1500.00
1600.00
1800.00
2000.00
2200.00
2400.QQ
2600.00
2800.00
3000.00
3200.00
3400.00
3600.00
3800.00
4000.00
4200.00
4400.00
4600.00'i800.00
5000.00

33.26000
33.63000
36.61000',3.02000
55.98000
60.75000
61.10000
79.30000
94.45000
106.50000
116.17000
124.12000
130.81000
136.50000
141.50000
145.70000
149.40000
152.70000
155.50000
157.10409
160.76845
163.64548
165.94875
167.82394
169.37318
170.66967
171.76700
172.70516
173.51(,49
174.21832
17G.83490
175.37861
175.86095
176.29122
176.67697
177.02442
177.3.3871

1663.000
3330.000
5071.000
7050.000
10655.000
1211(L 000
12227.000
19267.000
27983.000
38053.000
49204.000
61231.000
73990.000
87360.000
101260.000
115630.000
130390.000
145500.000
160920.000
176521.795
208324.<i42240776.921
27374('.528
307127.971
340852.435
374860.437
409107.056
443556.648
478180.5(18512955.422
547862.069
582884.530
618009.425
653225.443
688522.949
723893.680
759330.507

ORIGIIIAL

ATM

H-H298
J/r10l-10451.0DO-878'l.000-7045.000-5064.000-1459.000
0.000
113.000
7153.000
15869.000
25939.000
37090.000
49117 .000
61876.000
75246.000
89146.000
103516.000
118276.000
133386.000
148806.000
16<'(,07.795
196210.442
228662.921
261630.528
295013.971
328758.435
362746.437
396993.056
431"'42.6',8466066.548
500841.422
535748.069
570770.530
605895.425
641111.445

676408.949

711779.680
747216.507

JI'~IOL

763738.435
797746.437
831993.056
866442.648
901066.548
935841.422
970748.069
1005770.530
1040895.'125
1076111.443]]11408.949
1146779.680
1182216.507-174666.5fJO-138155.444-100216.338-61047.333-20678.277
20860.779
63',29.834
1070l'.6.5Z9
197300.363
291091J,20
388159.0~7

CYClOBUTADIENE

35

Example 4 (C sH l1 (g) by Method RRHO with Internal
Rotation)

Problem. -Calculate thermodynamic properties for a species
wi th internal rotation using the RRH0 method.
The comments for this species will be mainly with respect
to the method (METH RRHO) and the data records. The
remaining records are similar to those discussed in the first
three examples. The method RRHO is the rigid rotatorharmonic oscillator approximation. Please refer to tables II
and VII for the required data. The tert-pentyl radical is anonlinear molecule and thus has a total of 3N-6 fundamental
frequenci~s (Vi(dj)values) and internal rotors (INTROT value),
where N IS the number of atoms in the molecule. In this casethe number is 3(16)-6 = 42, with 38 frequencies and four
rotors. Fourteen unique frequencies are given on the data
records with their rimitiplicities given in parentheses. The rigid
rotator part requires either the moments of inertia (IA,IB,IC)or rotational constants (AO,BO,CO) for the nonlinear molecule._
For this example the individual moments of inertia in(g)(cm)2 X 10 39 have been multiplied together into one valueof 8590. with the label IAIBIC.
The four internal rotors are specified by the label INTROT
and its corresponding numerical value of 4 .. (Note that therecord ID on the data records are all blank, which is one ofthe permitted options.) The data records for the individual
rotors are identified by the number in column 80. The thirdand fourth rotors for CSH 1I have identical parameters so they
may be combined by using NROTOR = 2. on the data record
for the third rotor. The barrier potential for the first rotor isV3 = 1254. em -I. Inasmuch as no potentials are specified
for the other rotors, the program treats them as free rotors.
The IB values for the rotors are the moments of inertia in(g)(cm)2 X 10 39 and the ROSYM values are the symmetry
numbers for the rotors.

Input. - The input data set for CsH u ' example 4, is as follows:

Rec. Label
ID
1
1-6
7-12

Numerical
value 1
13-24

Label
2
25-30

Numerical
value 2
31-42

Label
3
A3-48

Numerical
value 3
49-60

Label
4

61-66

Numerical
value 4
67-78

Expl.
NAME TERT-P ENTYL RAD
WING T!SANG, J. AM . CH. SOC. , MAY 15,198 5, P2817 2.
32600.
HF298!JOULES
C5Hll
DATE L 5/87
a REFN WING TSANG, 'THE S TABILI rry OF ALKYL RADICA","S,' J. AM. CHEM. SOC.
a REFN MAY 15 ,1935, PP 28 72-288 o.
T
6000.
TEr~p
I
1000.
1000.
T
100.
T
CAL
JOULES
DMlESSOUTP ~1FIG
METH RRHO
V4(3)
V2(2)
137 O.
Vl(9)
N3(8)
2825.
1455.
2931.
V6(2)
1v7(2)
V8
1126.
1189.
1252.
V5
1279.
380.
Ivll(2) 541.
V12
V9(3)
VIO
733.
992.
V14(2)
IAIBIC
8590.
V13(1)
STAH·n 2.
990.
200.
INTROT 4.
NROTOR 1.
NEL
100.
IB
.48
V3
1254.
ROSYM
3.
NROTOR
1.
IB
2.1
ROSYM
1.
.48
NROTOR
2.
IB
ROSYM
3.
FINISHaaAll alphanumeric characters.

36

rJ9
-

80
4

1
1
2

3

Listed output. - Listed output for °51-1 11 , example 4, is as follows:
IIAME

I,mw TSANG, J , AM, CH. soc, , MAY 15',1985, P2872.

TERT-PErITYL RAD

C5Hll

HF293

DATE

l 5/87REFU

I·mw TSAllG, 'THE STABILITY OF ALKYl RADICAL S.' J. AM. CHEM. SOC.

RUN

MAY 15.1935. 1'1' 2872-2380.

TEMP

100,

DUTP

MFIG

11EiH

RRHD

1000,

1000.

6000.

JOUL lOS

DMlESS

MOL ECUL AR IH. =Exp1.

JOULES

326CC.

C'\L

71.14234

VI (9)

2931.

V2(Z)

2825,

V3(8)

1455.

V4( 3)

1370.

V5

1279.

V6(Zl

1252.

V7 (Z)

111\9.

VII

1126.

V9(3)

992.

Vl0

733.

Vll(2)

541.

V12

380.

V13Cl )

200.

VI4(2)

990.

STAnH

2.

IAIBIC

8590.

ImOTOR

1.

1254.

IB

.48

l.

IB

2.1

0.00
0.000

0.00
0.000

3585.371254.000

5.831830.00000

ItHROT 4,
l~ El

100.

ROSYM

5.

V3

ROSYM

l.

URDTOR

MItUMUM OF POTENTIAL

FUt~CTI ON

0.000 CMJOH -1)

IS

BARRI ER POTEln IAl COl/STANTS I N CAl/MOL
DR IN CM**(-l)
ROTATION COllSTMHS 114 CMHC-l)
ROSYM

3.

v= 0 FOR ROT OR

I-lROTOR

0.00000

0.00
0.000

o. 00
0.000

o. 00000

.48

IB

2.

0.00
0.000

2, US E elA 55 ICAl PART IT IOt~ FUlleTI 011 FOR FREE ROTOR (I ROTOR) .

F1.H SH
V=O FOR ROTOR

3. USE CLASSICAL PARTITION FUllCTIOIl FOR FREE ROTOR UROTOR).
ORIGItlALIlAR

TERT-PENTYL RAD

ORIGItJAl

TERT-PENTYl RAD

ASSIGNED H/R AT

o K

1558.273 K

CP/R(H-HO)/RT(H-H2nJlRT

SIR-(G-HOII"RT-{G-H29&)/RT

H/RT

-G/RT

6.60920
11.38955
30.82205
3'L265111
41.70940
42,67036
43.13628
43.39522

5.111211262
7.9241458
18.3487024
27.16111671
31.6782&37
34.3221130;;6.0433197
37.24&9471-17.81300B6
0.0000000
15.9861190
25.<;86375<'
30.8907559
33.7314672
35.5708030
36. !l551&32;;<'.7528978
44.0766593
69.2977936
93.90841411
110.3772014
122.5262009
132.1034232
139.9930650

21\.9<'00716
36.1525155
50.9490911
66.7402477
78.69a9178
83.2040879%.0601035
102.7441179

52.5659U6;;
4".0766593
53 ..5116746
67.'1215394
79.4864456
88.7947338
96 .5;'26202
103.1373813

21 .3955557
13.1506169
19.9069754
27 .9475036
32.1977030
3".7116813
37.5086593

n .3513420
30.9260424
49.39081&2
65.%11112
78.179493',
87.8145197
95.7<,1\(,(,39102.4&44057

S
J/MOl-K-(G-HO)
J/l40L-(G-H298 )J/l10L

H
J/MOL

J/MOl

288.953316
366.475&25
576.177198
730.802454
917.732y.5
1018.745323
1098.375233
1163.973739

24062.251
89621.043
42:;616.72&
1109324.913
1963028.816
2933495.084
3993463.456
5125601.972

43705.975
109264.767
4(<3260.452
1129468.637
1982672.540
2953138.807
4013107.180
5145245.696

17789.356
32600.000
165516.746
464736,270
803124.496
1154442.484
1511368,987
1871196.737

11105.975
76664.767
410660.452
1096&68.637
1950072.5(,02920538.807
3980507.130
5112645.696

S
CAL/MOL -K-(G-HO)
CAL/MOL-(G-H298 )CAVNOLH
CAl/MOL

CAl/MOL

69.061500
87.589824
137.709655
186.616265
219.343295
243.485976
262.517981
278.196400

5751.016
21419.943
101246.828
265254,520
469175. L<,7701122.152
954460.673
1225048.273

10445.'179
26114.906
105941.791
269949.483
473870.110
70531L115
959155.636
1229743.235

4251.758
7791.587
39559.452
111074.634
191951.361
275918.376
361225. &57
447226.754

2654.392
18323.319
98150.204
262157.896
46607S.523
698025.528
951364.0,,91221951.6"8

100.CO
298.151000.00
2000.00
3000.00
4000.00
5000.00
6000.00

OrIGINAL.;~ S lOllED

36.354,)74?>

TERT-PEtHYl RAD
H AT

K =

12956.276 J/MOl E

T
DEG-J(.

CP
J/MOl-K

H-HO
J/MOl

100.00298.151000.00
2000.00
3000.00
4000.00
5000.00
6000.00

54.95223
98.85578
256,27026
326.47595
346.79319
354.78317
358.65700
360.30997

4833.080
19643.724
152560,470
451779.994
790168.220
l!41486.208
1498412.710
1858240.461

H-H298J/MOl-14810.644
0.000132916.746
432156.270
770524.496
1121842.484
1478768.987
1838596.737

ORIGINAL

TERT-PWTYl RAD

ASSIGtlED H AT

K =3096.624 CAl/MOL E

T
DEG-K

CP
CAl/MOl-K

H-HO
CAl/MOt

H-H298CAl/MOL

100.00298.151000.00
2000.00
3000.00'\000.00
5000.00
6000.00

13.13390
23.62710
61.25006
78.02963
82.88556
84.79521
85.7210886.23565

1155.154
4694.963
36462.821
107978.010
188854.737
272821.751-3539.829
0.000
31767.865
103283.047
18<\159.774
268126.789~~~434 .270
439435.167

ORIGWAl.J-'jnl~IJ.233

444130.129

Il"R

-G

-G

TERT-1'EIHYl RAD

37

Example 5 (H20(g) by Method NRRA02 with Intermediate
Output)!'roblem. ~Calculate thermodynamic functions for H 20(g)usmg method NRRA02. List some intermediate results inaddition to final tables.
This is the only one of the eight examples discussed which
does not start with a NAME record. This optional record wasintentionally omitted to show that, as a result, the output tables
are not identified by species name on the bottom of the listings.
Therefore, while the NAME record is optional, it is generally
useful to include it.
A REFNCE record was used to indicate the example number.
This is followed by the formula record. It gives the formulawith all the stoichiometric coefficients and an assigned enthalpy(ASINDH) of -57103.5 cal/mol (CAL) at T= 0 K. The TEMP
record indicates a temperature schedule of only one value,
5000 K. The OUTP record calls for intermediate output(INTERM) and a many-figured table (MFIG) in energy unitsof joules (JOULES).

. The NRRAOl and NRRA02 methods are the only methods
10 p ~C91 that can accommodate the large variety of spectro-

SCOpIC constants available for H2 0(g). In addition to thefundamental frequencies IIi and rotational constants A0, B0,
and Co, other constants included are the anharmonicities x·and Yijk; vibration-rotation interaction constants a 1 (ALFAAi)'J
B
•
C
..
'
,
ai (ALFABl), and ai (ALFACI) for 1 = 1, 2 and 3; rotationstretching constant p; and symmetry number (SYMNO). These
spectroscopic constants appear on the nine data records
follOWing the METHOD NRRA02 record. The FINISH
record is last, as usual.
The intermediate output follows the input record images foreach electronic state plus one record. For this case there is
only the ground state and the intermediate output follows the
FINISH record. This output is discussed in section Intermediate
data with INTERM label in appendix C. The last item listed
is the many-figured table with properties at 5000 K and energy
units in joules.

Input. - The input data set for H2 0, example 5, is as follows:

Rec. label
ID
1
1-6
7-12

Numerical
value 1
13-24

a REFNCE

H201
TEMP If
5000.
OUTP INTERfi
METHO[DATA WI
3656.65
DATA )(12-15.14DATA Y233 -.81
DATA YI11 .47
DATA 1Y123 -1.72
DATA ~O
27.848DATA ~LFAA1 .750
DATA Al FAB~ - .160
DATA IALFAC~ .1445
FINISHa All alphanumenc characters.

38

Label
2
25-30

Numerical
value 2
31-42

Label
.3
43-48

ASINDH -57103.5

tAL

MFIG
NRRA02
V2
1594.78f-44.62
X33
Y333 ,....45
Yl12 1-.10
Y133 1.17
BO
14.5064
ALFAA2 -2.941
AlFAB3 .078.0000213RHOJOULES
V3

~1.3

X23
Y113

Numerical
value 349-60

Numerical
value 467-78

13755.79
f-165.48
1-19.99

O.

D<11

~22

f-45.18
f-17.04

Y122

1-0.1

rt223

79

-

80

Exp1. 5

T

.68
-.60
CO
19.28285
ALFAA3 1.253
lAlFACl .2018
STATvH 1.

rY222

label
4
161 66~.55

IsYMNO 12.
~LFABI .238
~LFAC2 .1392

Listed output. - The listed output for H20, example 5, is as follows:
Expl.

REFNCE
H201
TEMP

T

OUTP

IrHERM

O.

ASItlDH -57103.5

CAL

MFIG

JOULES

5000.

METHOD

NRRA02

MOLECULAR ~lT . =18.01528

DATA

VI

3656.65

V2

1594.78V33755.79X11-45.18DATA

X12-15.14X33-44.62

XU-165.48X22-17.04

DATA

Y233

-.81

Y333

-.45

X23

-19.99

DATA

Ylll

.47

Y1l2

-.10

Y113

.68

Yl22

-0.1

DATA

Yl23

-1.72

YB3

1.17

Y222

-.60

Y223

1.55

DATA

11.0

27.848BO

14.5064CO

9.28285

SYMNO 2.

DATA

ALFAA1 .750

AlFAA2 -2.941

ALFAA3 1.253

ALFAB1 .238

DATA

ALFAB2 -.160

ALFAB3 .078

ALFACI .2018

ALFAC2 .1392

DATA

ALfAC3 .1445

RHO

STAHIT 1-.0000213

FINISHAI = 0.0325387

ALPHA A = 0.7500000

ALPHA= 0.2380000

ALPHA C

0.2018000=1

AI =-0.0508216

ALPHA A =-2.9410000

ALPHA B ;;-0.1600000

ALPHA C

0.1392000

=2

ALPHA

0.0779999

ALPHA C

0.1445000=319.370178

THETA( 3)AI ;; 0.0329687
THETM1) =11.0= 27.847992
IAIBIC=
Y(l,l,1)
YO,3,3)

ALPHA A = 1.2529993
4.448227

THETA(2)

BO= 14.506399

CO=

0.000000

9.282849

0.005849E-117 (G~CM*~2)**3
0.470
Y(1,I,2)-0.100Y(1,1,3)
1.170
Y(2.2,2) = -0.600
Y(2.2,'))

Ye1,2,2)
Y(2,3,3)

0.680
1.550

-0.100-0.810Y(L2.3)Ye3,3.3)-1.720-0.450X(I, J)-42.7750-16.4000-162.6400-16.4000 -162.6400-19.0150 -19.3700-19.3700 -46.4650

V( 1) =3656.6499(1)

G

0.000

V( 2) =1594.7798(1)

G

0.000

V( 3) =3755.7898(1)

G

0.000

= 5000.000uU

o.1052215e+01

R0.3491637e+00

0.4589038e+OO

R

0.63197610+00

o..B93437e+00

0.1080742e+01

COiHRIBUTION
ELEC
H.O.
R.R.
RHO
THTA

o.1536484e+01
0.2717215e+Ol
S

0.15U646e+Ol0.5000e+00
0.631ge+01
0.5930e+04
o .1112e+01
0.1001e+01-0.69314718
1.84362507
8.68771458
0.10649991
0.00088938

IN Q

H-HO/RT
0.00000000
1.90765095
1.50000000
0.10649991-0.00089040

0.00000000
2.80335a08
1.50000000
0.21299932
0.00000076

FIRST ORDER CORRECTIOUS
ALFA
0.9546e+00
XIJ
0.1071e+01
YIJK
0.1004e+01
AXIJ
0.9930e+00-0.04642935
0.06857038
0.00428620-0.00702811-0.04005833
0.12646741
0.01142810-0.01502087-0.06193434
0.30334258
0.03873271-0.04562024

SECOND ORDER CORRECTIONS
XIJ20.1010e+01
XY
0.1003e+01AX20.9977e+OO

0.009750840.00264854-0.00226233

0.02659326
0.00939406-0.00755092

0.09222138
0.04116780-0.03202931

Q

CP/R

ORIGINALASSIGNED H AT

o K = -238921.044 J/MOLE

DEG-K

CP
J/MOL-K

H-HO
J/MOL

5000.00

61.13024

254611.490

T

ORIGltML

H-H298J/MOL

J/MOL-KS-(G-HO)
Jlt·10L

316.597784

1328377.430-(G-H298J
J/MOL

H

-0

JlMOl

J/~lOl15690.446

1567298.474

BAR

39

Example 6 (Mg(cr,f) by Methods READIN and COEF withEFTAPE and LSQS Options)
Problem.-Process data for an assigned reference element
to illustrate preparation of EF data. Select an element withmore than one condensed phase in temperature range ofinterest. The solid phase is in the crystalline form and this isindicated on the NAME record as Mg(cr). Also obtain leastsquares coefficients for each phase.
Magnesium in the solid and liquid phases was chosen to be
the assigned reference element. Referring to the input data set,
there is a NAME record for each phase. The information onthese records will be included with the first record of the leastsquares coefficients output on I/O units 6 and 10. See thesection NAME record in appendix B and table VIII. The
formula record contains the atomic symbol in the required
capital letters, the integer 1 and the letter S in parentheses.
The parentheses are a requirement for condensed species. As
was noted in the section Formula record, the letter S must
be used on the formula record of a reference element to specify
the solid state. However, a more descriptive letter (or letters)such as cr may be used in the NAME record. Also included
on the formula record is the assigned enthalpy at 298.15 K(HF298) which is 0 since this is a reference element. The
CODA89 label on the DATE record was chosen to indicate
a 1989 CODATA reference. The four REFN records give thefull reference and some comments on the data.
The two OUTP records list many options. The EFTAPE
label calls for the enthalpy and Gibbs energy data (EF data)
to be merged in an unformatted form with the data on I/O unit
13 for use in calculating ~fiT and 10gIOK values for future
calculations. The data are also listed in formatted form on I/Ounits 11 and 6 (see the second to last table for this example
printed in the output below). More discussion is given in thesection Saved Output in appendix C. The LSQS label calls
for least-squares coefficients. The MFIG label calls for manyfigured tables with joules as the energy unit (JOULES). The
CTAB label calls for a table to be listed for data calculated
from the least-squares coefficients. The temperature schedule
for the coefficients table is given on the CTEM recordnamely, from 200 to 5000 K in 200 K intervals. Roomtemperature (298.15 K) and phase transition temperatures arealways inserted by the PAC91 program in these schedules.
Data for the solid phase (Mg(s» are processed by method
READIN , whereas data for the liquid phase are processed bymethod COEF. The 18 data records (indicated by record ID
MG- SOL) give data for the solid phase from 25 to 923 K.
The melting point is given on the METHOD record as 923 ..
Also given on this record is the H298HO value of 4998 .. The

40

unit of llmol is specified by the label JOULES. Note that someof the enthalpy values are for H-HO (Hy. - H3) whereas
others are for H-H2 (Hy. - H~98.15)' This was done just to
demonstrate some of the options available.
The heat of melting is given on the second METHOD record(method COEF for the liquid phase) as DELTAH = 8477.
J/mol. The temperature schedule for thermodynamic functions
calculated from read-in coefficients is given on the TEMP
record preceding the COEF method record. Following thisMETHOD record are two data records for the liquid phase(records MG-LIQ). The first MG-LIQ record contains one
coefficient (C1 = 34.309), one exponent (E1 = 0.), and thetemperature range for which these coefficients are valid (923
to 6000 K). The PAC91 program automatically prepares andlists the read-in coefficients in the same format as the leastsquares coefficients (see table VIII). The TCOEF label (onthe second MG-LIQ data record for the liquid phase) has notemperature information following it. Therefore, the temperature
range for the liquid phase on the coefficient output justdiscussed is taken to be the same as the input temperature range
for the liquid.
As the listed output below shows, the least-squares
calculations for the crystalline phase were done by PAC91 after
reading the METHOD COEF record and before processing
the liquid data records. This is evidenced by the intermediate
output for the least-squares fit for the crystalline phase. Since
no LSTSQS records were included in the input, the default
parameters are used. The temperature interval starts at 200
K and ends at the 923 K transition which comes ahead of the1000 K midpoint. The functions are fit simultaneously andconstrained to fit at 298.15 K. The equation is the default
seven-coefficient function for C;~ (see eq. (17». The record
images described in table VIII are printed here (1/0 unit 6)
and on I/O unit 10.
This output is followed by the input data images for the liquid(record ID MG-LIQ). The TCOEF label indicates that thecoefficients on the data records are to be included with theleast-squares coefficients. In this case there is one coefficientfor the constant
The two required integration constantsfor enthalpy and entropy are calculated by PAC91 to fit theproperties calculated from the least-squares coef~cients forthe solid phase at 923 K plus the heat of meltmg. These
coefficients are also written on I/O unit 6 following the FINISH
record as well as on I/O unit 10. No least-squares calculations
were made for the liquid since the TCOEF option was used.
The final three tables are in order: the many-figured original
table in SI units, the dimensionless EF data, and the manyfigured coefficient table in SI units.

C;.

Input. - The input data set for Mg(cr ,@), example 6, is as follows:

Rec. Label
ID
1
1-6
7-12
a NAMEa NA~'Eaaaa

Numerical
value I
13-24

~g(cr)

IMg(l)

Label
2
25-30

Numerical
value 2
31-42

Label
3
143-48

Numerical
value 3
49-60

Label
4
61-66

Numerical
value 4
67-78

Magnes ium Hexagona 1 Crys ~al. CODATA 1989, 1P244.
Magne~ ium Liquid.
CODA ~A 1989, p2 G 4.
HF298
O.

179

-

180

Expl. 6

MGleS)DATE ICODA89
REFN teox,J. D. ; Wagman, D. D.; ~nd Medvede\l , V.A. : CODATA Key Values for
REFN
Ther ~odynamics. Hemis phere Publ. Corp. , 1989.
REFN CODATt $ value at 75 K '" as obvi ousl_')I wrong and correc-f ed by interpolatia n.
REFN Hand S for crystc 1 at 923 adjusted Iso rou ~ded liq val ues rna tch CODATA.
OUTP EFTAPE
MFIGJOULESLSQS
OUTP CTAB
CTEM T
200.
200.
I
rrJOULES 6000.
~'ETHOD READIti
H298HO 4998.
MEL TPT 923.
~'G-SOLT
25.
CP
0.781
S
.246
H-HO
5.
~'G-SOlT
50.
CP
5.740
S
2.104
H-HO
79.
MG-SOLT75.
11.542
CP
5
5.578
H-HO
297.
~1G-SOL T
100.
CP15.762
S
9.505
H-H2 -4356.
t1G-SOL T
150.
20.474CPS
16.910
H-HO
1563.
MG-SOLT200.
CP22.724S
23.143
H-H2 -2349.
NG-SOLT250.
CP24.018528.364
H-HO
3820.
MG-SOLT
298.15CP
24.869S
32.671
H-H2
0000.
MG-SOLT300.
CP24.897
S
32.825
H-112
46.
MG-SOLT
350.
25.568CPS
36.715
H-HO
6306.
MG-SOLT400.
CP26.144
S
40.167
H-H2
2601.
~'G-SOl T
450.
CP26.668S
43.277
H-HO
8920.
MG-SOLT
SOD.
CP
27.171
S
46.113
H-H25268.
t'1G-SOl T
600.
CP28.184
S
51.156H-H28035.
r'1G-SO LT
700.
CP29.279S
55.581
H-H2 10907.
MG-SOLT800.
CP30.507
S
59.569
H-H2 13895.
MG-SOLT900.
CP31.895
S
63.241
H-H2 17014.
MG-SOlT
923.
CP
32.238S
64.0498
H-H2 17751.2
TE~1P
T
923.
T
1000.
I
100.
6000.
T
t'1ETHOI: COEF
DElTAt' 8477.
JOUL ES~1G-l I QT
923.
6000.
T
el
34.309El
O.
MG-LI~ TCOEF
FINISI':a All alphanumeric characters.

41

Listed output. - Listed output for Mg(cr,Q), example 6, IS as follows:
NAME

Mg(cr)

Magnesium Hexagonal Crystal. CODAIA 1989. p244.

NAME

Mg< 1)

11agnesium Liquid.

MGl (5)

o.

HF293

DIITE

CODA89REfN

Cox.J.D.; Hagman. D.O.; and Medvedev,V.A.: CODATA Key Values for

REFU·;hermodynamics.

Expl. 6

CODATA 1989. p244.

Hemisphere Publ. Corp .• 1989.

REFU

CODATA 5 value at 75 K was obviously wrong and corrected by interpolation.

REFU

Hand 5 for crystal at 923 adjusted so rounded liq values match CODATA.

OUTPEFT APE

OUTP

CTAB

CTEM

MFIG

ZOO.

I1ETHODREAD I N

LSQS

JOULES

200.

T

H298HO

4993.

JOULES

6000.
MEL TPT

923.

MG-SOL I

25.

CP

0.781

. 246

H-HO

5.

MG-SOL T

50.

CP

5.740

2.104

H-HO

79.

MG-SOl T

75.

CP

11. 542

5.5n

H-HO

297.

MG-Sen T

100.

CP

15.762

9.505

H-H2

-4356.

~G-SOl T

}.50.

CP

20. "74

16.910

H-HO

1563.

t1G-SOL T

200.

CP

22.72423.143H-H2-2349.

MG-SOL T

250.

CP24.01828.364

H-HO

3820.

MO-SOl T

298.15CP

24.86932.671

H-H2

0000.

MG-SOl T

300.

CP

24.89732.825

H-H2

46.

MO-SOl I

350.

CP

25.56836.715

H-HO

6306.

'''MG-SOl T

400.

CP

';>(,

144

40.167

H-H2

2601.

f1G-SOl T

450,

CP

26.66843.277

H-HO

8920.

MG-SOL T

500.

CP27.17146.113

H-H2

5268.

MG-SOL T

600.

CP28.18451.156

H-H2

8035.

Me-SOL T

700.

CP29.27955.581H-H210907.

r'IG-SOL T

800.

CP

30.50759.569H-H213895.

MG -SOL T

900.

CP

31.8956.3.241

H-HZ

17014.

r'W-SOL T

923.

CP

32.23864.0498

H-H2

177 51. Z

TEtW

'lB.

1000.

100.

METHODCOEF

DELTAH

8477.

6000.

JOULESLEAST SQUAREST

CP/R INPUT
INPUT-CALC
2.7330534
0.0000564
2.l\886l\5G-0.0002834
2.9910362
0.0000000
2.9944038
0.0000012
3.0751060-0.0004514
3.1443825-0.0000330
3.2074049
0.0001651
3.2679015
0.0002393
5.3897367
0.0000399
3.5214342

CP/R CALC
HH/RT INPUT
HH/RT CALC$/R Hl?Ui
S/R CALC' .
-GH/lH 11l?\JT-GH/RT CALCINPUT-CALC
FRACTIOIl
FRACTI ON
1 tlPUT-CAf.C
FRACTI 011
ItWUT-CALC
FRACT 1011
2.7329970
1.5929933
1.5928976
2.7834473
2,7834025
1.1904490
1.1')05050
0.0000206
0.0001007
0.0000632
0.0000447
0.0000161-0.0000560-0.0000470
25G. aD
2. BB8'>734
1.B377511
1.8377226
3.4113856
3.4113582
1. 5736345
I 5736357-0.0000998
0.0000286
0.0000155
0.0000274
0.0000080-0.0000011-0.0000007
298.15
7. '19111362
2.0161590
2.0161590
3.92')3957
3,9293957
1.9132367
1.9132367
0.0000000
u. uCOOOO\}
0.0000000
O.ooooooa
o.ooaoooo
O.OODOOOO
0.0000000
300.002.9944025
2.0221677
2.0221811
3.9(,79176
3.9479080
1.9257499
1.925726&
0.0000004-0.0000135-0.0000067
0.0000096
0.0000024
0.0000231
0.0000120
350.003.0755575
2.1669519
2.1670665
4.415774"
4.4158074
2.241>8225
2.2487409-0.00014(,8-0.0001l46-0.0000529-0.0000330-0.0000075
0.0000816
0.UOO0363
400.003.}(,4(d552.2848610
2.2850201
4.8309522
4.3310306
2.5460911
2.5460605-0.0000105-0.0001590-0.0000696-0.0001285-0.0000266
0.000012!)
0.0000306
450.003.2072398
2.3840511'>
2.3840347
5.204')970
5.205104'1
2.8209453
2.8210701
0.0000515
0.0000170
0.0000071-0.0001078-0.0000207-0.0001249-0.0000443
500.003.2676623
2.4694179
2.4693854
5.5460875
5.5461530
3.0766696
3.0767721
0.0000732
0.0000325
0.0000132-0.0000705-0.0000127-0.0001031-0.0000335
600.003.3396963
2.61Z5011
2.6125225
6.1526175
6.15262('83.5401164
3.5401023
0.0000118-0.0000213-0. 0000032-0.0000073-0.0000012
O. 0000141
0.0000040
700.003.5215153
2.7327442
2.7328045
6.6848197
6.6848772
3.9520755
3.9520727-o.ooooall -0.0000230-0.0000604-0.0000221-0.00Q0576-0.0000086
0.0000028
0.0000007
800.003.6691278
3.6690433
2.8403658
2.8404281
7.1644631
7.1645425
4.3240973
4.3241144
0.0000845-0.0000623
0.0000230-0.0000219-0.0000794-0.0000111-0.0000171-Q.0000040
900.003.8360649
3.8359739
2.9415778
2.9415776
7.6061007
7.6061272
4.6645229
4.6645(1960.0000910
0.0000237
0.0000002
0.0000001-0.0000265-0.0000035-0.0000267-0.0000057
923.003.8773181
3.8773931
2.9643383
2.9643784
7.7033764
7.7034439
4.7390381
4.7390654-0.0000750-0. 0000193-0.0000401-0.0000135-0.0000675-0.0000088-0.0000274-0.0000053
MAX REL ERR CP/R
0.000147
TEMP
350.
AVER REL ERR CP/R
0.000039
REL lST SQ ERR CP/R
O. 000057
MAX REL ERR HH/RT
0.000070
TEMP
400.
AVER REL ERR HH/RT
0.000023
REL LST SO ERR HH/RT
0.000032
l'IAX REL ERR S/R
0.000027
TENP
400.
AVER REL ERR S/R
R[l LST SQ ERR S/R
0.000010
0.000012!lAX REL ERR GH/RT
0.000047
TENP
200.
AVER REl ERR GH/RT
0.000016
REl lST SO ERR GH/RT
0.000023
r1AX ERR CP/R
0.000451
TEI1P. =350.
AVER ERR CP/R
0.000124
LST SQ ERR CP/R
0.000177
r1AX ERR HH/RT
0.000159
TEMP =
400.
AVER ERR HH/RT
o. 000050
l5T SQ ERR HH/RT
0.000068~'AX ERR S/R
0.000128
TEMP =
400.
AVER ERR S/R
0.000051
LST SQ ERR S/R
0.000063
MAx ERR GH/RT
0.000125
T El1P =450.
AVER ERR GH/RT
0.000039
LST
SQ
ERR
GH/RT
0.000055
CP/R-7.3537794e+03TIOl-2.0 -6. 9826242e+Ol TH-l. a
3.2083651e+OOTlOE 0.0
2.2508743e-04TJEI( 1.0
2.0515951 -07TlOl 2.0
5.6911573e-l0Tlnl 3.0-1. 057 323ge-13TH ".0(H-HO )/R COUSTAIH = O. 48294728etOl, H/R COIlSTAIlT =-0.59628833e+03. SIR COUSTANT =-0.1470711\3,,+02
200.00Mg( cr)42

Mg( 1)

THERMODYNAMIC DATA COEFFICIENTS, RECORD IMAGES Mg(cr)Magnesium Hexagonal Crystal. CODATA 1989. p244.
Expl. 6
1 CODA89 MG 1.00
0.00
0.00
0.00
0.00 124.30500
0.000
200.000
923.000 7 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0
4998.000-7.35377939d+03 -6.982624I6d+OI 3.20836507d+00 Z.2S087426d-04 2.05159514d-07
5.69115784d-l0 -1.05732390d-13 O.OOOOOOOOd+OO -5.96288332d+02 -1.47071833d+Ol
MG-LIQT

923.

T

el

6000.

34.309Elo.

MG-lI~1COEF

FIt/ISH
COEFFICIENTS ADJUSTED TO FIT UPPER PHASE AT

923.00

THERMODYNAMIC DATA COEFFICIENTS, RECORD IMAGES Mg(l)Magnesium Liquid.
CODATA 1989. p244.
1 CODA89 MG 1.00
0.00
0.00
0.00
0.00 224.30500
0.000
923.000 6000.000 1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
4998.000
4.12640071d+00 O.OOOOOOOOd+OO O.OOOOOOOOd+OO O.OOOOOOOOd+OO O.OOOOOOOOd+OO
O.OOOOOOOOd+OO O.OOOOOOOOd+OO O.OOOOOOOOd+OO -6.54121412d+02 -1.93654933d+Ol

ORIGINAL

Mg(cr)ASSIGlIED H AT

K=CP

Mg( 1)-4998.000 J/MOLE

T
DEG-K

J/MOL-K

H-HO
J/MOL

25.00
50.00
75.00
100.00150.00200.00250.00298.15300.00350.00400.00450.00500.00600.00700.00800.009GO.OU
923.00923.001000.00
1100.00
1200.00
1300.00
1400.00
1500.00
1600.00
1700.00
1800.00
1900.00
2000.00
2100.00
2200.00
2300.00
2400.00
2500.00
2600.00
2700.00
2800.00
2900.00
3000.00
3100.00
3200.00
3300.00
3401.'.00
3500.00
3600.00
3700.00
3800.00
3900.00
4000.00
4100.00
4200.00
4300.00
4400.00
4500.00
46GO.00
4700.00
4800.00
4900.00
5000.00
5100.00
5200.00
5300.00
5400.00
5500.00
5600.00
5700.00
5800.00
5900.00
6000.00

0.78100
5.74000
11.54200
15.76200
20.47400
22.72400
24.01800
24.86900
24.89700
25.56800
26.14400
26.66800
27.1710023.18400
29.27900
30.50700:)1 .8<:JSOO
32.23800
34.30900
34.30900
34.30900
34.30900
3ft. 30900
54.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.309(J034.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900

5.000
79.000297.000
642.000
1563.000
2649.000
3820.000
4998.000
5044.000
6306.000
7599.000
8920.000
10266.000
13033.000
15905.000
18893.000
22012.000
22749.200
31226.200
33867.993
37298.893
40729.793
44160.693
47591.593
51022.493
54453.393
57884.293
61315.193
64746.093
68176.993
71607.893
75038.793
78469.693
81900.593
85331.493
88762.393
92193.293
95624.193
99055.093
102485.993
105916.893
109347.793
11277IL693
116209.593
119640.493
123071.393
126502.293
129933.193
133364.093
136794.993
140225.893
143656.793
147087.693
150518.593
153949.493
157330.393
160811.293
164242.193
167673.093
171105.993
174534.893
177965.793
181396 .6H
184827.593
188258.493
191689.393
195120.293
198551.193
201982.093
205412.993

ORIGINAL

H-H298S

J/~tOL

J/MOL-K-4993.000-4919.000-4701.000-4356.000-3435.000-2349.000-Il78.000
0.000
46.0001308.000
2601.000
3922.000
5268.000
8035.000
10907.000
13895.000
17014.000
17751.200
26228.200
28869.993
32300.893
35751. 793
39162.693
42593.593
46024.493
49455.393
52386.293
56.H7.193
5974&.093
63178.993
66609.893
70040.793
73471.693
76902.593
80333.493
83764.393
87195.293
90626.193
94057.093
97487.993
100918.893
104549.793
107780.6':13111211.593
114642.493
118073.393
li:l504.293
124935.193
128366.093
131796.995
135227.893
138658.793
142089.693
145520.593
148951.493
152382.393
155813.293
159244.193
162675.093
166105.993
169536.893
172967.793
176398.693
179829.593
183260.493
186691.393
190122.293
193553.193
196984.093
200414.993

0.246000
2.104000
5 578000
9.505000
16.910000
23.143000
28.36(,000
32.671000
32.825000
36.715000
40.167000
43.277 000
46.113000
51.156000
55.581000
59.569000
6:'.241000
64.049800
73.233982
75.983026
79.253023
82.238297
84.934482
87.527052
39.894129
92.108381
94.188351
96.149399
n.01l4391
99.764213
101.438155
103.034210
104.559306
106.019483
107.420045
108.765669
110.060502
111.308239
Il2.512187
Il3.675315
114.800302
115.889568
116.945312
117.969538
118.964071
119.930586
120.870617
121.785578
122.676771
123.545400
124.392579
125.219341
126.026649
126.815397
127.586418
128.340492
129.078349
129.800670
130.508097
131.201232
131.880640
132.546855
133.200380
133.841688
134.471229
135.089426
135.6%680
136.293374
136.879867
137.456502

MgCl}-(O-HO)
J/MOL-(G-H298)
J/MOL

J/MOL

J/MOL

1.150
26.200121.350
308.500
973.500
1979.600
3271.000
4742.859
4803.500
6544.250
8467.800
10554.650
12790.500
17660.600
23001.700
28762.200
34904.90tl
36368.765
36368.765
42Il5.033
49879.433
57956.163
66519.134
7(f946.280
83818.700
92920.017
102235.904
111753.725
121462.251
1.31351.433
141412.232
151636.469
162016.710
172546.167
183218.620
194028.345
204970.061
216038.876
227230.250
238539.953
249964.042
261493.823
273140.838
284886.835
296733.756
308678.716
320718.991
332852.004
345075.314
357386.606
369783.679
382264.441
394826.899
407469.152
420189.387
432985.871
445856.945
458801.023
471816.583
484902.166
498056.372
511277 .854
524565.320
537917.523
551333.265
564811.391
578350.786
591950.375
605609.120
619326.020

4999.150
5024.200
5119.350
5306.500
5971.500
6977 .600
8269.000
9740.859
9801.500
11542.250
13465.800
15552.650
17788.500
22658.600
27999.700
33760. ZOO
39'HIZ.900
41366.765
41366.765
47113.033
54877 .433
62954.163
71317.134
79944.280
88816.700
97918.017
107235.904
116751.725
126460.251
136349.433
146410.252
156634.469
167014.710
177544.167
188216.620
199026.345
209968.061
221036.876
232228.250
243537.953
254962.042
266496.823
278138.838
289884.835
301731.756
313676.716
325716.991
337850.00(,
350073.314
362384.606
374781.679
387262.441
399a24.899
412467.152
425187.387
437983.871
450354.945
463799.023
476814.583(f89900 .166
503054.372516275.854
529563.320
542915.523
556351.265
569809.391
583348.78(,596948.375
610607.120
624324.020-4995.000-4919.000-4701.000-4356.000-3435.000-2349.000-1178.000
0.000
46.0001308.000
2601. 000
3922.000
5268.000
8035.000
10907.000
13895.000
17014.000
17751.200
26228.200
23369.993
32300.8'J355731.793
39162.693
42593.593
46024.493
49455.393
52836.293
56317.193
59748.093
65178.993
66609.893
70040.793
73471.693
76902.593
80333 J.93
83764.393
87195.293
90626.193
94057.093
97487.993
100918.393
1043(,9.793
107780.693
1]1211.5<)3
114642.493
113073.395
121504.293
124935.1Q3
128366.093
131796.993
135227.893
138658.793
142089.693
145520.593
148951. 493
152332.393
155813.293
159244.1<)3
162675.093
166105.993
16<)536.893
172967.793
176398.693
179829.5')3
183260.4')3
1866Q1.3Q3
190122.2Q3
193553.193
196984.093
200414.993

4999.150
5024.200
5119.350
5306.SoJO
5971.500
6977.600
8269.000
9740.859
9801.500
11542.2S013465.800
15552.650
17788.500
22658.600
27999.7JO
33760.200
H902.910
41366.765
41366.7·) 5
47113.033
54877.433
62')54.163
71517.134
79944.230
88816.7ilO
97918.017
107233.904
116751. 725
126460.251
136349.433
146410.232
156634.469
167014.7LO
177544.167
188216.620
199026.3(,5209968.061
221036.876
232228.2';0243537.95.'i
254962.042
266496.823
278138.853
28938(•. 8.';5301731.756
313676.716
525716.991
337850.004
350073.314
362384.606
374781.67')587262.4'd399324.89')412467.152
425187.337
437983.871
450854.945
4637')9.023
476814.533
489900.166
503054.372
516275.854
529503.320
542915.523
55633L ,265
56<JB0,).391
583348,7%
5%9(18.375
610607.120
624324.020

H

-G

EFD4

MGlS
CODA89HO/R
25.00
0.024054
75.00
0.476276
150.001. 253251
250.001.837751
3lJO.OO
2.022168(100.00
2.284861
500.002.469418
700.002.732744
900.UG
2.941578
923.004.068935
1100.00
4.078182
1300.00
4.085600
1500.00
4.091040
1700.00
4.095200
1900.00
4.098485
2100.00
4.101143
23IHl.OO
4.10B40
2500.00
4.105184
2700.00
4.106756
2900.00
4.108111:5100.00
4.109291
3300.00
4.110328
3500.00
4.111246
3700.00
4.112065
3900.00
4.112801
4100.00
4.113464
4300.00
4.114066
4500.00
4.114614
4700.00
4.115115
4900.00
4.115576
SIOO.OO
4.116001
5300.00
4.116393
5500.00
4.116757
5100.00
4.117095
5900.00
4.117411-601.1178HP
0.005552
0.19(.600
0.780563
1.573635
1.925750
2.5't6091
3.076670
3.952076
4.664523
4.739038
5.453712
6.135625
6.720671
7.232990
7.688667
8.098993
8.472183
8.814404
9.130404
9. (.23918'L 697933

9.954880

10.196761
10.425246
10.641740
10.847439]1.043370
11.230418
11.409353
11.580851
11.745504
11.903839
12.056322
12.203371
12.345359

ORIGINAL

COE:FFICIEIITSASSIGIIED H AT

Mg(cr)

Mg(c,.)o K=

925.DOOONT
0.190029
0.772144
1.592998
2.016159
2.166952
2.3B(,052
2.612501
2.8',0366'2.964338
4.073360
4.082200
4.088515(,.093250
4.096934
4.099880
4.102291
4.10(.300
4.106000
4.107458
4.108720
4.109826
4.110801
4.111667
4.112('43
4.113141
4.113772
4.114346
4.114870
4.115351
4.115793
4.1162014.116578
4.116929
4.117256
4.117561

70.0000
0.063022
0.371038
1.190449
1.913237
2.248822
2.8209(,53.5(.0116
4.324097
4.739038
5.065245
5.808737
6 .... 38510
6.984778
7.467115
7.898928
8.289805
8.61\6840
8.975428
9.279770
9.563199'J.82SI\06

10.077593
10.312585
10.5.H912
10.745871
10.946567
11.137953
11.320855
11.495993
1l.663999
11.825431
11.980785
12.130502
12.274976
12.414562

Mg(11

Hg(l)

-4998.000 J/MOlE

CP

T
DEG-K

J/HOl-K

H-HO
J/MOl

200.00298 .15400.00600.00800.00923.00923.001000.00
1200.00
1400.00
1600.00
1800.00
2000.00
2200.00
2400.00
2600.00
2800.00
3000.00
3200.00
3400.00
3600.00
3800.00
4000.00
4200.00(,(,00.00
4600.00
4800.00
5000.00
5200.00
5(,00.00
5600.00
58(;0.00
6000.00

22.72353
24.86900
26.14427
28.18367
30.50630
32.2?>862
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
3('.30900
34.30900
34.30900
34.30900
3'1.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900
34.30900

2648.833
1\998.000
7599.529
13033.106
18893.414
22749.508
31226.508
33868.301
40730.101
47591.901
54453.701
61315.501
68177.301
75039.101
81900.901
88762.701
95621\.501
102486.301
109348.101
116209.901
123011.701
129933.501
136795.301
1G3657.101
150518.901
157380.701
164242.501
171104.301
177966.101
184827.901
191689.701
198551.501
205413.301

COEFFlC I EilTS

44

50.00
100.00200.00298.15350.00450.00600.00800.00923.001000.00
1200.00
1(,00.00
1600.00
1800.00
2000.00
2200.00
2400.00
2600.00
2800.00
3000.00
3200.00
3400.00
3600.00
3800.00
4000.00
4200.00
4400.00
4600.00
4800.00
5000.00
5200.00
5400.00
5600.00
5800.00
6000.00

H-HZ98J/HOl-2349.167
0.000
2601.529
8035.10613895.414
177 51.508
26228.508
28870.301
3S7?i2.101
42593.901
49455.701
56317.501
63179.301
70041.101
76902.901
83764.701
90626.501
97488.301
10'1350.101
111211.901
118073.701
12(,935.501
131797.301
138659.101
145520.901
152382.701
159244.501
166106.301
172968.101
179829.901
186691.701
193553.501
200415.301

Mg{cr)

5
J/MOl-K-(G-HO)

23 142628
32.671 000
40.168068
51.156060
59.569660
64.050361
73.234543
75.983588
82.238858
87.527614
92.108942
96.149960
99.76(,774103.034771
106.020045
108.766230
111.308800
113.675877
115.890129
117.970099
119.931147
121.786139
123.545961
125.219903
126.815958
128.341053
129.801231
131. 201793
132.547(j17133.842249
135.089987
136.293935
137.451063

1979.693
4742.859
8461.698
17660.530
28762.314
36368.975

MQ(I)J/~IOL3~368.975

42115.287
57956.529
74946.758
92920.607
111754.',28131352.248
151637.396
172547.206
194029.497
216040.140
238541.329
261500.312
284888.436
308680.t128
332853.829
357388.543
382266.491
407471.314
432988.1'.5458805.409
484904.665
511280.465
537920.246
564814.226
591953.322
619329.079-(G-H29&1
J/MOL

H
J/I'10l-G
J/MOl6977.69J
9740.859
13465.698
22658.530
33760.314
41:366.975
41366.975
47113.287
62954.529
79944.758
97918.607
116752.428
136350.248
156615.3%
177545.206
199027.497
221038.140
243539.329
2664?8.312
289886.436
3136H .1\28337851.829
362386.543
387264.491
412(,69.314
437986.145
463801.409
489902.665
516278.465
542918,246
569812.226
596951.322
624327.079-2349.167
0.000
2601.529
8035.106}3895.414
17751.508
26228.508
28870.301
35752.101
42593.901
49455.101
56317.501
63179.301
70041.101
76902.901
83764.701
90626.501
97488.301
1014350.101
111211.901
1180B.701
124935.501
131797.301
138659.101
145520.'101
152382.701
159244.501
166106.301
172968.101
179829.901
186691.701
193553.501
200415.301

6977 .693<1740.859
1.5465.698
22658.530
33760.314
41366.975
41366.975
47113.287
62954.529
79944.758
97918.607
116752.428
136350.248
156635.3'l6
177 545.206
199027.497
221038.140
243539.329
266498.312
289886.436
313678.428
337851.829
362386.5G3
387264.491
GI2469.:514
437986.145
463801.409
489902.665
516278.465
542918.2'.6
569812.226
596951.522
624327 .079

Example 7 (MgO(g) by Method JANAF with LSQS andLOGK Options)
Problem. -Calculate thermodynamic functions for a species
with excited electronic states using method JANAF. Obtainleast-squares coefficients and tables with ~fIy and loglOKcolumns.
Except for the missing TEMP records, the LOGK label on
the OUTP record, and the data records, the input is similar
to that in the previous examples. With no TEMP records,
PAC91 uses the default temperature schedule of 100 (100)6000 K and T = 298.15 K. LOOK calls for rounded tables
with columns for AjRyand log 10K. The data records are for
15 electronic states including the ground state as indicated by
the numbers in columns 79 and 80. The excitation energies
are given by the TO numerical values. The remaining labels
are defined in table VII. Since no statistical weight was given
for the ground state PAC91 assigns a value of 1.

As with the last example, with LSQS on the OUTP recordand no LSTSQS records, all the default temperature ranges, .
constraints, and exponents in equation (11) are set by the
program. The default temperature range is 200 to 1000 K forthe first interval and 1000 to 6000 K for the second interval.
The default constraint temperature is 298.15 K for the firstinterval and 1000 K for the second interval. This may be seenin the least-squares output table where the errors at 298.15
K are zero and the values of the thermodynamic functions are
identical at 1000 K for both the first and second intervals.
Finally, the last two tables in the output are rounded andinclude columns for AjRyand log 10K. One table contains theoriginal data and the other contains data calculated from theleast-squares coefficients. Both used the EF data for Mg stored
in example 6.

Input. - The input data set for MgO, example 7, is as follows:

Rec. Label
ID
1
1-6
7-12
a NAME

MGIOl
DATE
OUTP
CTEM
CTEM
METH
DATA
DATA
DATA
DATA
DATA
DATA
DATA
DATA
DATA
DATA
DATA
DATA
DATA
DATA
DATA
DATA
DATA
DATA
DATA
DATA
DATA
DATA
DATA
DATA
DATA
DATA
DATA
DATA
DATA

FrNrS~

Numerical
value 1
13-24

MGO
J12/74JOULES
T
T
JANAF
~oJE

STATWlBE
STATWTBE
STAHoJlBE

STATWTBE
STAH·nBE
STAHH
BE
STATWlBE
STAH·nBE
STATWlBE
STATHTBE
STATWT
BE
STAHH
BE
STAH·nBE
STAH·.J1
BE

200.
3000.
785.1
6.
.5050
2.
.5050
3.
.5822
1.

.5822
3.
.501
6.
.501
2.

.5014
3.
.501
1.

.5008
1.
.5273
6.
.5615
2.
.5615
6.
.5249
2.
.5249

a All alphanumeric characters.

label
2
25-30

Numerical
value 2
31-42

Label
3
43-48

Numerical
value 349-6 a

Label
4

61-66

Numerical
value 4
67-78

Magnes p. urn Oxide.
HF298
58158.

JANAF Dec.1974, pl 472.
JOULES

LOGK
r

CTAB
T

1000.

LSQS
r

200.

BE

.5743
664.4

ALPHAI
~~EXE

.0050
3.9

664.4

WEXE

3.9

824.1

~~EXE

4.8

824.1

~'JEXE

4.76

632.5

~oJEXE

5.3

632.5

WEXE

5.3

632.5

~~EXE

5.3

632.5

WEXE

5.3

632.4

~oJEXE

5.2

632.4

~~EXE

5.2

710.

WEXE

5.

710.

loJEXE

5.

790.

~~EX.~

5.

790.

loJEXE

5.

~oJEXETO
ALPHAITO
ALPHAlTO
ALPHAITO
ALPHAITO
ALPHAITO
ALPHAITO
ALPHAITO
ALPHAITO
ALPHAlTO
ALPHAITO
ALPHAlTO
ALPHAITO
ALPHAITO
ALPHAl

100.
5.18
2300.

1-'~E

.004
3503.3WE.004
14000.
~JE. 004~
20004.
WE.0045
28000.
toJE.0048
29000.
~~E.0048
29775.
~~E.004~

30000.
~'lE.0048
30004.
loJE.0048
37684.
WE.0048
37000.
WE.005
37879.
~'1E.005
39000.
~~E.005
39868.
~~E
.005

79

-

~O

Expl. 7

1

2
2
3
3

~

5
5
6
6

7
7
8

8
9
9

10
10
11
11

12
12
13
l~

l'

Ie
P

IS

Listed output. - Listed output for MgO, example 7, is as follows:

NAME

MGO

I~G101DATE

J12/74OUTP

JOULES

CTEM

T

200.

T

3000.

METH

JANAF

DATA

JANAF Dec.1974, p1472.

HF298

JOULES

58158.

CTAB

LOGK

CTEM

110LECULAR m. =Magnesium Oxide.

100.

T

NEXE

5.18

BE

2300.

lSQS
200.

1000.

40.30440

WE

785.1

DATA

STAnn

6.

TO

DATA

BE

.5050

ALPHAIDATASTATVn

2.

TO

DATA

BE

.5050

ALPHAI

Dt,TA

STAnlT

3.

TO

Dt TA

BE

.5822

ALPHAI

DATA

STAnn

1.

TO

DATA

BE

.5822

ALPHAIDATA

STAH-:r

3.

TO

DAfA

BE

.501

ALPHAlDt-TA

STATWT

6.

TO

DATA

BE

.501

ALPHAIDATASTATWT

2.

TO

DATA

BE

.5014

ALPHAIDATA

STATln

3.

TO

DATA

BE

.501

ALPHAI

WE

DATA

STAnn

1.

TO

DATA

BE

.5008

ALPHAl

DATA

STAnn

1.

TO

DATA

BE

.5273

ALPHAl

DATA

STAnn

6.

TO

DATA

BE

.5615

ALPHAI

DATA

STAnn

2.

TO

DATA

BE

.5615

ALPHA1

DATA

STAnn

6.

TO

DATA

BE

.5249

ALPHA1DATASTATNT

2.

TO

DATA

BE

.5249

ALPHAI

.5743
664.4

ALPHA 1
~IEXE

.0050

3.9

.004

3503.3

!'lE

664.4

WEXE

3.9

I·JE

824.1

~IEXE

4.8

.0045

20004.

WE

824.1

WEXE

4.76

WE

632.5

~~EXE

5.3

\-.lE

632.5

WEXE

5 . .3

7

~IE

632.5

WEXE

5.3

8

7

.0048
30000.

6
6.0048

2977 5.

5
5.0048
29000.

4
4.0045
28000.

3
3

.004

8
HE

632.5

~~EXE

5.3

.0048

9
9

MGO

30004.

WE

632.4

WEXE

WE

632.4

vlEXE

5.2

.0048

37684.

:HOOO.

5.2

vIE

710.

HEXE

5.

WE

710.

J.-IEXE

5.

13

13
~IE

790.

~IEXE

5.

14

HE

790.

~~EXE

5.

15

.005

39868.

12

12

.OOS
39000.

11
11

.005

37879.

10
10

.0048

14

.005

FINISH

BAR

2
214000.

BAR

46

Expl. 7MGO

IS

L~ASTSQUAREST

CP/R INPUT
CP/R CALC
HH/RT INPUT
HH/RT CALCSIR II!PUTSIR CALC-GH/RT It/PUT-GH/RT CALCINPUT-CALC
FRACTIONINPUT-CALC
FRACTIONIIlPUT-CAlC
FRACTIOIlIIWUT-CALC
FRACTIOt~
3.6222350
3.6230253
3.5211248
3.5245108
24.1596692
24.1625724
20.6385444
20.6380617-0.0007903-0.0002182-0.0033859-0.Ou09616-0.0029032-0.0001202
0.0004827
0.0000234
298.153.8695880
3.8695830
3.5939207
3.5939207
25.6505882
25.6505882
22.0566675
22.0566675
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
O.oooooon
300.003.8745991
3.8746711
3.5956373
3.5956363
25.6745422
25.6745402
22.0739049
22.0789039-0.0000719-0.0000186
0.0000010
0.0000003
0.0000020
0.0000001
0.0000010
O.OOOOOO~
400.004.1834225
4.1803965
3.7020302
3.7017295
26.8292628
26.8289409
23.1272326
23.1272114
0.0025260
0.0006038
0.0003007
0.0000812
0.0003219
0.0000120
0.0000212
0.0000009
500.004.6225831
4.6241862
3.8397236
3.8393366
27.8071580
27.8066531
23.9674344
23.9673165-0.0016032-0.0003468
0.0003369
0.0001008
0.0005049
0.0000182
0.0001179
0.0000049
600.005.1811418
5.1827699
4.0157194
4.0157747
28.6981979
28.6981068
24.6324784
24.6823321-0.0016281-0.0003142-0.0000553-0.0000138
0.0000911
0.0000032
0.0001463
0.000005.
700.005.7472747
5.7457533
4.2233515
4.223577 5
29.5401461
29.5400372
25.3167947
25.3166597
0.0015214
0.0002647-0.0000260-0.0000062
0.0001089
0.0000037
0.0001349
0.0000053
800.006.2013558
6.2012364
4.4438496
4.'i457241
30.3389662
30.3386969
25.8951166
25.8949723
0.0001194
0.0000192
0.0001255
0.0000282
0.0002693
0.0000089
0.0001438
0.0000056
900.006.4815119
6.4823453
4.6563835
4.6563580
31.0873489
31.0871685
26.4309654
26.4308104-0.0008335-0.0001286
0.0000255
0.0000055
0.0001804
0.0000058
0.0001550
0.0000059
1000.00
6.5903910
6.5901425
4.8456316
4.8455819
31.7772400
31.7770331
26.9316084
26.9314511
0.0002485
0.0000377
0.0000497
0.0000103
0.0002070
0.0000065
0.0001573
0.0000058
MAX REL ERR CP/R
0.000604
TEMP
400.
AVER REL ERR CP/R
0.000195
REL LST SQ ERR CP/R
0.000263~'AX REL ERR HH/RT
0.000962
TEMP
200.
AVER REL ERR·HH/RT
0.000121
REL L5T SQ ERR HH/RT
0.000307~'AX REL ERR SIR
0.000120
TEMP
200.
AVER REL ERR SIR
0.000018
REL LST SQ ERR SIR
0.000039
MAX REt ERR GH/RT
0.000023
TEI1P
200.
AVER REL ERR GH/RT
0.000006
REl LST SQ ERR GH/RT
0.000009
MAX ERR CP/R
0.002526
TEMP.=
400.
AVER ERR CP/R
0.000934
LST SQ ERR CP/R
0.001238
MAX ERR HH/RT
0.003386
TEMP =
200.
AVER ERR HH/RT
0.000436
LST SQ ERR HH/RT
0.OUI083
I1AX ERR SIR
0.002903
TEMP =
200.
AVER ERR SIR
0.000459
LST SO ERR SIR
0.000946
MAX ERR GH/RT
0.000483
TEM? =
200.
AVER ERR GH/RT
0.000136
lST SQ ERR GH/RT
0.000139
Cf'/R
3.778230ge+05T**-2.0 -6.0817323e+03T**-1.0
4.1615823e+OlT** 0.0 -1.185198ge-OlTKA 1.0
1.9434161e-04T*~ 2.0-1.4549526e-07T** 3.0
4.0351763e-llT** 4.0(H-HO)/R CONSTANT = 0.28401570e+05, H/R CONSTANT = 0.34324803e+05. SIR CONSTANT =-0.20182814e+03
200.00T

1[lOO.OO
1100.00
1200.00
1300.00
1400.00
1500.00
1600.00
1700.00
1800.00
1900.00
2000.00
2100.00
2200.00
2300.00
2400.00
2500.00
2600.00
2700.00
2800.00
2900.00
3000.00
3100.00
3200.00
3300.00
3400.00
3500.00
3600.00
3700.00
3800.00
3900.00
4000.00

CP/R ItIPUT
IIIPUT-CALC
6.5903910
0.0002485
6.5673619-0.00395&0
6.4621804
0.0013655
6.3137782
0.0036313
6.1506734
0.0025789
5.9898031
0.0002882
5.8401423-0.0016<:)26
5.7056142-0.0027131
5.5871912-0.0027 591
5.4843087-0.0020893
5.3956633-0.0010442
5.3196368
0.0000721
5.2548048
0.0010516
5.1995323
0.0017577
5.1525519
0.0021435
5.1127103
0.0022156
5.0790145
0.0020136
5.0506094
0.0016115
5.0267711
0.0010651
5.0068916
0.0004556
4.9904468-0.0001577
4.9770043-0.0007144
4.9661894-0.0011766
4.9576880-0.0015158
4.9512419-0.0017095
4.9466200-0.0017604
4.9436377-0.0016699
4.9421373-0.0014508
4.9419801-0.0011287
4.9430465-0.0007362
4.9452504-0.0002937

CP/R CALCFRACTION
6.5901425
0.0000377
6.5718199-0.0006026
6.4603150
0.0002113
6.3101469
0.0005751
6.1480945
0.0004193
5.9895149
0.0000481
5.8418349-0.0002898
5.7083273-0.0004i'5:;5.5899504-0.0004938
5.4863980-0.0003810
5.3967080-0.0001935
5.3196147
0.0000135
5.2537533
0.0002001
5.1977745
0.0003381
5.1504084
0.0004160
5.1104947
0.00043.B
5.0769959
0.0003974
5.0489979
0.0003191
5.0257060
1),0002119
5. 0064360
0.0000910
4.9906046-0.0000316
4.9777187-0.0001435
4.9673659-0.0002369
4.9592038-0.0003057
4.9529514-0.0003453
4.948380(,-0.0003559
4.9453076-0.0003378
4.9435882-0.0002936
4.9431088-0.0002284
4.9437827-0.0001489
4.9455440-0.0000594

BAR

HH/RT INPUT
ItIPUT-CALC
4.8456316
0.0000'i97
5.00'i0302-0.0003036
5.1303682-0.0003367
5.2272787-0.0001365
5.2990894
0.0001108
5.3504543
0.0001994
5.3856640
o .OOOU85
5.4083633-0.0000039
5.4215156-0.0001598
5.4274607-0.0002810
5.4280310-0.0003460
5.42463'i0-0.0003521
5.4183512-0.0003035
5.4100046-0.00023,+8
5.400229~-0.0001427
5.3895044-0.0000479
5.3781910
0.0000349
5.3665705
0.0001027
5.3548470
O.n001462
5.3431807
0.0001675
5.3316379
0.0001667
5.3204565
0.0001477
5.3095484
0.0001134
5.2990103
0.0000698
5.2888708
0.0000190
5.2791548-0.0000308
5.2698727-0.0000780
5.2610321-0.0001182
5.2526350-0.0001495
5.2446814-0.0001690
5.2371664-0.0001771

HH/RT CALCFRACTIOIl
4.8455819
0.0000103
5.00(13389-0.0000617
5.1307549-0.0000754
5.2274152-0.0000261
5.2989786
0.0000209
5.3502549
0.0000373
5.3855255
0.0000257
5.'i083672-0.0000007
5.4216733-0.0000295
5.4277417-0.0000518
5.4283770-0.0000637
5.4249861-0.0000649
5.4186597-0.0000569
5.4102395-0.0000434
5.4003721-0.0000264
5.3895523-0.0000089
5.3781561
0.0000065
5.3664673
0.0000191
5.3547008
o .\l00027:5
5.3430132
0.0000313
5.3315213
0.0000313
5.3203088
0.0000278
5.3094350
0.0000214
5.298940(10.0000132
5.2888519
0.0000036
5.2/91856-0.0000058
5.2699506-0.0000148
5.2611504-0.0000225
5.2527845-0.0000285
5.2448504-0.0000322
5.2373435-0.0000338

S/R INPUT
H1PUT-CALC
31.7772400
0.0002070
32.4051630-0.00UI608
32.9725516-0.0002727
33.<,841208-0.0000(,41
33.9460831
0.0002030
34.3649022
0.0003019
34.7466245
0.00025<,435.0965646
O.OOOll71
35.4192597-0.0000437
35.7185218-0.0001756
35.9975185-0.0002570
36.2588887-0.0002792
36.5048226-0.0002529
36.7371545-0.0001905
36.9574251-0.0001059
37.1669325-0.0000158
37.3667814
0.0000678
37.5579187
0.0001336
37.7411535
0.1l001874
37.9171920
0.0002143
38.0866465
0.0002186
38.2500543
0.0002030
38.4078906
0.0001728
38.5605739
0.0001322
38.7084752
0.0000839
38.8519289
0.0000335
38,9912333~0.0000159

39.1266625-0.0000567
39.2584538-0.0000932
39.3368366-0.0001163
39.5120094-0.0001293

SIR CALC
FRACTIOtl
31.7770331
0.0000065
32.4053238-0.0000050
32.9728243-0.0000083
33.<1841648-0.0000013
33.9458301
0.0000060
34.3646003
0.0000088
34.7463101
0.0000073
35.0964475
0.0000053
35.4193034-0.0000012
35.7186974-0.0000049
35.9977755-0.0000071
36.2591679-0.0000077
36.5050755-0.0000069
36.7373'i50-0.0000052
36.9575310-0.0000029
37.1669483-0.0000004
37.3667136
0.0000018
37.5577801
0.0000037
37.7409661
0.1l000050
37.9169778
0.0000057
38.0864279
0.0000057
38.2498514
0.0000053
38.4077178
0.00000(,538.5604417
0.0000034
38.7083913
0.0000022
38.8518954
0.0000009
38.9912492-0.0000004
39.1267192-0.0000014
39.2585470-0.0000024
39.3869530-0.0000030
39.5121387-0.0\)00033-GH/RT rtlPUT
ItlPUT-Cl\lC
26.9316034
0.0001573
27.4011327
0.0001478
27.8421834
0.0001140
28.2568<,21O. 0000925
23 .6469937
0.0000922
29.0144<,790.0001025
29.3609605
0.0001160
29.6882013
0.0001210
29.9977(+620.0001161
30.2910611
0.0001054
30.5694876
0.0000390
30.8342547
0.0000729
31.0864715
0.0000556
31. 3271499
0.0000('4431.5571957
0.0000368
31.7774281
0.0000320
31.9885904
0.0000329
32.1913482
0.0000360
32.3863065
0.0000(,12
32.5740114
0.0000468
32.7549536
0.0000519
32.9295978
0.0000553
33.0983422
0.0000594
33.2615636
0.0000624
33.4196044
0.OD00649
33.5727741
0.00006(1333.7213606
0.0000620
33.8656304
0.0000615
34.0053188
0.O1l00563
34.1421553
0.0000527
34.27(,8'i30
0.000\)478-GH/RT CMC
FRACTION
26.9314511
0.0000053
27.4009849
0.000005 /,27.8(,20694
0.0000041
Z3. 2567(+96
0.000U03:;
23.6469015
0.0000032
29.0143453
0.000003.5
29.3608445
0.0000039
29.6380803
0.0000041
29.9976301
0.0000039
30.2909557
0.OOOD035
30.5693985
0.0000029
30.83'+1813
0.0000024
31.0364159

O.ooooon

31. 3271055
0.0000014
31.5571589
0.0000012
31.7773961
0.0000010
31.9085575
0.0000010
32.1913122
U.OU00011
3Z.3862653(1.000001:'
32.5139645

0.0000014
32.7549066
0.0000016
32.9295426
0.0000017
33.0982823
0.0000013
33.2615013
0.0000019
33.4195395
0.OC00019
33.57270')3
0.OU00019
33.7212986
0.DU00015
33.8655633
0.0000013
34.0057625
0.0000017
34.142102.',0.0000015
34.2747952

O.OOOllOI"

MGO

.+7

4100.00

4.9485103
4.9483438
5.2300825
5.2302585
39.6341581
39.6342894
34.4040756
34.4040309
0.0001665
0.0000536-0.0001760-0.0000337-0.0001313-0.0000033
0.00004(,7
0.0000015
4.9527482
4.9521454
5.2234278
5.2235896
39.7554544
59.7535760
34.5300266
34.5299865
0.0006028
0.0001217-0.0001618-0.0000310-0.0001216-0.0000031
0.0000402
0.0000012
4300.00
4.9579160
4.9569212
5.2171907
5.2175306
59.8700514
39.8701565
34.6528606
34.6528260
0.0009941
0.0002006-0.0001398-0.0000268-0.0001052-0.0000026
0.0000347
0.0000010
4400.00
4.9639549
4.9626494
5.2113657
5.2114755
39.9841010
39.9841776
34.7727355
34.7727021
0.0013055
0.0002630-0.0001098-0.0000211-0.0000766-0.0000019
0.0000332
0.0000010
4500.00
4.9708240
4.9695107
5.2059412
5.2060183
40.0957288
40.0~51753
34.8897876
34.8897570
0.0015133
0.0003044-0.0000771-0.0000148-0.0000465-0.0000012
0.0000306
0.0000009
4600.00
4.9784954
4.9768861
5.2009125
5.2009532
40.2050650
40.2050766
35.0041526
55.0041234
0.0016095
0.0003232-0.0000407-0.0000078-0.0000116-0.0000003
0.0000292
0.0000003
4700.00
4.9869234
4.9855545
5,1962681
5.1962743
40.3122230
40.5121997
35.1159549
35.1159255
0.0015691
0.0003146-0.0000063-0.0000012
0.0000235
0.0000006
0.0000295
O.OOOOOO!!
4800.00
4.9960817
4.9946897
5.1920023
5.1919759
40.4173114
40.4172548
55.2253091
35.2252789
0.0013919
0.0002786
0.0000264
0.0000051
0.0000566
0.0000014
0.0000302
0.0000009
4900.00
5.0059449
5.0048605
5.1881027
5.1880521
40.5204267
40.5203449
35.3323240
35.332292a
0.0010844
0.0002166
0.0000506
0.0000098
0.0000819
0.0000020
0.0000312
O.OOOOOO?
5000.00
5.0164955
5.0158267
5.1845655
5.1844966
40.6216671
40.6215657
55.4371 01 5
35.4370691
0.0006687
0.0001353
0.0000689
0.0000133
0.0001014
0.0000025
0.0000324
O.OOOOoO~
5100.00
5.0277036
5.0275592
5.1813784
5.1813030
40.7211166
40,7210066
35.5397382
35.5397036
0.0001644
0.0000327
0.0000753
0.0000145
0.0001100
0.0000027
0.0000346
0.0600010
5200.00
5.0395491
5.0399376
5.1785355
5.1784642
40.8188581
40.8187508
35.6403226
35.6402866-0.0003886-0.0000771
0.0000713
0.0000138
0.0001073
0.0000026
0.0000360
0.0000010
5300.00
5.0520177
5.0529496
5.1760302
5.1759723
40.9149710
40.9148751
35.7389408
35.7389028-0.0009319-0.0001845
0.0000578
0.0000112
0.0000959
0.0000025
0.0000381
0.0000011
5400.00
5.0650799
5.0664895
5.1738529
5.1738188
41.0095223
41.0094509
35.8356694
35.8356321-0.0014095-0,0002783
0.0000541
0.0000066
0.0000714
0.0000011
0.0000373
0.0000010
5500.00
5.0787232
5.0804571
5.1719980
5.1719937
41.1025859
41.1025458
35.9305878
35.9305501-0.0017339-0.0003414
0.0000043
0.0000008
0.0000421
0.0000010
0.0000378
0.0000011
5600.00
5.0929281
5,0947372
5.1704597
5.1704863
41.1942248
41.1942139
36.0237651
36.0237271-0.0018091-0.0003552-0.0000265-0.0000051
0.0000109
0.0000003
0.0000374
0.0000010
5700.00
5.1076726
5.1091983
5.1692276
5.1692840
41.2844981
41.2845161
36.1152105
36.1152520-0.0015251-0.0002987-0.0000564-0.0000109-0.0000180-0.0000004
0.0000385
0.0000011
5800.00
5.1229418
5.1236919
5.1682978
5.1683731
41.3734610
41.3734997
36.2051633
56.2051266-0.0007501-0.0001464-0.0000755-0.0000146-0.0000386-0.0000009
0.0000567
0.0000010
5900.00
5.1387049
5.1380521
5.1676607
5.1677318
41.4611648
41.4612090
36.2935041
36.2934712
0.0006528
0.0001270-0.0000771-0.0000149-0.0000442-0.0000011
0.0000329
0.0000009
6000.00
5.1549559
5.1520945
5.1673117
5.1673606
41.5476667
41.547&831
36.3803551
36.3803225
0.0028614
0.0005551-0.0000490-0.0000095-0.0000164-0.0000004
0.0000326
0.0000n09
MAX REt ERR CP/R
0.000603
TEMP
1100.
AVER REt ERR CP/R
0.000259
REt tST SQ ERR CP/R
0.000298
MAX REt ERR HH/RT
0.000075
TEMP
1200.
AVER REt ERR HH/RT
0.000023
REt lST SQ ERR HH/RT
0.000029
MAX REt ERR SIR
0.000009
TEMP
1500.
AVER REt ERR SIR
0.000003
REl tST SQ ERR S/R
0.000004
MAX REt ERR GH/RT
0.000006
TEMP
1000.
AVER REt ERR GH/RT
0.000002
REt LST SQ ERR GH/RT
0.000002
HAX ERR CP'R
0.0039SB
TEMP.~
1100.
AVER ERR CP/R
0.001377lST SQ ERR CP/R
0.001625
MAX ERR HH/RT
0.000387
TEMP ~ 1200.
AVER ERR HH/RT
0.000123
lST SQ ERR HH/RT
0.000155
MAX ERR SIR
0.000302
TEMP ~ 1500.
AVER ERR $/R
0.000119
tST SQ ERR S'R
0.000144
MAX ERR GH/RT
0.000157
TEMP = 1000.
AVER ERR GH/RT
0.000059
tST SQ ERR GH/RT
0.000067
CP'R-I. 3876702e+071-J(-2. 0
3. 3903403e~OHlEJ(-1. a -2.1906072~+0ITWW 0.0
1.0456393e-02TwX 1.0 -2.2225473 -06TI(K 2.0
2.4662915e-l0TKK 3.0 -1.0961026e-14TKJ( 4.0(H-HO)/R CO~STA"T = -0.22S86827~+06. H/R CONSTANT =-0.21994504et06, S'R CONSTANT = O.20063928et03
420l'.00

BAR

T~ERMODYNAMICMGODATA COEFFICIENTS, RECORD IMAGES -Magnesium Oxide.
JANAF Dec.1974, 1'1472.
Expl. 7
2 JI2174 MG 1.000
1.00
0.00
0.00
0.00 040.30440
58158.000
200.000 1000.000 7 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0
8909.226
3.77823092d~05 -6.08173235d+03
4.16158227d~01 -1.1851989Id-01
1.94341615d-04-1.45495255d-07 4.03517625d-l1 O.OOOOOOOOd+OO 3.43248026dt04 -2.01828144df02
1000.000 6000.000 7 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0
8909.226-1.38767024d+07 3.39034027d~04 -2.19060721dtOl 1.04563934d-02 -2.22254732d-06
2.46629150d-10 -1.09610259d-14 O.OOOOOoOOd+OO -Z.19945038d+05 2.00659280d+02

MOO

ORIGItlAl

48

BAR

MGO

ORIGINAL

MGO

T
DEG-K

CP
J/MOL -K

H-tl296

S

J/MOL -I(-{G-H298 )/T
J/MOL-KH
KJ/MOLDEL TA H
KJ/MOL

LOG K

KJ/j·1DL

0100
200
298.15300
400
500

29.12530.11732.17452.21534.78338.435-8.909-6 • 001-3.054
0.000
0.060
3.403
7.053

180.487
200.876213.272
213.471223.072231.203240.496
216.146213.272
213.273214.565217.09649.24952.15755.10458.15858.21861.56165.21158.58759.40558.88758.15358.14457.44756 .901-26.6232-11.1490-6.1132-6.0503-3.5336-2.0403

600
700
800
900
1000

43.07947.78651.56153.89154.796

11.12415.67120.65025.93531.380238.61l245.612252.254258.476264.212220.071223.224226.442229.660
232.832

69.28273.82978 .808
84.09339.53856.62456.67256.99357.45749.314-1.0523-0.34820.1817
0.5%8o .8943

1100
1200
1300
1400
1500

54.60953.75052.49651.14049.80236.85742.27947.59252.77457.820269.433
274.151278.404
282.245285.727235.926238.918241.795
244.54't
247.130

95. 015
100.437105.750
110.932
1l5.'t78

49.60549.82149.91049.85449.6481.1292
1.32591.49291.63611.7599

1600
1700
1800
1900
2000

48.55847.43946.45545.59944.86262.737
67 .536
72.23076.83181.35421\8.901
291.811294.494296.982299.302249.690252.084
254.366
256.54(1258.625120.895
125.694130.388134.989139.51249.29948.82048.22347.52346.731

1.8676
1. 9618
2.04472.11782.1826

2100
2200
2300
2400
2500

44.23143.69143.23242.84142.51085.80790.20394.54398.851103.118

301.475
303.520305.451307.283309.025260.614262.518264.343
266.095
267.777

143.965148.361152.706
157.009161.276

45.85944.91743.91342.856
41. 7522.24022.29152.33742.37852.4153

2600
2700
2300
2900
3000

42.23041.99 ...
41.79541.63041.493107.355
111.566
115.755
119.926124.082

310.686312.276
313.799315.263316.672

269.396270.955
272.458
273.909275.311165.513169.724173.913178.084
182.240

40.60639.42338 .20736.96335.6942.44842.47822.50502.52922.5510

3100
3200
3300
3400
3500

41.38141.29141.22141.16741.129128.225132.359
136.484
140.604
144.718318.030
319.343320.612321.842323.035

276.667277.981279.253
280.483
281.687

186.383
190.517194.642198.762202.87634.40331.09131.76330.41829.0612.57072.58852.60452.61902.6321

3600
3700
3800
3900
4000

41.104
41. 091
41. 090
41. 09941.117148.830
152.940157.049
161.158
165.269

324.193325.319326.415
327.482328.523

282.851
283.984285.086286.160
287.206

206.988
211.098
215.207219.316223.42727.69226.31224.92523.52922.1272.64382.6544
2.66,,92.67252.6801

4100
4200
4300
4400
4500

41.14441.18041.223
41. 27 341.330169.382
173.498
177 .618
181.743
185.873329.539330.530331.500:n2.448333.376288.226
289.221290.193291.143292.071227.540231.656235.776
2.'>9.901
244.031

20.72019.31017.89616.48015.0632.68692.69302.69842.70312.7073

4600
4700
48!l0
4900
5000

41.39441.464
41. 540
41.62241.710190.009194.152
191L302202.460
206.626

334.285335.176
336.050
336.907337.749292.979293.868
294.737295.589296.424248.167
252.310256.460
260.618264.784

13.64512.22810.8129.398
7.987

2.71092.71402.71672.71902.7208

5100
5200
5300
5400
5500

41.80341.90142.00542.11442.227210.802214.987
219.182
223.388227.605338.576
339.389
340.188
340.974
341.748297.242298.045298.833
299.606
300.365268.960
2n.145277.340
281.546285.763

6.578
5.175
3.776
2.382
0.995

Z. 72232.72352.724 ...
2.72492.7252

5600
5700
5800
5900
6000

42.34542.46842.59542.72642.861231.834
236.074240.328244.594248.873342.510343.260
344.000
344.729345.448301.111301.344302.564303.273303.970289.992294.232
298.486302.752
307.031- 0.386-1.759-3.124- 4.480- 5.8272.72522.72512.72472.72(,1
2.7233¥.A CHANGE IN PHASE OF AN ASSIGUED REFERENCE ELEMENT HAS OCCURRED BEnrEEN THIS TEtlPERATURE MIO THE PRECEDItW OllE,
923.000

MG--

COEFF1CI fHTS
T

MGO
CP
J/MOl-l{

H-H298ll.J/MOL

S
J/MOl-1(-( G-H298 lIT
J/MOl-l{H
KJ/MOL

DEll A H
KJ/MOl

LOG K-8.909-3.048
0.000
0.060
3.402
7.052

200.900
21.3.272
213.471223.069
231.199216.141213.272
213.273214.564217 • 095

49.24955.11058.15853.21861.56065.21058.58758.89358.15858.14457.44656.899-11.1492-6.1132-6.0503SOD

30.12432.17432.21634.76238.448

600
700
800
900
1000

43.09247.77351.56053.89854.79411.12415.67120.64925.935
31. 379238.611245.611252.251258.475
264.210220.070223.223226.441229.658232.331

69.28273.82978.80784.09389.53756.62556.67256.99357.45649.314-1.0524-0.34820.18170.59670.8942

1200
1400
1600
1800
2000

53.71951.11848.57246.47844.87142.28252.77362.73672.23281.359274.153282.243288.899294.494299.304

238.918
244.549249.689254.365258.624100.440
110.931120.894130.390139.51749.82449.85349.29748.22646.7371.3253
1.6361
1. 8675
2.0446
2.1826

2200
2400
2600
2800
3000

43.68242.82342.21341.78641.49490.20898.854107.354115.752
124. 078

303.522307.284
310.686315.798316.670262.518
266.094269.396272.458275.311148.366
157. 012
165.512173.9Ul
182.23644.92242.85940.60538.204~5. 69 0

2.29152.37852.44842.50502.5510

DEG-K

0
200
298.15300
400

Y<A CHANGE Itl PHASE
tlG-- 923.000-~.5336-2.0403

OF AN A$5IGtIED REFERENCE EL EMENT HAS OCCURRI;O IIETWEE'l THIS TEMPERATURE AllO THE PRECEDItW OtIE,

COEFF ICI fNTS

BAR

MGO

49

Example 8 (Na2C03(1,2,i) by Methods READIN and
COEF with LSQS and LOGK Options)
Problem. -Calculate thermodynamic properties for acondensed species with more than two phases. Use different
methods for processing the data, if needed. Obtain least-squares
coefficients and tables with f}.flT and 10glaK columns.
The species selected for this example is Na2C03 which has
three condensed phases-two solid and one liquid. This
example illustrates the following features:(1) The NAME records identify the three phases as
Na2C03(1), Na2C03(2), and Na2C03(f). These names appear
as identification in the least-squares coefficient output.
(2) The data for the two solid phases are processed by
METHOD READIN, while the liquid phase is processed by
METHOD COEF. The energy unit for input data is in calories
as indicated by the CAL label on the METHOD records.
(3) The heat of formation at 298.15 K is specified to be-270.26 kcal/mol by HF298 and KCAL on the formula
record.
(4) The OUTP record contains the labels LOGK, JOULES,
and LSQS. The LSQS label calls for output tables of functions
calculated from least-squares coefficients. Separate sets ofcoefficients will be generated for each phase. The LOGK labelcalls for tables of rounded functions including ~flT andlog 10K. The label JOULES specifies that the unit of energy
in the output tables is injoules.
.
(5) The first METHOD record specifies that the energy umt
on the input data records following it is in calories (CAL).

50(Note that while the input is in calories the output, as discussed
in (4) above, is to be in joules.)(6) The heat of transition between the first and second phaseis given by the value of 165. for the DELTAH label on thesecond METHOD record. The energy unit is cal/mol (CAL).
(7) No enthalpy or entropy values are given on the first data
record for the second phase at the transition temperature of723.15 K. These values are calculated by the program fromthe DELTAH value of 165 cal/mol and the enthalpy andentropy values of the first phase at 723.15 K.
(8) The heat of transition of 7090. between phases 2 and3 (the heat of fusion) is given on the third METHOD record
as the DELTAH numerical value. The energy unit is cal/mol(CAL).
(9) On the first data record for the liquid phase, Cl is given
as 45.30.
(10) On the second data record for the liquid phase, only
the TCOEF label appears. The purpose of the TCOEF label
was discussed in the example for Mg(f).
(11) The listed output consists of a table of the input records,
a table of least-squares coefficients and errors, and a table ofrounded thermodynamic functions. Note that at each transition
temperature (T = 723.15 and 1123.15 K) values of -(0H298)/T and LOGK are identical for the two phases. The
columns headed DELTA H and LOOK do not contain data
for temperatures at 2400 K and higher, inasmuch as the EFdata for Na(f) exist only to 2300 K.

Input. - The input data set for Na2C03 (1,2,Q), example 8, is as follows:

Rec. label
ID
1
1-6
7-12
a NAMEa NAMEa NAME

Numerical
value 1
13-24

~A2C03 (1)NA2C03 (2)NA2C03 (L)NA2CI0 3(S)DATE J 3/66
OUTP LOGK~1ETHOI: READIN
T
100.
200.
T
298.15
T
300.
T
400.
T
500.
T
~oo.
T
~OO.
T
t723.15METHOD READIN
T~23 .15
T
~OO •
T
900.
1000.
T
T
1100.
T
1123.15
TEMP T
1123.15
METH COEF
T
1123.15
TCOEF
FINIS\-'

rr

Label
2
25-30

Numerical
value 231-42i'-abel3~3-48

Numerical
value 3
49-60

Label
4
61-66

Numerical
value 4
67-78

JANAF pATA. MARCH 1966.
JANAF DATA. MARCH 1966.
JANAF DATA. MARCH 1966.
HF298 -270.26
KCAL
JOULES
H298HO 4974.
14.637CP
22.5000
CP
26.530CP
26.590CP
29.900CP
33.990CP
39.030CP
44.830CP
46.220CP
DElTAti
165.
34.360CP
36.650CP
39.730CP
42.830CP45.900CP
46.630CP
1200.
T
DELTAH 7090.0
6000.
T

-

80

Expl. 8lSQS
MELTPT 1123.15
S
10.334S
23.367$33.173S
33.33841.421
SS
48.520S
55.153S~ 1.597S~3. 078
CAL

CAL
H-H2
H-H2
H-H2
H-H2
H-H2
H-H2
H-H2
H-H2
H-H2

-4348.
-2424.
0.0
49.0
2867.
6056.
9702.
13890.
14944.
17837.
21655.
25782.
30220.
31291.
6000.
0.0

S
S
S
S
S
S
I

175.729f"79.956
200.

H-H2
H-H2
H-H2
H-H2
H-H2
H-H2
T

Cl

45.30

El

~AL

79

~6.889~ 1. 383~O.920a All alphanumeric characters.

51

Listed output. - Listed output for Na2 C03 (1,2,Q), example, 8, is as follows:
NMtE

NA2C03(1)NAME

llA2C03( 2)tiM1E

NA2C03(L)NA2CI03(S)DATE

J 3/66OUTP

LOGK

MARCH 1966.

JAtlAF DATA.

MARCH 1966.

JANAF DATA.

MARCH 1966.

HF298 -270.26

METHODREADIN
T

DATA.

JMlAF

KCAL

JOULESlSQS

H293HO 4974.

MELTPT

100.

CP

14.637200.

ep22.5000

T

298.15CP

26.530

T

300.

cr

26.590400.

CP29.900500.

GP33.990Expl. 8S

1123.15

CAL

10.334H-H2-4348.

23.367H-H2-2424.

33.173

H-H2

0.0

33.333

H-H2

49.0

S

41. 421

fj-HZ

2367.

S

48.520

H-H2

6056.

S

600.

CP

39.030S

55.153

H-H2

9702.

T

700.

CP

<14.830

S

61.597

H-HZ

13390.

T

723.15CP

46.220S

63.078H-H214944.

METHDDREADWDELTAH165.

CAL

lEAST SQUARESCP/R rrlPUT
CP/R CALC
HH/RT IIlPUT
HH/RT CIILC
S/R rtlPUT
S/R CALC-GH/RT IIIPUT-GH/RT CALCINPUT-CALC
FRACTIONFRACTIONIIlPUT-CAlC
It/PUT-CALC
FRACTIOtl
INPUT-CALC
FRACTIOIl
11.3223750
6.4142146
11.7536638
11 .7561738
5.3426513
5.3419592
11.3213318
6.4160125
0.0004931
0.0024900
0.0002118
0.0006921
0.00012'15
0.0002802
0.0000436
0.0017979
293.1513.3503331
8.2981043
8.2981043
3.3951021
16.6932065
13.3503331
8.39510Z1
16.6'132065
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
0.0000000
300.0013.3305311
16.1758823
8.3507123
8.3501292
13.3807015
8.4255244
3.4257531
16.7762'372-0.0001704-0.0002287-0.0000271
0.0000212
0.0000699-0.0000127
0.0003549
0.00058'36
400.0010.9802053
15.0461783
10.9794328
9.8689109
20.8437375
20.8491163
15.0471258
9.8643047-0.0009475-0.0004670-0.0002531-0.0007725-0.0000704-0.0000630-0.0053787-0.0046062
500.0017 .1043345
24.4179923
11.1014685
24.4160726
13.3151130
15.3165238
17.1006858
11.1009596
U.0036487-0.000045&-0.0019197-0.00007&6-0.0014103-0.0001060
0.0002135-0.UOO5089
600.0019.6405465
12.3071219
27.7538865
15.4452291
15.4467646
19.6447778
12.3086796
27.7539085-0.000099(,-0.0042313-0.0015355
0.0000008
0,0015578
0.0001266-0.000215<1
0.0000223
700.0017.4371910
22.5592031
13,5609703
13.5599048
30.9970958
17.4356667
30.9966370
22.5547150
0.0044881
0.0000786-0.0000148-0.0015243-0.0000874
0.0010655-0.0004588
0.0001939
723.15Z3.2586743
17.8832127
17.8816097
Z3.2615218
13.3602912
13 .8591431
31.7419008
31.7423558-0.0028475-0.0000896
0.0000328-0.0004549-0.0000143-0.0016030-0.0001224
0.0011481
MAX REL ERR CP/R
0.000138
0.000215
TEMP
600.
AVER REL ERR (P/R
0.000109
RH LST SQ ERR CP/R
~IAX REL ERR HK/RT
0.000467
41\0.
0.01l0203
TEr1P
AVER REL ERR HH/RT
REl LST SQ ERR HH/RT
O.OOOU'J
IIAX REl ERR S/R
0.000122
AVER REL ERR S/R
REL LST SO ERR S/R
0.000258400.
0.000075
TEMP
MAX REl ERR GH/RT
0.0001300.000089
TEMP
zoo.
AVER REL ERR GH/RT
0.000082
REL LST SO ERR GH/RT
MAX ERR CP/R
AVER ERR CP/R
LST SO ERR CP/R
0.002753
0.004483
700.
0.002103
THlP.
MAX ERR HH/RT
0.001925
1).004606
LST SQ ERR HH/RT
TEMP
4ll0.
AVER ERR HK/RT
0.001364
MAX ERR S/R
0.005379
0.002218
400.
AVER ERR S/R
LST SO ERR S/R
TEMP
0.001385
t1AX ERR GH/RT
0.001154
0.001603
AVER ERR GH/RT
TE~lP
723.
0.00).015
LST SQ ERR GH/RT
CP/R
2.7690834e+05T**-2.0 -6.29257 4e+03Tu-l.0
5.4857058e+01T** 0.0 -1.3550634e-oiT** 1.0
2.3061993e-04T** 2.0-l.4673680e-07T** 3.0
3.45827 4e-llTU 4.0(H-HO)/R CONSTANT = Q .2.7187630e+05, H/R CONSTANT ~-0.11l31471e+06. $/R COHSTANT =-0.284029Qge+03
200.00

THERMODYNAMIC DATA COEFFICIENTS, RFCORD INAGES NAZCD3Cl)
JM1AF DATA. MARCH 1966.
Expl . 8
1 J 3/66 riA 2.00e
1.000-1130767.840
0.00
3.00
105.98874
0.00
200.000
723.150 7 -Z.O -1.0 0.0 1.0 2.0 3.0 4.0 0.0
20311.216
2.76908339dt05 -6.29257045d+03 5.48570580dtOl -1.35506338d-Ol 2.30619932d-04-1.467368Dod-07 3.45827436d-ll O.OOOOOOOOd+OO -1.11314706d+05 -2.84029095d+02
T

723.15CP

34.360

T

800.

CP

36.650

T

900.

CP

39.730H-H2
S66.889H-112

17337.

71.383

H-HZ

21655.

tlA2C05{11

l'

10UO.

CP

42.830

T

1100.

CP

45.900T

1123.15CP

46.630TEMP
METH1123.15
eOEF

s
S

lZ00.
DELTAH7090.0

75.729H-H2

79.956H-H230220.

80.92.0

ii-H2:H291.

200.

T

6000.

NA2C03(l)25782.

CAL

HA2eO?,(1)52

NA2C03(2)NA2C03(21UA2C03CL)

lEAST 5QUI\RES
CP/R tIlPUT
HH/RT HlPUT
CP/R CALC
HH/RT CAI.C
SIR rtlPUT-GH/RT IUF"UT-GH/RT Ci\l.C
SIR CALCIHPUT-CAlC
FRAClI 011
ItiPUT-CAlC
FRACTION
fRACTIOn
ItlPUT-CAlC
FRACTIONINPUT-CAlC
17.2905246
17.29052ft6
17.8816097
13.9751093
13.9739612
31.8567190
31.8571739
17.8832127
0.0000000
0.0000000
0.0011481
0.0000822-0.0004549-0.0000143-0.0016030-0.0000896
800.0018.4428908
14.34859(,214.3(,78323
18.4427379
33.6596596
33.6605661
19.3110654
19.3127337
0.0001529-0.001668(.
0.0000083
0.0007619
0.0000531-0.0000864-0.0009065-0.0000269
900.0019.9921981
14.888(.219
55.9217 5(.821.052()52(.
19.9927417
14.8890629
35.9211153
21.()333BO
0.0000564
0.0000431-0.()O06396-0.0000178-0.0012806-0.0000609
0.0000028
0.0006410
1000.00
21.5527698
21.5527326
15.4769318
15.4770866
38.1080949
38.1091833
22.6311631
22.6320967
0.0000372
0.0000017-0.0001548-0.0000100-0.0010885-0,0000286-0.0009336-0.00004U
1100.00
23.0976450
23.0977521
16.0994725
40.2351917
40.2356566
24.1350032
24.1361841
16.1001885-0.QOOI071
0.00004(,5-0.00046(.8-0.0000046
0.0007160-0.0000ll6-0.0011808-0.0000481
1123.15
23.4649931
16.2474895
16.2481880
40.720S117
24.4721046
2'i.47302Z2
23.4649481
40.7202?26
0.0000450
0.0006985
0.0000430-0,000005('-0.0009176-0.0000375
0.0000019-0.0002191
MAX REl ERR CP/R
0.000008
AVER REl ERR CP/R
0.000004
T Er1P800.
0.000003
REL lST SQ ERR CP/R
MAX REl ERR HH/RT
0.001)032
TEl\P
723.
AVER REL ERR HH/RT
Q.IH10046
0.000051
REI. LST SQ ERR HH/RT
MAX REl ERR SIR
TEMPAVER REl ERR SIR
0.0000291000.
0.000017
0.000019
REI. LST SQ ERR SIR
MAX REL ERR GH/RT
0.000090
AVER REL ERR GH/RT
0.000064
TEMP
723.
0.000061
REl LST SQ ERR GH/RT~I,'\X ERR CP/R
0.000153
AVER ERR CP/R
THW.
800.
0.000066
lST SQ ERR CP/R
0.000083
0.001148
AVER ERR HH/RT"1 AX ERR HH/RT
Tn1P
723.
0.000745
0.000687
I.ST SQ ERR HH/RT
HI\X ERR SIR
0.001088
TEMP
1000.
AVER ERR SIRLSI SQ ERR SIR
0.000694
0.000629
MAX ERR GH/RT
0.001668
TE~IP
AVER ERR GH/RT
LST SQ ERR GH/RT
0.001298800.
0.001264
CP/R-1.1212220e+08TX*-2.0
1.64315<'i2e+00Txx 1.0 -9.0577776e-04T~x 2.0
6.40506 6e+05Tu-l.0 -1.4442432e+03Tx. 0.0
2.000349ge-07TYX 3.0(H-HO)/R CONSTANT = -0.36<'i65252e+07. H/R CONSTANT =-0.37850275e+07. SIR CONS TAlIT ~ 0.93420894e+04
T

72:,,15

T~ERMODYNAMIC DATACOEFFICIENTS. RECORD HIAGES -tJA2C03(2lJAI/AF DATA. MARCH 1966.
1 J 3/66 ~A z.oac
1.000
3.00
0.00
0.00 2105.98874-1130767.840
723.150 1123.150 6 -2.0 -1.0 0.0 1.0 2.0 3.0 0.0 0.0
20811.216-1.12122199dt08 6.40S06661dt05 -1.44424316dt03 1.64315419d+00 -9.05777755d-04
2.00034993d-07 O.OOOOOOOOd+OO O.OOOOOOOOdfOO -3.78502749d t 06 9.34208940d+03
T1123.15

T

6000.

Cl

45.30

E1

0.0

TCOEF
F 1111 SH

COEFFICIENTS ADJUSTED TO FIT UPPER PHASE AT 1123.15

11112C03(1)11112C03(2)NAZCD3'L)

THERMODYNAMIC DATA COEFFICIENTS. RECORD IMAGES NA2C03(L)
JANAF DATA. MARCH 1966.
1 J 3/66 NA 2.00e
1.000
3.00
0.00
0.00 3105.98874-1130767.840
1123.150 6000.0001 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
20811.216
2.27957150dtOl O.OOOOOOOOdtOO O.OOOOOOOOd'OO O.OOOOOOOOd+OO O.OOOOOOOOd.OO
O.OOOOOOOOdtOO O.OOOOOOOOd+OO O.OOOOOOOOdtOO -1.42289169d+05 -1.16217533dt02

ORIGINAL

NA2C03(1)t~A2C03' 2)

t~A2C03( L )53

ORIGINAL

NA2C03(1)CP
J/MOL-K

H-H298200
293.15
300
400
500

loa

T
DEG-K

NA2C03(2)NA2C03(l)KJ/NOLS-{G-H298)/T

J/MOL-K

J/~lOL-K

KJ/MOLDELTA HKJ/MOL

61, 241
94.140111. 002
111.253
125.102142.214-20.811-18.192-10.1420.000
0.205
11 .99625.33843.23797.768133.796139.486
173.305203.008

225.158
148.478138.796138.803143.317152.:)31-1151.579-1148.960-1140.910-1130.768-1130.563-1118.772-1105.430-1124.585-1129.073-1130.627-1130.768-1130.765-1135.691-1134.481

575.9119280.3333
183.6135
182.3971
133.1291
103.4801

600
700
723.15723.15
800
900
1000

163.302187.569
193.384
143.762
153.344
166.230
179.201

40.59358.11662.52663.21674.63090.605107.872230.760
257.722263.918264.373279.864298.666
316.850

163.105174.699
177.(.55
186.576
197.995
208.978-1090.175-1072.652-1068.242-1067.552-1056.138-1040.163-1022.896-1131.600-1126.656-1125.185-1124.494-1122.900-1l19.8<'i}-1115.648

83.7484
69.701967.012167.012159.2143
51.0787
44.5907

11 00
1123.151123.15
1200
1400
1600
1300
2000

192.046
195.100
189.535
189.535
189.535
139.535
139.535
189.535

126.440130.922160.586
175.152
213.059
250.966
288.873526.180

334.536
33&.569364.981377.525406.742432.051454.375474.345219.590222.003
222.003231.566254.558
275.198293.89031.0.955-1004.327-999.846-970.182-955.616-917.709-879.802-341.895-803.988-1110.316-U08.925-1079.260-1075.023-1064.586-1055.196-1047.130-1040.691

39.3048
38.2188
38.218835.010728.3572
23.4137
19.6006
16.5716

2200
2400
2600
2800
3000

189.535
189.535
189.535
189.535
189.535

364.687402.594440.501
47&.408516.315492.410508.901524.072538.118551.195

326.643
341.154354.649367.258
379.090-766.081-728.174-690.267-652.360-614.453-10.:.6.189

14.1062

3200
3400
3600
3800
4000

189.535
189.535
189.535
189.535
189.535

554.222592 .129630.036667.943705.350

563.427574.918585.751595.999605.721390.233
400.762410.741420.224429.258-576.546-538.639-500.731-462.824-424.917

4200
4400
4600
4800
5000

189.535
189.535
189.535
189.535
139.535

743.757
781.665
819.572857.479895.386

614.968
623.785632.211640.277648.014437.883446.134454.043461.636468.937-387.010-349.103-311.196-273.239-235.382

5200
5400
5600
5800
6000

189.535
189.535
189.535
139.535
189.535

933.293971.200
1009.1071047.014
1084.921

655.443662.601
669.494676.145632.571475.969432.749489.296495.625501.750-197.475-159.568-121.661-83.754-45.8470lE

177 .455

H

LOG K*A CHANGE IN PHASE OF AN ASSIGNED REFERENCE ELEMENT HAS OCCURRED BETWEEN THIS TEMPERATURE All!) THE
371.010NA--

ORIGINAL

54

NA2C03(1)NA2C03(2)NA2C03(L)PRECEDIt~GOUE,

References
I. McBride, B.1.; and Gordon, S.: FORTRAN IV Program for Calculationof Thermodynamic Data. NASA TN D-4097, 1967.
2. Huff, V.N.; Gordon, S.; and Morrell, V.E.: General Method andThermodynamic Tables for Computation of Equilibrium Composition
and Temperature of Chemical Reactions. NASA Rept. 1037, 1951.
(Supersedes NACA TN's 2113 and 2161.)
3. Rossini, F., et al.: Selected Values of Chemical Thermodynamic Properties.
NBS-Cire. 500, NBS, 1952.
4. McBride, B.1.; Heimel, S.; Ehlers, J.G.; and Gordon, S.: Thermodynamic
Properties to 6000 K for 21 0 Substances Involving the First 18 Elements.
NASA SP-3001, 1963.
5. Burcat, A.: ThemlOchemical Data for Combustion Calculations. Combustion
Chemistry, W.e. Gardiner, Jr., ed., Springer-Verlag, New York, 1984,
Chapt. 8.
6. Chase, M.W., Jr., et al: JANAF Thermochemical Tables. Third ed., Parts
I and II, J. Phys. and Chern. Ref. Data, vol. 14, Suppl. I, 1985.
7. Marsh, K.N., et al.: TRC Thermodynamic Tables, Non-Hydrocarbons,
Vols. I to VIII; and Hydrocarbons, Vols. I to XII. Thermodynamics
Research Center, Texas AIM University, College Station, TX, 1988.
8. Gurvich, L. V.; Veyts, 1. V.; and Alcock, e. B.: Thermodynamic Properties
of Individual Substances. vol. 1, Parts 1 and 2, Fourth ed., Hemisphere
Publishing Corp., 1989.
9. Cox, J.D.; Wagman, D.D.; and Medvedev, V.A.: CODATA Key Values
for Thermodynamics. Hemisphere Publishing Corp., 1989.
10. Cohen, E.R.; and Taylor. B.N.: The 1986 CODATA Reconunended Valuesof the Fundamental Physical Constants. J. Res. Nat. Bur. Stand., vol.
92, no. 2, Mar.-Apr. 1987, pp. 85-95.
II. McChesney. M: Equilibrium Shock-Wave Calculations in Inert Gas,
Multiply Ionized Debye-Huckel Plasmas. Can. J. Phys .. vol. 42, no.
12, Dec. 1964, pp. 2473-2494.
12. Downey, J.R., Jr.: Calculation of Thermodynamic Properties of Ideal
Gases at High Temperatures: Monatomic Gases. AFOSR-TR-78-0960,
1978. (Avail. NTIS, AD-A054854.)
13. Zemansky, M.W.: Heat and Thermodynamics. Fourth ed., McGraw-Hili,
1957, p. 438.
14. Hilsenrath, J.; Messina, e.G.; and Evans, W.H.: Tables of Ideal Gas
Thermodynamic Functions for 73 Atoms and Their First and Second
Ions to 10,000 K. AFWL-TDR-64-44, National Bureau of Standards,
1964. (Avail. NTIS, AD-606163.)
15. JANAF Thermochemical Tables. The Dow Chemical Co., Midland, MI,
Dec. 31, 1960 to Mar. 31, 1966.
16. Myers, H.; Buss, 1.H.; and Benson, S. W.: Thermodynamic Effects of
Coulombic Interactions in Ionized Gases. Planetary Space Sci., vol. 3.
1961, pp. 257-270.
17. Herzberg. G. (l.W.T. Spinks, trans.): Atomic Spectra and Atomic Structure.
Second ed., Dover Publications, 1944.
18. Moore, e.E.: Atomic Energy Levels. Vols. 1,2, and 3, NBS-Circ.
467-VOL-l,-2,-3, 1949 to 1958.
19. Moore, C.E.: Atomic Energy Levels. Vols. I, II, and III, NSRDSNBS-35-VOL-l,-2,-3, Dec. 1971.
20. Kuhn, H.: Atomic Spectra. Academic Press, 1962.
21. Herzberg, G.: Molecular Spectra and Molecular Structure. Vol. I, Spectraof Diatomic Molecules. Second ed., D. Van Nostrand Co., Inc., 1950.
22. Herzberg, G.: Molecular Spectra and Molecular Structure. Vol. 2, Infrared andand Raman Spectra of Polyatomic Molecules. D. Van Nostrand Co.,
Inc., 1945.
23. Mayer, J.E.; and Mayer, M.G.: Statistical Mechanics. John Wiley andSons, Inc., 1940.
24. Kassel, L.S.: The Calculation of Thermodynamic Functions From
Spectroscopic Data. Chern. Rev., vol. 18, no. 2, Apr. 1936, pp.
277-313.
25. Wilson E.B., Jr.: The Effect of Rotational Distortion on the Thennodynamic
Properties of Water and Other Polyatomic Molecules. 1. Chern. Phys.,vol. 4, no. 8, Aug. 1936, pp. 526-528.

26. McDowell, R.S.: Centrifugal Distortion Corrections to Calculated
Thermodynamic Functions. 1. Chern. Phys., vol. 39, no. 3, Aug. 1963,
pp. 526-528.
27. Stripp, K.F.; and Kirkwood, J.G.: Asymptotic Expansion of the Partition
Function of the Asymmetric Top. J. Chern. Phys., vol. 19, no. 9, Sept.
1951, pp. 1131-1133.
28. Woolley, H.W.: Effect of Darling-Dennison and Fermi Resonance on
Thermodynamic Functions. 1. Res. Nat. Bur. Stand., vol. 54, no. 5,
May 1955, pp. 299-308.
29. Pennington, R.E.; and Kobe, K.A.: Contributions of Vibrational
Anharmonicity and Rotation-Vibration Interaction to Thermodynamic
Functions. J. Chern. Phys., vol. 22, no. 8, Aug. 1954, pp. 1442-1447.
30. Woolley, H.W.: Calculation of Thermodynamic Functions for Polyatomic
Molecules. J. Res. Nat. Bur. Stand., vol. 56, no. 2, Feb. 1956,
pp. lOS-liO.
31. Woolley H. W.: The Calculation of Thermodynamic Functions for
Asymmetric Rotator Molecules and Other Polyatomic Molecules. Ph.D.
Thesis, Univ. of Michigan, 1955.
32. Lewis, J.D.; Malloy, T.B., Jr.; Chao, T.H.; and Laane, J.: Periodic
Potential Functions for Pseudorotation and Internal Rotation. 1. Mol.
Stmct., vol. 12, no. 3, 1972, pp. 427-449.
33. Janz, OJ.: Estimation of Thermodynamic Properties of Organic Compounds.
Academic Press, Inc., New York, 1958.
34. Reid, R.C.; Prausnitz, J.M.; and Poling, B.E.: The Properties of Gasesand Liquids. Fourth ed., McGraw-HilI. New York, 1987.
35. Benson, S.W., et al.: Additivity Rules for the Estimation of Thermochemical
Properties. Chem. Rev., vol. 69, no. 3, 1969, pp. 279-324.
36. Benson, S.W.: Thermochemical Kinetics: Methods for the Estimationof Thermochemical Data and Rate Parameters. Second ed., John Wileyand Sons, New York, 1976.
37. Stein, S.E.; and Fahr. A.: High Temperature Stabilities of Hydrocarbons.
J. Phys. Chern .. vol. 89, no. 17, 1985, pp. 3714-3725.
38. Scott. D.W.: Correlation of the Chemical Thermodynamic Properties
of Alkane Hydrocarbons. 1. Chern. Phys., vol. 60, no. 8, 1974,
pp. 3144-3165.
39. Pedley. 1.B.; Naylor. R.D.; and Kirby, S.P.: Thermochemical Data of
Organic Compounds. Second ed., Chapman and Hall, New York, 1986.
40. Zeleznik, FJ.; and Gordon, S.: Simultaneous Least-Squares Approximationsof a Function and Its First Integrals with Application to Thermodynamic
Data. NASA TN D-767, 1961.
41. Gordon, S.; and McBride, B.1.: Computer Program for Calculation ofComplex Chemical Equilibrium Compositions, Rocket Performance.
Incident and Reflected Shocks. and Chapman~Jouguet Detonations.
NASA SP-273, 1976.
42. McBride, B.1.; Gordon, S.; and Reno, M.A.: Thermodynamic Functionsfor 50 Reference Elements. NASA TP-3287, 1992.
43. Wilhoit, R.C.: Thermodynamics Research Center Current Data News.
vol. 3, no. 2, 1975.
44. Ervin, K.M., et al: Bond Strengths of Ethylene and Acetylene. J. Am.
Chern. Soc., vol. 112, no. 15, 1990, pr. 5750-5759.
45. Jacox, M.E.: Electronic Energy Levels of Small Polyatomic Transient
Molecules. J. Phys. Chern. Ref. Data, vol. 17. no. 2. 1988, pp. 269-511.
46. Chao, 1.; and Zwolinski, B.l.: Ideal Gas Thermodynamic Properties of
Ethylene and Propylene. J. Phys. Chern. Ref. Data. vol. 4. no. I. 1975.
pp. 251-261.
47. Knippers, W., et al.: Raman Overtone Spectroscopy of Ethylene. Chem.
Phys .. vol. 98, no. I, 1985, pp. 1-6.
48. Frenklach, M.. et al.: Mechanism of Soot Fonnation in Acetylene-Oxygen
Mixtures. Combust. Sci. Technol.. vol. 50, nos. 1-3.1986. pp. 79-115.
49. Burcat, A.; Zeleznik, F.1.; and McBride, BJ.: Ideal Gas Thermodynamic
Properties for the Phenyl, Phenoxy and o-Biphenyl Radicals. NASA
TM-83800, 1985.
50. Atomic Weights of the Elcmcnts, 1985. Pure & Appl. Chen1., vol. 58.
no. 12, 1986. pp. 1677-1692.

55

TABLE I. - FILL PROCEDURE PARAMETERS

b (or

c *)

AtomicnumberChemicalsywbo I

1
2
3

H

2

2

He

1

4

Li

Be
B
C
N
0

8
13
6
15
20
15

2

4
5

F
Ne

6
1

Na

18
33
16
75
170
215
156
61
42
426
1260
3855
7992
11676
12216
9135
4780
1666
362
61
30
159
380
495
366
145
74

6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37

Mg
Al
Si
P
S
Cl

Ar
K
Ca

Sc
Ti
V
Cr
Mn

Fe
Co
Ni
Cu
Zn
Ga
Ge
As
Se
Br

Kr
Rb

I:gi

Atomicnumber

i

4

2
12
30
40
30
12
2
4

2
12
30
40
30
12
2
4

a1170
a3780
a810a
a12096a12852
a9720
a5130
a180a
2
4

2
12
30
40
30
12
2

38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57

Chemicalsymbol
Sr
Y
Zr

Nb
Mo

1: gi

b (or

c*)

i
670
1260
3855

4
a1170
a3780
a8I00

7992
a120~)611676
a12852
Ie
12216
a9720
Ru
9135
Rh
a5130
4780
a18DO
Pd
1666
Ag
394
2
Cd
125
4
In
92
2
Sn
351
12
Sb
860
30
Ie
1135
40
I
846
30
Xe
337
12
124
Cs
2
Ba
1138
4
a1170
La
2200
Lan than ide 5 e r i e s'- 4 f 5 he 1 1 filled
a3780
72
Hf
3855
a8100
73
Ta
7992
a12096W7411676
a12852
12216
75
Re
a9720
Os
76
9135
a5130
Ir
77
4780
a1800
Pt
78
1666
79
Au
434
2
Hg
80
205
4
81
II
132
2
82
591
12
Pb
83
Bi
1460
30
Po
84
1935
40
85
At
1446
30
86
Rn
577
12

aThis is the c* value which represents the total quantum weight for eachvalue of n above the ground state principal quantum number. In BLOCK
DATA, these values are given as negative values in order for the PAC91
program to differentiate the b values from the c* values.

56formula
number1

RRBO aYes

PANOKband
IANAf cYes

NRR.~Old NRRAOZ 6Yes

TABLE 11. - SOME TERMS IN- Sub-

MethodYes

In Qm

sed ptinequatioll
(9)

T~
dT
terms

tE;rmsm
TZ dZ(lnzQ ) termsdT-ze zTo
-T-

czTo
-T-

CzTO
In gm - ~e

In Q AND THEIR DERIVATtVES

Remarks
Definitions

Type of molecule
Oiatomic

Li nearpolyatomic

1inear

Yes

Yes

Yes

NOIl-

~ hc/kz
gm ~ statistical weightC

To - electronic exci tat ion energy

Yes

Yes

Yes

Yes

V

E

i-I

n

n

n

2

E

d i In (Si)i-I

diu i rjS j

E d.ur.s.(u.s.
- 2)
1 \

i-I

I

\

I

Yes

Yes

Yes

I

d i - degeneracyn - number of unique frequencies
u i - c 2 v/T
r . • e-ui
I

3

4

5

Yes

Yes

No

Yes

Yes

Yes

Yes

Yes

Yes

Yes

R

R

For diatomic and linear molecules.
czOoa-In -T-1

For nonlinear molecules.

3/2

11'[0";',"0 (~r]
No

No

p

pT

for IANAf only, pT

-1

-3/Z

0

si • 1/(1 - r i )"1 - we - 2c.J e x e + 3.Z5w eYe + 5w e z e

Yes

No

No

Yes

Yes

Yes

a - symmet ry number

Yes

Yes

No

<1 1 «z<13
BO - Be - 2 + '4 + 8"

No

No

Yes

AO - A - 2d.(I,.
ei-I 1 \

No

No

Yes

Bo - B - 2:

\-1

1

n

1

1

e

No

Yes

Yes

Yes

p

For diatomic and linear polyatomic.

3 3
20
2pT + 10p2r Z + 29° 1 - 38 03

zpT • ZOp2 r Z + z95p3r3

20p ZT2 + 592p3T3

l:n d<1.B1I

l: d.1 C1

No

No

Yes

Co - C

Yes

Yes

No

This line for IANAF only;

e

p = 4
Sa

- 2:

A

En

•

(1 .

1-1

(Dr)
~

"l c z0

•

Yes

Yes

No

p

Yes

No

No

Do - De -Q

p = --2
czB O(except for JANAF)
1S

given or

"1

~2

~3

.

2 + 4 + B ; \ f nol

0

4B 3

given. De -

T
c.J
e

No

'J)

......

YesNo

DO = 0000.--

'..Il:>0

TABLE [[
formulanumberMethodRRHO aPANOKbNRRAOt d

NRRAOZ e

andlANAFc

Sb

No

Yes

Subscript
inequation

In QrnCant inued
1'2 d2j~~Om) terms

l' ~
dT
terms

rerms

(9)

Yes

Yes

p

For spherical top,s.!Eel 4slr 2 1035p3TJ
16+ <\+
2+<\
16875 4T4
JO O

+~-4B

R ¥
+

+

45p2r2~8 +Rema~ks

Diatomic

Linearpolyatomic

Nonlinear

No

No

Yes

45 2 2
JI05pJT3
P T +23 3+ 310~e T +- 16875p4T4

Oefini tions

Type of molecule

Spherical top only
5 = 'CZOo/I°0/C2B6

p -+- 50625p 4T4

a

5c

No

Yes

Yes

Yes

p

For symmetrical top.
(2pz -

PIT +-

2

p~l

T-

~op,

5d

No

Yes

Yes

Yes

p

For asymmetrical

6

No

Yes

Yes

Yes

e

3
2
1
10 ( 1 +- 6- +- -e Z • 6- )T

T

PIT +- (2Pz - p~)TZ

?

r3

pT

pT

0

~el Z6Z 363) 1-T+-?+-Tf ~(29, + 66z2 • 12633 )!.T

No

Yes

Symmetrical top only
(see' for defini tion of'
PI and PZ)

No

No

Yes

Asymmetrical top only
(see" 'for definition of
p for asymmetrical top)

Yes

Yes

No

61 •

_ p~)12

(2PZ

r

No

T

o.e

c B

2 O
-3-., 92

(C B )2z o= -1-5- ,4(C B )3z o

63·~

- [T d(l:To.er

No

No

Yes

Cz [
AoSO
6 1 - 12 2(Ao + Bo .Gol ---c;;-_ AOGO _ BoCa]
6
A
0
O
No

No

Yes

2[

c2
62 = 480

2
2
2
lO(A o • 60 +-Col +-12(A oBO+- AoCo +- BoCol - 12
+

No

Yes

2 2 2 2)(",2 A2~ ,2e2)]

BoCo +- BoC o
AoGo + AoCO
A
+
6
0
o

+7
No

~i'oGo•Ao'i

63 - 0.JLQ+.JLQ+~
cci
B~
A;

TABLE I I. - Cone luded.
MethodFormulanumber

RRHO

a

b
PANDK
and
JANAFCd NRRA02 e

In

rf

T~
terms
dT

terms

2
T d

2

m

(~~Q ) terms~quation

Yes

Yes

Triatomic I inear molecules whereFermi resonance occurs

W

Remarks
Type of 810 lecu Ie

Diatomie

(9)

No

No

7

NRRAOlSubscript
in~)
1 - r1In Qw (5 -C) ,,22

T

In

QW[2u~rwSw(1 + rws,,) No2+ 2u r s (1 + r s 1
2 2 Z
2 2
+ 5Z _ 25 - 2

0

2 2
2" rwSwSz(l - r 1 )jLinearpolyatomic

Non1inear

Yes

No

] j

_ r 1u 1 (u 1 + 2$ - 2) ]
1 - r

1

aRigid-Rotator Harmonie-Osci IlaUJr approximation.
bModi fied PelUlington and Kobe method.
crOinl Army Navy Air Force method.
dNonrigid-Rotator Anharmonic-Oscillator 1.
eNonrigid-Rotator Anharmonic-Oscillator 2.
'For symmetrical top molecules, (see ref. 8)
P1 • - -12[ (8 + 4m + 31112 )D

4c B
2 o
P2

J

+ (2m + 3m2 )DrK+ 3m2 DK]1

3
[
2
3
4 2
2
3
4
4 (
1 2 )
21
--2-4 (128 + 64m .. 48m + 40m + 35m )D ... 2(16m + Z4m + 30m + 35m )D/D
+ 2(8m Z + 20m3 + 35m)
DjD + 2" D
+ 2(10111 3 + 35m 4 lDJKD K + 35m 4DKJ
K
JK
JK
J
32c B

K

2 O

where

Bo/ Ao'ID -"ror asymmetrical top molecules. (see ref. 8)P

1_ [3(:aaaa + 'tbbbb + 't eccc\

16c 2

\

A~

For planar molecules'C aace

'J>

-c

•

B~

'tbebe· 't

c~")
acac

(~C)2 't aaaa +(C)Z~ 'l:aabb+ 2 ('t aabb + 't bbce + 't aaec\

AOB O

BoCa

Aoeo "}+

4~a'oab~liBO\1+ 't bebe + 't acac

BoCa

AOC O

)J

- O. and also the following relations hold:"tbbcc -(~)2"t bbbb+~)2't aabb't

ecce)2 aace +...QG)2 'tb'occ
B

c
_...Q
( AO

't

O

Defini t ions"0 • Fermi resonance cons tantUw -2c Z"2/T

r

e

W

~

-uW

Sw - 1/(1 -r W)
S ~ (1 + 2rWSW)UW + 2(r 2 u2 s Z - 1)0\o

TABLE II I. - TERMS IN
FormulanumberIn Qm

MethodPANDK aNRRAOl c

NRRAOZ

terms

Remarksd

No

Diatomic

Yes

Defini tions

Type of molecule

and
b
JANAF

8

In Q~

e

Linearpolyatomic

NonlinearE . [1122]
i=l diajrjS i 1 + 2 ais i + 6 ais i (1 + f i )Yesd= degeneracyir. = d- Uj
1

Uj = C 2\1 j IT
Sj = 1/(1 - r i )n = number of unique frequencies
Yes

No

No

\11 = we - zwex e + 3.25we Ye + 5w e z e

Yes

No

No

a 1 .. (~1 - <;1.2 - 0.75<>(3)/B O

2:
B n

B

No

Yes

No

ai =

ai

(1+5ij)CL ij

28

j~l

o

0

C' s;C)

No

No

Yes

1 <>'j(Xj<>'iai ~ Z
+
+

Yes

Yes

No

Pi = ai(a i + 1)

Yes

No

No

For PANDK, a 1 - (<>'1 - 2<1 2 - 3.25<>'3)/BO and for JANAF I

t; a;;

n

9

Yes

No

No

l: d.P.r.s.
1 1 1 1

i=1

a

10

No

Yes

Yes

.Ii
n

[2
diaii!isi(aisi + ai!isi + 1) +1-

I:n didjai/i!jSiSj

J-

=

(a

1

- CL Z - 0.75 <>'3)/6 e(~)' +(~) {~)

No

No

Yes

Pi ..

ai (a2i

Yes

No

No

all -

(-«2 - ~ 3) /B O

No

Yes

No

a jj = a i /B O

No

No

Yes

ai j = 0

Yes

6

12 1

n
2 ]
+ ~ djdjajaij(l + 6ij)rifjSiSj

1

Yes

Yes

i j -

1
+ 1) +"40:{O1 forfOf

i ~ jj .. jTABLE II!. - Continued.
FormulanumberIn QID

Method
a

PANDK
and b
JANAF

NRRA01 c

11

No

Yes

Yes

12

No

Yes

Yes

terms

e

NRRAOZ dRemarks
Def ini t ionsType of molecule
Diatornie

Linearpolyatomic

Nonlinear

all1r1s~(1 + 4f 1 + r~) (diatomies only)

Yes

No

No

a

- T

Yes

No

No

For PANDK, Xu = -wex e + 4.5w eYe + 14.5we 2 eczt

d i (d j + °i i )\/irjsisj

lll

i=1

• -cx /B
3 O
andfOf JANAF, X = (-wex e + 4.5w e Ye + 14.5Ule Z e )V/we
ll

i=i

n

-

No

Yes

Yes

Xii = xii + (1.5 d i + 3)Yiii

d

+.Ef

Yiik

k=1

k"i
n

No

Yes

Yes

Xij = Xij + (d i + l)Yiij + (d j + 1)Yijj +

k=l
hi

13

No

Yes

Yes

C 2 t di(d + °ij)(d + 5-Tkik + °jk)YijkrirjrkSiSjsk
j
i=1

i=i

Yes

No

No

Yn1 '" weY e + Bwez e

No

Yes

Yes

Yijk = Yijk

Yes

No

No

G.

No

Yes

Yes

G _ {O if i" j
i - (gii + B )/3 if
O

k=j

n
14

Yes

No

No

C2.E di(d + 0ij)(\j + Gj)rifjSiSj
-T
j
i-1
j-i
24e

4 4

15

No

Yes

Yes

- -r-2 Ul e Z e f 1 S 1 (diatomics only)

16

No

Yes

Yes

- Cz.ET
2g r s 2 (1 - 2a i f i s i )ii i i

n
i,.l
n
17

No

Yes

Yes

1:2.E
2
- T
di(d j + 0ij)(l + °ij)aiXi/ifjSiSj
i-I
j=l

0'

1

=

0

i -

i

d

'l:::t

Yijk

0-

N

TABLE III. - Continued.
FormulanumberIn Qrn

MethodpA.~DKa
and b
IANAf

NRRAOlNo

No

c

NRRA02

termseRemarksdType of moleculeDefini tions

Diatomic

Linearpolyatomic

Nonlinear

Yes

Yes

Yes

!jiik ~ (2 - Sjk)(l + 0ij)(l + 0ik)di(d j + cij)(dk + 0ik)

Yes

Yes

Yes

9 iik = 2(1 + 0ij)(l + 0ik + 0jk)(d i + 0ij)dj(d k + 0ik + 0jk)

Yes

Yes

Yes

!jijkll. = 2(1 + &ij)(1 + &ik + Sill,)di(d j + &ij)(d k + &ik)

Cz):E .
2 n

18

Yes

2
2 2
di(d j + °ij)(l + °ij)Xijrirjsisj

2"1 T

i=l
j=i

19

No

No

Yes

1 (~)
2

2

f;

T

i=1
j=l

2

!j i jkXi j\k r if irks is i 5 k

k-j
2

20

No

No

Yes

1(Cz
) En
- 2

i-I

T

2 2

~i jkXi j Yi jkfi f /kSj S j 5 k

j=i

hI
21

No

No

Yes

-21 (ezY-T i=1En

2

EJi jkll,\ j Yjkll, r i f j fkfll,Sj SjSksll,

x (dll, + Ii i Q. + &kJl.)

i-I
k=1
Il=k

22

No

No

Yes

23

No

No

Yes

(CT2) 2 Eg··f.S.{1+8f.+f.)
n 2
4
Z
i_III

1 1

1

(Cz)z
T
.Iin 2g ii \ j r i f j sis3 j [11

+ 7& i j + f i (1 + 5& i j )]

1-

i=1

(C

24

No

No

Yes

21 TZ)

25

No

No

Yes

2" T

Z

E

255
n
4a. [X .. d. (d. + 1) 1 f. S .
i-I
1
11 1
1
I 1
2

1

(Cz) ~n 9ijaiXijfifjSiSj
2
3 2
1-

j-l

Yes

Yes

Yes

2
!jij - (1 + Sij) d j (d j + 0ij)

TABLE 111. - Conc luded.
In Qm

MethodFor~

mulanumberPANDK aNRRA01 c

terms eRemarks

NRRA02 d

and
b
IANAF

26

No

No

Yes

Defini tions

Type of molecule

1
2"

(r
C2

T

n

.

Diatornic

Linearpolyatomic

Non1inear

Yes

Yes

Yes

~i jk m (1 + 0ij) (1 + 0ik)d i (d j + OJ i )(d k + 0ik)

Yes

Yes

Yes

~iik = (1 + 0ij)(l + 0jk)(2 - 0ik)di(d j + Sij)f(1 + Sik)d k

3.

~ ~iika/ij\kr//ksisisk(l + r i )

j 1
k=l

27

No

No

Yes

m

YE

-12 (c-T2~Mod if i ed Penn i ng t on and Kobe me t hod.
cloint Army Navy Air Force method.
iOllrigid-Rotator Anharmonic-Osci llator 1.
Nonrigid-Rotator Anharmonic-Osci llalor 2.

n
i.1
j=1
km 1

2 2

~i jkai \ jXjkr i r /kSi SjSk

+ &ik + °jk + 0ijOjk 1

eDerivatives:
where
where

0'
'..,..Jcm
In Qc =~i,.J

In Qc.

J

J

2:

=

and

2
2:j In QC i S.) and T2 [d 2 (ln Qm)/dT] - 2: In Q [2: m.u~ r sh (r sh + 1) - 2S .... S~ - P.]
C
j
Cj
i
1
ihi i h i i)))

In Qc.

is a constant; n(n .... m.rh.s h .) - P J••
1

I

1

is any term in formulas 8 to 27 which has the formula)Pj = 0, 1. or 2; C j

S.
uh
Iii
m

T[d(ln Qm)/dT]

1

In Qc.
)

i

and

m.

I

are integer exponents; and

hi

=

p.
(c/T) ICi

IT. rh~sh~
n. m.
1

I

is an integer subscript. and where

1TABLE IV. - BR[Ef' DESCRIPTION Of' CO~n::-;TS Of INPUT RECORDS
RecordID

Labe Is

Comments

Opt ional?

Gives temperature schedule for tables calculated from coefficients if different than original data.
This may be a single value or the beginning or end of aninterval.
This must be preceded by a lower and followed by a higher T
value.

Yes

All data records following a METHOD record must have the S<Jme
record m including the possibi lily of al t blanks. Contentsof the remainder of the record may vary with method.

No

Numerical value

CTEM
T

T, K

I

T increment. K

Yes

data

(See table VI I)

DAn:(Any six
c:ha rac tel's)(blank)Label will appear in the

FINISH(blank)(blank)Indicates the end of a set of input data for a species.

No

formulaSee comments

Chemical formula of species (columns 1 to 12). for remainder ofrecord, see table V. (The word "formula" does not appear on
the record.)No

LISTEf(blank)Calls for listing contents of EF data sets stored in [/0
unt t 13.

Yes

LSTSQSaEXP

qi values in eq. (11).
Fit is to be made with no constraints.
No heat capaci ties to be used in least-squares fi t.
No enlhalpies to be used in least-squares fit.
No entropies to be used in least-squares fit.
Use "old" polynomial form for eq. (11) (e.g., qi; 0,1.2.3.4).

Yes
Yes
Yes
Yes
Yes
Yes

aNOCNSaNOCfJ

aNOH
a~OS

OLD

See comments(blank)T exponent(blank)(blank)(b lank)(blank)(blank)least~squares coefficients

output.

Yes

T

T. K

Temperature at the beginning or end of interval to be fi t.

Yes

TeONST

Constraint T, K

Calls for the data at this tempeiature to be fitted exactly.
Numerical value of T mllst be the saune as some value in
the T schedule. Default value is 298.15 K.

Yes

TPROP

Proper ties T, K

Used in conjunct ion wi th NOH and/or NOS. Speci f ies temperature at which a value of enthalpy and/or entropy is gLven
to obtain integration constants.

Yes

METHOD-----~------

See table VI for details.

No

NAME

------------

Columns 7-24 are reserved for species name and columns 25-80
for comments. 80th to be included with coefficients. See
table VI I I.

Yes

OUWliT

A.TM(bl<3nk)

CTAB
D\ILESS(blank)(blank)(blank)Calls for pressurf1 to be in units of atmospheres. (Default
uni ts are bars.)
Calls for the energy units in the tables to be calories.
Calls for tables of functions calculated from coefficients.
Calls for many-figured tables in dimensionless units.

Yes

CAL

EnAPE

(blank)Calls for the H~ value as well as theYes~fH~ and -tG~ - H~)/RT

Yes
Yes
Yes

data to be put on 1/0 units 11 and 13 for future [og10K
and ~fH~

INTLIl\\JOULf:S
LOCK

LSQS
"WIG

Calls
Calls
Cal Is
Calls
Calls

REF~CEAny a lphaHumer ic
charac tel's

Any a I phamune I' i ccharacters

TF:MP

T

Temperature. K

aM<IY

64

(blank)(blank)(blank}(blank)(blank)requ ira 8n i lit ege r in co I Ufiln 80.

calculations.

for intermediate output data.
for the energy uni ts in the tables to be joules.
for rounded tables including columns for C.fH~ and loglOK.
for least-squared fit of functions.
for tables of many-figured functions.

Yes
Yes
Yes
Yes
Yes
Yes

This may be a single value or the beginning or end of aninterval.

See discuss iOIl in sec t i 011 .. LSTSQS record."

YesTABLE V. - CONTENTS m' F'OR~fl.'LA RECORDS
Labels 2, 3. or 4
HF29S -

Numerical value

Commen t s

An ass igned enthalpy,

Numerically equal to heat offormation at 298.15 K

H~98. 15~

ASI\DH

Use
only
one

DELTAHAn assigned enthalpy. HO
T

Requ i res cor respond i ng
temperature

Heat of forma t ion fromthe assigned reference

Requires corresponding
temperatureelements(ClfHf.)Temperature

T

CAL

....

(Blank)

KCAL
Use
only
one

IO\JU:SKJOlILE
INVCM

EV

...

~ot

required with HF298['ni ts are cal/mol(Blank)Ulli ts are kcal/mol(Blank)Ulti t s are llmol(B lank)IIni ts are k)/ma I(Blank)Uni ts are cm-l/mol(B tank)Uni Is are eV/mol

TABLE VI. - CONTI::HS OF METHOD RI::CORllS
Type ofspeciesAll

Method code(any label)

LabelsNumer ieal

1. 2.3 I
or -l

value

COEF

(blank)Calculate functions from empirical equations.

DMU:SS(b lank)

Coefficients on data records are those ofeqs. (11) to (13).

MEI.TPT

Melting point

See MEL.TPT under

DELIAHHea t oftransi t ion

Used between two phases of the s<Jme species:
code is on MHHOD record of second phase.

DELTAS

Entropy oftransition

Mav be used in lieu of a heat of transition(see label DI::LTAil).

CAL

All

CanU!len ts(blank)See READI ~ be Iow.

REAlll~.

JOULES(blaok)See READIN below.

KCAI.

(blank)See RF.ADIN below.

KJOULE(b lank)

See READ IN be low.

(blank)Read in functions directly.

Rr..\DIN
H2981l0,\IELTPT

H~98 .15 - H~

Uscd in obtaining

Me I t i ng po i n t

Optional information whcn a set of input data
has both sol id and i iquid phCtses.

H~ - il~values when

H~ - H~98.15 values are given.

CAL(blank)Energy units of properties on METIIOD andfollowing data records are calories.

JOULES(blank)Energy uni ts of proper I ies on METHOD andfollowing data records are joules.

KCAL(blank)Energy uni ts for entha tpies on METHOD andfollowing data records are kilocalories.
Other properties are in cnlories.

KJOUL.E(blank)Energy units for enthalpies on MI::THOD andfollowing data records are kilojoulcs.
Other properties are in joules.

65

TAIlU~Type or

species\IH t hod (;ode(any lab~! I)

Lahels
1,2.3.

VI. - COliC luded.

NUlllcriea I
va I Ul~

Commell Is

or-t
MOllatlJRlil.:gases

AI.I.N

FII.L
Mona tomic

FIXEIlN

lor; ludp, a II Ieve Is g i veil in i IIpU t .

(blank)Labels in data recorus are(eq. (7)).

(h IClnk)

See FILL option under FIXF:DN.

Highest principal quantullI
Ilumber tll be
i lie luded incillculat iOlls

gases

Monatomic(blank)2J III +- 1

All llnergy Ip,vels whose principal quantum
Illllllher is less tl18n or oqual to this number

will be inc \ ueled .

(blank)SIlC GLI\Bf:l. np Ii on unde r ALLN.

FII.!.

(blank)Missing energy levels wi II be cstimated andincludlld as discllssed in the sectioll"lm:lusiotl of predicted levels,"(blank)'Cut orr all levels above "reduced" ionizatioll
potential. (Sec section "Internal
Partition Function fur Monatomic CaSES.")

GL.AIlF:l.

(blank)Sec GLAlIE:L opt ion under ALLN.

fiLL(b lilllk)

Sec FILL opt ion under FIXmN.

(0Ii1l1k)(blank)No labels ror this method.

(blank)Calculatiun methud of ref. Ii (see tables II
and III).

{blank)Wi Ihoit exlr<lpolutiun method.
only for linear molecules.

(bl ani<.}Calculation method of refs. 30 and 3l (sec

TEMPERADO=

GLi\!W.1.

gilsesDiatol1lic andpolyalomicgillg;.lses

Diatomic andpo Iya tomi C
gilseslANAI"

Diatomic and(.lolyatomic
gilsesWILl!

l}iatomi c andpolyatomic

NRIlWlLIN!':

t all los II and [II).

gAses\}\atomic andpo Iya tOIRl G
gilsesNHIIM32(blank)Same as NRRA01 wi th some higher ordercorref:tions (see tables II and (II).

Diatomic alllipolya tomi c
gases

PANOK

(bl allk)

Calculation method of ref. 29 (sec tables I [and Ill).

DiatomiG and

RRIIO(blank)Rigid-rotator harmonic-oscillator
approximation (see table 11).

polya tonde
l'.ilSeS

66

LI~E required

TABLE VII
MethodADD

READ IN

COEr- CONTENTS or DATA RECORDS

Labels
1, 2, 3, or 4

Numer ica I
value

Conunents(Group name)

Quanti ty of that group

SYMNO
STATWT

Synune t ry numbe r
Statistical weight

The group names are given in table IX. Each group name isfollowed by the Quant i ty of that group in the species.
Taken to be 1 if ami tted.
Taken to be 1 if omitted.

HRCO~/R cor reC t ion

Any adjustment to ~/R.

SRCO

S~/R cor rec t ion

Any adjustment to S~/R.

T

Temperature, K

One value on each record.

CPCO

Ei ther one of these values on each record.

CP/R

CO/R
p

H-HO

K; - H~

H-H2~ - H~98.15

H-HOIT(~ - HgllTH-H2IT(K; - H~98.15)/T

H-HORT(~ - Hgl/RTp

Anyone of these values on each record.

H-H2RT(H~ - H~98.15)/RT

S

SO
T

SIR

S~/R

-G-HO

-(G~ - Hg)-G-H2-(G~ - H~98 .15)

-GHo/T-(G~ - Hg)/T

Anyone 0 f these va I ues on each record.

-GH2IT-(G~ - H~9B.15)/T-GHORT-(G~ - Hg)/RT-GH2RT-(G~ - H~9!L15)/RT

See conunen t s....

_-----------~----First record may be the same as aforement ioned READIN record
with CO or CO/R value omitted. The data will be used inpp
and b ' inobtaining the integration constants, b2leqs. (12) and (13).

T

Temperature at beginningor end of tempera turerange

Ei (i ~ 1,
2, ...• or 8)

qi

Ci (i " 1.

a.

FIXEDN.
ALLN. orTEMPERaa.1 x R

or

in

a.

1

-~

.....

_----

wi lh DMLESS code in METHOD record.

eq. (11)

CH

b

CH/R

b

CH-HO

b

CHHO/R

b

CS

b

CS/R

b

TCOEf

-------- -- --- ----- --- ---- - - - - - --------- ----_ ... - -- --- - - -in eq. (ll)12, ...• or 8)

Two T labels must precede exporrents and coefficients for thetemperature range.

x R

1

in eq. (12)Use one ifb

Use one ifbl

has not been set by previous enthalpy value.

(eq. (12)

1

x R -

1

Hg (eq. (12) )- Hg/R (eq. (12 ))1

x R (eq. (13))

2(eq. (13»2Temperature at beginningor end of temperature
range included wi thcoefficient outout

IP

Ionization potent ial in
cm- 1

1m value

c

Ihc

m

.

In em

-1

(eq. (7) )2

has not been sel by previous entropy value.

Ca it s for coef f ie ient 5 lo be written on liD units 6 and 10 insame format as least-squares coefficients. Temperature
values should be omi t led if they are the same as the Tvalues above.
Required only wi th TEMPER.

Jm value(1) Does nol have to be right or ie f t -adjus ted.
(2) May be integer, O. or decimal number (if decimal, it canhave only 5 or 0 to right of decimal point).
(31 Must not be left blank'(if 0 tvoe in 01.

afor fILL option (METHOD record) or FIXEDN. the principal quantum number for the data on each record must be incohmms 79 to 80. right-adjusted.

67

TABLE VII. - Continued.
Method1RRHO,
PANDK.
JANAf,NRRAOl, or
NRRA02 bLabels2, 3 or 4

Comments

Numerical
value

SYMNO

Svmmetrv number·

Taken to be I if ami t ted.

STATWT

Taken to be 1 if ami t ted.

BE

Statistical weightI
TO' cmI
BO' cmBe· em- I

WE

we'

WEXE

wexe,

TO
BO

em- 1

Use with excited electronic state.
Be. BO' or 10 value must be included for all molecules.
See comments for label BO. Use only for linear molecules.
Diatomics only.

cm- I
weYe, cm- I
weze. cm- I

WEYE
WEZE

Anharmonic constant oneorder higher thanweze. cm- I(le' cm- I

Diatomics on ly.

<1e :: 0:.1

ALPHAi,(i i 3)<1.1

Bv = Be - (11 (v +~) + (12 (v + ~ALFABi(i 5. 6)/Xi' cm-

Ai j(i. j 5.. 6)<X

ALFAAi(i i 6)<Xi' em

WX4

ALPHAE1y+ <l.3(v +~yLinear polyatomics only.

~.~)]-2: (V d) ttn<' ( d)(-?: <X~(Vin<6ij, cm- 1

8[vl

~

B
e

<1 i

i + ;

<X ij

-

Vi +

vj

i~l

n<6

A

-1

Nonlinear molecules only.

+ d-2 i )A

rvl = Ae

1=1
are the vibrat ional quantum number anddegeneracy respect ively for the i th fundament a I frequency.

v.

where

I

and

di

n<6

B

ALFABi(i ~ 6)

<X.

em
i•

-1

Nonlinear molecules only.

B[vl = Be -!= (l~(Vi +"2?: +"2

di )

I~l

n<6

<1Ci , em-1

ALFACi(i ~ 6)

Nonlinear molecules only.

DE

De' cmBETAi (i i 3)

°i' crnVi

Vi (d i ) or

Vi

I

cm

-1

-1

Yijk' emWO

W (Fermi resonance-1

cons tant) , cm

DO

0

RHO

p, K- IAD

A ' emCO

CO' em

+

=

v.

I

+

and may be omi t ted when

L

Polyatomics only.
Linear polyatomics only.

-1

-1

or

+

Polyatomics only.

o

0000

+

is degeneracy (an integer) ofI
IYiik (i ~ 6,
j .5. 6. k .5. 6)

or

d.

d.
x ij ' crn

00,.

.1) ~2(v ~)2 ~3(V ~yov0e- lB (v +
2

gii' em.- ..

Di a tami cs on ly, where

Xi j ( i .5- 6,
j .5. 6)Gii (i ~ 6)di)Diatamics only.

-13

Vi (d ) ari
(i i 20)<1?(V i

1=1

---

---

-1

Cry] = Ce -Linear palyatomics only.
Polyatornies only.

000

Polyatomics only.
-1

O

-1

Z

An

[A

or

1\0

must be included for all non t inear po lyatomics.

An

Ie

or

Co

must be inc luded for all nonlinear polyatomies.
39

IB

IBxI039, (g)(crn )

B

/1B·

See cammen t s for label BO.

IA

I xl0 39 , (g)(crn2 )A-39
2
AO = h/81T cIA = 2.7992774xlO
II A'

See comments for label AO.

Ie

Ie lO

39

2
, (g)(cm )o - h/81T"2 CIB - 2.7992774XIO-

Co = h/8

lT2 crC = 2.7992774xlO

-39

/ Ie'

See comments for label co.

bFor excIted electroniC states. the data far each state shauld be put on separate records with an identifying nwnber incolumns 79 to 80. Data records for each state must be groupud together.

68

TABLE VI I. - Cone 1uded.
MethodLabelsNumerical
value

1, 2, 3, or 4RRHO,
PANDK,
JANAF.
NRRA01. or
NRRA020(concluded)

Comments'AlBIC

IA'B'CX10117, (g)3(cm)6

Replaces individual values for

I NT ROT

Total number ofinternal rotors

Remaining labels in this table, which appear on records folloll'ing the INTROT record, arc parameters pertaining to internalrotation. Integer in column 79 or 80 indicates to whichrotor parameters belong (maximum of four unique rotors).

AJ'iGLES<201

The number of phase angles in 2". radians (see eq. (10)).
number is not assigned, defaul t value is 201.

BROT

BO' cm- 1

Same as Bo but for internal rotation
BROT = 2.7992774XI0- 39 IIB'

NEL

<187

Number of energy levels to be calculated.

NOUT

<187

Number of energy levels to be printed.

NROTOR1, 2, 3, or 4

Integer speci fying the number of rotors wi th ident ieal
parameters.

ROSY),{

Rotor s~11ll1\etry number

V

Potential, cm- 1

See eq. (10).

Vn(n S- 6)Vnn-fold barrier

IPRINT

lA, IS, and

IC.

If

Default is 187.

Default is O.

Vn (see eq. (10)).

Calls for listing the potential corresponding to the various
phase angles. (Not used to obtain the partition function.)bF'or exci ted electronic states, the data for each state should be put on separate records wi th an identi fying number incolumns 79 to 80. Data records for each state must be grouped together.

69

TABLE VIII. - GENERAL THER\tODYN:UtIC COEFFICIENTS FOR\lAT

General Format:
Contents

RecordFormatSpecies name or formula
Comments - data source

1

Columns

A24

1 to 24A56

25 to 80

Number of T intervals
Optional identification code
Chemical formula. symbols and numberso for gas and non-zero for condensed
Molecular weight
Heat of formation at 298.15 K, J/mol

5(A2.F6.2)
11
F13.5
F15.3

52
53 to 65
66 to 80

Temperature range°
Number of coefficients for Cp

2FIO.311

2 to 21
23

T exponents in empirical equation for Cp
H~98.15 - Hg, J/mol

8F5.1
F15.3

24 to 63
66 to 80

4First five coefficients

5016.81 to 80

5Last three coefficients for3016.81 to 48~D16.849 to 80

2

3

12
A6

a

.
I ntegratloncons t an t s f or

Repeat 3,

CO
P
HOIRT
T

an d

SOT/R

2

.!.

4 to 911 to 50

and 5 for each interval.

4,

Examp Ie:
S1H+
S1LYL1DYNE ION. JANAF DEC, 1971.
2 J12/71 81 1.00H
1.00E -1.00
0.00
0.00 a29.09289
1147671.200
298.150 1000.000 7 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0
8654.259-4.28447370d+04 3.85838948d+02 2.55865994d+00 -6.98804091d-04 5. 22573029d-06-4.84510719d-09 1.45288S97d-12 O.OOOOOOOOd+OO 1.34921l90d+05 8.95659370d+00
1000.000 6000.000 7 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0
8654.259

1.70438606d+05 -1.04392569d+03

4.83677344d+OO

1.28725833d-04 -6.90835693d-08

1.42207295d-l1 -7.87210915d-16

O.OOOOOOOOd+OO

1.43159900d+05 -7.5396S976d+OO

Empirical equations for above example (from eqs. (11) to (13)):

Hea t capac i ty:

70

Enthalpy:

HO
TRT

En t ropy:

SO
T
R

'=

b
T.'). .
-1
T3 +
T4
1
T
-2
-a 1T + azT
In T + a 3 + a 4 Z + a+ a a7 5 + T
6 4
5 3

-a 1

T- 2
2

azT

-1

2

+

a

3

T
In T + a T + a 2
4

5

+

3
T4
a6 T
+ a
+ b
7 4
2
3

TABLE IX. - GROUP NOTATION AND STRUCTURE
Group

number

PAC91
group

Benson notation

Structure

Atoms
contained
in group

Referenceforthe rmod.ynam i c
data

C#C#C

C

36

C

36

C

37

C

37

C

37

CH

37

C----e;-e

C

36

c-l-o

C

36

C

36

CH

36

CH

37

(ref. 36 )labe 1

1

CA

Ca

2

CBC

CB - (C)3

CBCB

CB - (CB)

4:

CBCD

CB - (Cd)5

CBCT

CB - (Cd6

CBH

CB - (H)7

CDC2

Cd - (Cb

8

CDCBC

Cd

9

CDCDC

Cd - (Cd)(C)-(CB) (C)10

CDHC

Cd - (H) (C)

11

CDHCB

Cd - (CB)( H)

O-e
0-0
(ty=

O--c=
OCH
1::-;':;

.

:lr

JL I

C-€-C=

H
'J:

~:C-C

H

=CD

.. ,.........

71

TABLE IX. - Continued.
Group

PAC91

nLUllbe r

group

Benson no ta t ion(ref. 36)

Structure

Atoms

contained
in group

Label

II

Referenceforthermodynamic
data

12

CDHCD

Cd - (Cd) (H)

EC~=

CH

37

13

CDHCT

Cd - (Ct)(H)

~
?d-e=

CH

37

14

CDH2

Cd - (H)2

¥C#H

CHZ

37

15

CHC3

C - (H) (C)3

C~e-C

CH

36

CH

36

CH

36

CH

36

CHZ

36

m

C

16

CHCBC2C - (CB ) (C )2(H)

17

CHCDCZC - (Cd )( C)2(H )

.' H
,':k,

C1D
C
.,

,

C~1'=
C

H

18

CHeTCZC - (Ct) (C)z (H)J{C--¥:-c=
C

19

CH2C2

C - (H)2(C)2:~

C-41-C::'1;':~H

72

TABLE IX.
Group
number

PAC91
group
label

Benson notation(ref. 36)~

Continued.

Structure

Atoms
contained
in group

Referenceforthermodynamic
data

20

CH2CBCC - (CB)(C)(H)2

~

c~
H

CHZ

36

21

CH2

36

22

CH2

36

23

CH2CDCC - (CdHC) (H)2

24

CH2CTCC - (Ct)(C)(H)Z

25

CH3C

C - (H)3(C)

26

CTC

Ct - (C)

~gC~

C

36

27

CTCB

Ct - (CB)

;$~

C

37

36

CH2

36

36

73

TABLE IX. - Concluded.

74

Group
number

PAC91
group
label

28

Benson notation(ref. 36)

Structure

Atoms
contained
in group

Referenceforthermodynamic
data

CTCD

C

37

29

CTCT

c

37

30

CTH

Ct - (H)

CH

37

31

HC2H

H - ACETYL

32

HPHEN

33

34

It-C=C-HH

see

H - PHENYL

H

see "Input"

HVIN

H - VINYL

H

see "Input':

HVINS

H - STABILIZED
VINYL

H

see "Input"'1

I npu t "

TABLE X. - GROUP ADDITIVITY COEFFICIENTSCA
2 BEN76 C 1.00
0.00
0.00
0.00
0.00 012.01100
17210.010
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0
6.20131064d-Ol 6.55685438d-03 -8.40971939d-06 5.34237173d-09 -1.34221334d-12
1.67980617d+04 -2.13964424d+00
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
1.70014134d+OO 2.13036557d-03 -1.46491180d-06 4.57867726d-IO -5.30959813d-14
1.65796625d+04 -7.34011722d+00

CBe

2 BEN76 C 1.00
0.00
0.00
0.00
0.00 012.011002772.724
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0
1.10379898d+00 -1.40207754d-03 1.01721889d-05 -1.04915786d-08 3.35530569d-12
2.43522265d+03 -1.01067689d+Ol
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
1.18859776d+OO 2.62679100d-03 -1.40397450d-06 3.62315999d-lO -3.62315999d-14
2.1S954456d+03 -1.17034055d+Ol

CBCB

2 S&F85 C 1.00H 0.00
298.150 1000.000 5 0.0

0.00
0.00
1.0 2.0 3.0

0.00 0
4.0

12.011000.000-9.07225320d-Ol 1.21274570d-02 -1.59921140d-05 1.06772290d-08 -2.88771260d-12
2.34891290d+03 -2.17231890d+OO
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
1.·64937250d+00 2.43505820d-03 ~1.40110120d-06 3.74624350d-lO -3.82283850d-14
1.78059830d+03 -1.47139470d+Ol
eBCD
2 S&F85 C 1.00H 0.00
0.00
0.00
0.00 012.011000.000
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0
1.89361290d+00 -3.63320180d-03 1.33476670d-05 -1.32062840d-08 4.38875210d-12
2.36121080d+03 -1.41160640d+01
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
6.57951850d-Ol 3.79153180d-03 -2.18052300d-06 5.80353650d-10 -5.87829120d-14
2.50341600d+03 -8.72472110d+00
CBCT
2 S&F85 C 1.DOH 0.00
0.00
0.00
0.00 012.011000.000
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0
1.89361290d+OO -3.63320180d-03 1.33476670d-05 -1.32062840d-OS 4.38875210d-12
2.36121080d+03 -1.58018030d+Ol
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
6.57951850d-Ol 3.791531S0d-03 -2.18052300d-06 5.80353650d-l0 -5.87829120d-14
2.5034160od+03 -1.04104590d+Ol
CBH
2 S&F85 C 1.00H 1.00
0.00
0.00
0.00 013.01894
0.000
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0-8.59079180d-Ol 1.01575080d-02 -6.05790130d-06 1.11817290d-10 8.76799660d-13
1.51812920d+03 7.93471810d+OO
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
8.12920500d-Ol 5.70326930d-03 -2.94688640d-06 7.32625720d-IO -7.11722860d-14
1.07063610d+03 -6.86258470d-Ol
eDe2
2 BEN76 C 1.00
0.00
0.00
0.00
0.00 012.01100
5203.260
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0
1.57567141d-02 1.20990725d-02 -2.3939S157d-05 2.39017773d-08 -9.01711547d-12
4.82932602d+03 -9.21726687d+00
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
2.25642353d+OO 1.36203978d-03 -7.27986777d-07 1.87867555d-10 -1.87867555d-14
4.34871092d+03 -1.99090723d+Ol
75

TABLE X. - Continued.

CDCBC
2 BEN76 C 1.00
0.00
0.00
0.00
0.00 012.011004347.792
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0-Z.15050677d+00 2.56218701d-02 -4.82075840d-05 4.17875044d-08 -1.37198166d-l1
4.19996194d+03 -9.32804085d-Ol
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
3.04446083d+00 4.86442777d-04 -2.59995277d-07 6.70955554d-11 -6.70955554d-15
3.27765919d+03 -2.51782099d+Ol

CDCDC

2 BEN76 C 1.00
0.00
0.00
0.00
0.00 012.011004468.564
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0-2.15050677d+OO 2.56218701d-02 -4.82075840d-05 4.17875044d-08 -1.37198166d-ll
4.32073394d+03 -9.32804085d-01
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
3.04446083d+OO 4.86442777d-04 -2.59995277d-07 6.70955554d-l1 -6.70955554d-15
3.39843119d+03 -2.51782099d+Ol

CDHC

2 BEN76 C I.OOH
1.00
0.00
0.00
0.00 013.01894
4322.631
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0
3.87658435d-01 6.91462635d-03 -4.92473068d-06 3.06564147d-09 -1.19103098d-12
3.93773106d+03 -6.55229S55d-02
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
1.76953318d+OO 3.63735034d-03 -1.323928S0d-06 1.71399S42d-lO -2.18997389d-15
3.4800192Dd+03 -7.46676354d+00
CDHCB
2 S&F85 C 1.DOH
1.00
0.00
0.00
0.00 013.01894
0.000
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0-1.77479380d+OO 2.03672900d-02 -2.92063140d-05 2.13900470d-08 -6.19476560d-123.25431500d+03 8.37139370d+00
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
2.16078460d+OO 3.89973620d-03 -1.87505280d-06 4.40575310d-10 -4.10819930d-14
2.44872450d+03 -1.05679580d+01
CDHen
2 S&F85 C 1.00H
1.00
0.00
0.00
0.00 013.01894
0.000
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0-1.77479380d+00 2.03672900d-02 -2.92063140d-05 2.13900470d-08 -6.19476560d-123.25431500d+03 8.37139370d+00
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
2.16078460d+OO 3.89973620d-03 -1.87505280d-06 4.40575310d-10 -4.10819930d-14
2.44872440d+03 -1.05679580d+Ol
CDHCT
2 S&F85 C 1.00H
1.00
0.00
0.00
0.00 013.01894
0.000
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0-1.77479380d+00 2.03672900d-02 -2.92063140d-05 2.13900470d-08 -6.19476560d-123.25431500d+03 9.20168260d+00
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
2. 16078460d+00 3.89973620d-03 -1.87505280d-06 4.40575310d-10 -4.10819930d-14
2.44872450d+03 -9.73766950d+00
CDH2
2 S&F85 C 1.00H
2.00
0.00
0.00
0.00 O.
14.02688
0.000
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0
7.08636360d-Ol 5.71738370d-03 3.97432860d-06 -8.14882140d-09 3.39759220d-12
2. 66405290d+03 8.03997270d+00
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
7.62035270d-Ol 7.90072810d-03 -3.83366760d-06 9.04921890d-10 -8.42780610d-14
2.55458540d+03 7.24431290d+OO
76

TABLE X. - Continued.
CHe3
2 BEN76 C 1.00H 1.00
0.00
0.00
0.00 013.01894-956.112298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0-1.21199942d+00 1.57135839d-02 -1.58129928d-05 8.16308832d-09 -1.79427286d-12-1.16875169d+03 -3.21908314d+OO
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
4.21180248d+00 8.18242540d-OS 1.33950798d-06 -6.698623S9d-10 9.41347774d-14-2.66361789d+03 -3.11576551d+Ol
CHCBC2
2 BEN76 C I.OOH
1.00
0.00
0.00
0.00 013.01894-493.152298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0-2.70626696d+00 2.55442809d-02 -3.35585641d-05 2.09055818d-08 -5.02705367d-12-5.64094599d+02 3.00591586d+OO
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
3.92458678d+OO 2.09170394d-03 -1.11797969d-06 2.88510888d-10 -2.88510888d-14-2.12756082d+03 -2.99433080d+01
CHCDC2
2 BEN76 C 1.00H
1.00
0.00
0.00
0.00 013.01894-744.761
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0-2.69178809d+OO 2.27174202d-02 -2.67597650d-05 1.50516772d-08 -3.18914467d-12-7.43740880d+02 3.74363064d+OO
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
2.00129268d+00 5.30222627d-03 -2.83394852d-06 7.31341554d-10 -7.31341554d-14-1.74761503d+03 -1.92282945d+Ol
CHCTC2
2 BEN76 C 1.00H 1.00
0.00
0.00
0.00 013.01894-865.533
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0-2.29967144d+OO 2.07315703d-02 -2.60278088d-05 1.75696487d-08 -4.99182528d-12-9.03749304d+02 2.30198068d+OO
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
I I.48247630d+OO 5.93460188d-03 -3.17194238d-06 8.18565776d-10 -8.18565777d-14-1.70025797d+03 -1.60989330d+Ol
CH2C2
2 BEN76 C 1.00H
2.00
0.00
0.00
0.00 014.02688-2480.858
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0
2.95576901d-Ol 8.26548665d-03 2.02730929d-06 -8.22251499d-09 3.84394234d-12-2.93983603d+03 5.66809199d-Ol
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
8.95359335d-Ol 8.82630650d-03 -4.51610338d-06 1.11218836d-09 -1.07950628d-13-3.18218807d+03 -2.98904913d+OO
CH2CBC
2 BEN76 C I.OOH
2.00
0.00
0.00
0.00 014.02688-2445.633
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0-1.61079486d+00 2.13020824d-02 -2.44229173d-05 1.42423100d-08 -3.20026830d-12-2.72304502d+03 8.492S0374d+00
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
2.81096829d+00 5.93460188d-03 -3.17194238d-06 8.18565777d-10 -8.18565777d-14-3.81247249d+03 -1.36149824d+01

CH2CBD2 BEN76 C I.DOH
2.00
0.00
0.00
0.00 014.02688-2158.799
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0-2.99489148d+DO 2.49586869d-02 -2.77613624d-05 1.47398773d-08 -2.60172081d-12-2.15783856d+03 1.58638825d+01
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
I.17752700d+OO 8.75596999d-03 -4.67991499d-06 1.20772000d-09 -1.20772000d-13-3.03586486d+03 -4.40568818d+OO
77

TABLE X. - Continued.
CH2CD2
2 BEN76 C 1.00H 2.00
0.00
0.00
0.00 014.02688-2158.799
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0-2.99489148d+OO 2.49586869d-02 -2.77613624d-05 1.47398773d-08 -2.60172081d-12-2. 15783856d+03 1.58638825d+Ol1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
1.17752700d+00 8.75596999d-03 -4.67991499d-06 1.20772000d-09 -1.20772000d-13-3.03586486d+03 -4.40568818d+00

CH2CDC
2 BEN76 C 1.00H 2.00
0.00
0.00
0.00 014.02688-2395.311
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0-9.84166104d-01 1.4l467063d-02 -7.15413971d-06 -2.15080256d-09 2.42261065d-12-2.66434595d+03 6.65325780d+OO
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
8.B7674198d-Ol 9.14512421d-03 -4.88791121d-06 1.26139644d-09 -1.26139644d-13-3.13410437d+03 -2.90870113d+00
CH2CTC
2 BEN76 C I.OOH 2.00
0.00
0.00
0.00 014.02688-2380.215
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0-7.61851269d-01 1.30343429d-02 -7.51763250d-06 4.44629802d-lO 9.34733367d-13-2.66730666d+03 5.96602298d+00
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
3.688578l6d-Ol 9.77749982d-03 -5.22590507d-06 1.34862066d-09 -1.34862066d-13-2.94558197d+03 2.32409280d-01
CH3C
2 BEN76 C 1.00H 3.00
0.00
0.00
0.00 015.03482-5132.810
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0
9.67091211d-Ol 4.54272496d-03 1.40931220d-05 -2.03529587d-08 8.18255263d-12-5.71121159d+03 7.97556073d+00
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0-6.27511183d-Ol 1.36690420d-02 -7.30586729d-06 1.88538511d-09 -1.88538511d-13-5.43213903d+03 1.52438529d+Ol
CTC
2 BEN76 C 1.00
0.00
0.00
0.00
0.00 012.01100
13863.619
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0
8.02437417d-01 3.49837285d-03 -4.15397270d-06 4.07988802d-09 -1.75083632d-12
1.34983448d+04 -2.26753348d+OO
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
1.24244195d+OO 2.09170394d-03 -1.11797969d-06 2.88510888d-10 -2.88510888d-14
1.33531243d+04 -4.58500863d+OO
CTCB
2 S&F85 C 1.00H 0.00
0.00
0.00
0.00 012.011000.000
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0-3.49384520d+00 2.72321320d-02 -4.76891040d-05 3.86559630d-08 -1.19225380d-l1
1.33155360d+04 1.68245410d+Ol
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
2.28560130d+OO 8.22574900d-04 -4.14361390d-07 1.03588260d-10 -1.03983680d-14
1.22382860d+04 -1.04535l80d+Ol
ClCO
2 S&F85 C 1.00H 0.00
0.00
0.00
0.00 012.011000.000
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0
7.72587840d-Ol 1.44159610d-03 2.24535910d-06 -3.27337130d-09 1.18176800d-12
1.38820450d+04 -1.66930970d+00
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
4.49136330d-Ol 3.36057940d-03 -1.88820530d-06 4.95862840d-10 -4.98295890d-14
1.39278700d+04 -2.35699140d-01

78

TABLE X. - Concluded.

CTeT
2 S&F85 C 1.00H 0.00
0.00
0.00
0.00 012.011000.000
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0
9.09050340d-03 9.68282400d-03 -1.61930660d-05 1.34477210d-08 -4.31250880d-12
1.25675030d+04 6.29563560d-Ol
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
1.61375010d+00 1.75286410d-03 -9.50741270d-07 2.44108940d-lO -2.42282270d-14
1.22902950d+04 -6.81710090d+00

CTH

2 S&F85 C 1.00H 1.00
0.00
0.00
0.00 013.01894
0.000
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0
3.22062990d-01 1.23444940d-02 -1.94881630d-05 1.58382730d-08 -4.95581450d-12
1.30498420d+04 7.64972930d+00
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0
2.08408360d+OO 3.00946820d-03 -1.27530500d-06 2.64569910d-l0 -2.18420530d-14
1.27910130d+04 -3.35539540d-Ol
HVIN
C2H4 - C2H3
2 L 2/91 H 1.00
0.00
0.00
0.00
0.00 01.00794-625071.953
0.000
200.000 1000.000 5 0.0 1.0 2.0 3.0 4.0 0.0 0.0 0.0
7.46735360d-01 -9.08531026d-03 3.11780593d-05 -3.33930685d-08 1.22733472d-11
O.OOOOOOOOd+OO O.OOOOOOOOd+OO O.OOOOOOOOd+OO -7.52125326d+04 -2.33376993d+OO
1000.000 6000.000 5 0.0 1.0 2.0 3.0 4.0 0.0 0.0 0.0
0.000-3.59257940d-01 2.99014152d-03 -1.07409461d-06 1.73348003d-10 -1.03738147d-14
O.OOOOOOOOd+OO O.OOOOOOOOd+OO O.OOOOOOOOd+OO -7.53284072d+04 1.23891111d+00
HVINS
C2H4 - C2H3 + 8 kcal correction on H.
2 L 2/91 H 1.00
0.00
0.00
0.00
0.00 01.00794-591599.953
0.000
200.000 1000.000 5 0.0 1.0 2.0 3.0 4.0 0.0 0.0 0.0
7.46735360d-Ol -9.08531026d-03 3.11780593d-05 -3.33930685d-08 1.22733472d-11
O.OOOOOOOOd+OO O.OOOOOOOOd+OO O.OOOOOOOOd+OO -7.11867993d+04 -2.33376993d+00
0.000
1000.000 6000.000 5 0.0 1.0 2.0 3.0 4.0 0.0 0.0 0.0-3.59257940d-Ol 2.99014152d-03 -1.07409461d-06 1.73348003d-10 -1.03738147d-14
O.OOOOOOOOd+OO O.OOOOOOOOd+OO O.OOOOOOOOd+OO -7.13026738d+04 1.23891111d+00
HPHEN
C6H6 - C6H5
2 L 1/91 H 1.00
0.00
0.00
0.00
0.00 01.00794-254320.000
0.000
200.000 1000.000 5 0.0 1.0 2.0 3.0 4.0 0.0 0.0 0.0-2.06302352d-01 -8.15243200d-04 1.43769315d-05 -1.9S9SS059d-08 8.17474280d-12
O.OOOOOOOOd+OO O.OOOOOOOOd+OO O.OOOOOOOOd+OO -3.0S819013d+04 1.10333770d+OO
1000.000 6000.000 5 0.0 1.0 2.0 3.0 4.0 0.0 0.0 0.0
0.000
3.06920100d-Ol 2.32195120d-03 -8.16396860d-07 1.29838420d-10 -7.68981960d-15
O.OOOOOOOOd+OO O.OOOOOOOOd+OO O.OOOOOOOOd+OO -3.08941277d+04 -2.51191430d+OO
HC2H
C2H2 - C2H1
2 L 3/91 H 1.00
0.00
0.00
0.00
0.00 01.00794-331613.472
0.000
298.150 1000.000 5 0.0 1.0 2.0 3.0 4.0 0.0 0.0 0.0-3.22796852d+00 1.87214852d-02 -3.02272137d-OS 2.39352994d-08 -7.26880375d-12
O.OOOOOOOOd+OO O.OOOOOOOOd+OO O.OOOOOOOod+OO -3.95302119d+04 1.38493147d+Ol
0.000
1000.000 3000.000 5 0.0 1.0 2.0 3.0 4.0 0.0 0.0 0.0-5. 51834000d-02 3.119S2519d-03 -1.41953706d-06 3.15909714d-l0 -2.79158072d-14
O.OOOOOOOOd+OO O.OOOOOOOOd+OO O.OOOOOOOOd+OO -4.00479060d+04 -8.06478801d-Ol

70

TABLE XI. - INDEX OF INPUT RECORD ID'S AND LABELS
Input

Type

Example nwnber(appendix D)

code
ADO

ALtN
ALPHAE
ALPHAiALFABi
ALFAi j
ALFAAiALFABi
ALFACiANGLESaASINDHa
ATM
AD
BAR
BE
BETAl
BROT
BO
Ci
CAL
CH
CH/R

CH-HO
CHHQ/R
COEF
CP

CP/R
CS
CS/R
CTAB
CTEM

CO

Label
Label
Labe tLabel
Labe 1
Label
Label
Label
Label
Label
Label
Label
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2

Pages
where discussed

VI
VI , VI I

6,10,17, 18,19,23~24
6,10,15.16,19.22

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7

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5

VII
VII
VII
VI I

0

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5

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5

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18

3

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11,19

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7

5
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6,8
3,6,8

11

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VI I
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10,11,16,19.24

1,6,7

IV

9,19,21

6,7

IV

8,9,12,15,16,21,24

5

VI I

aprogram checks first four characters only.

80

Table
numberTABLE XI. - Con t i nued.
Input
code
data

DATE
DE:
D~;LTA.H

DELTAS
DMLF.SSa
DO
0000

Ei
EFDA
EFTAPEaEV
EXP
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FINISHaFIXEDNa
formula b-G-HO-CHO/T-CHORT-G-H2-CH2/T-GH2RT
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numberPages
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IV,VI.VII
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VI

1,3,4

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9.10.11,15,16,17,18,19,21
9,15.17,2:.l7,12,16
7 . 12,16
9.19,21

8,10,11,15,17,23
9,10.17,19,21,23
10,18
6,12,16,22
8,9.10,15,17,24
6.10,15,16,19.22
71

9.15,17,2:.l16

aprogram checks first four characters only.
bFirst 12 columns of record are reserved for chemical formula.
81

TABLE XI. - Continued.
Input
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Type

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11, 17

IV
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VII
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4

aprogram checks first four characters only.
cLabels are nwnerical values of 1m or gm (eq. (7)).

82

VII
IV

7,18

TABLE XI. - Continued.

Input
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Type

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where discussed
IV

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83TABLE XI. - Cone 1uded .
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T4-;1 ~1.'O:t ~I~,oK T=TOForm Approved
OMB No. 0704-0188

REPORT DOCUMENTATION PAGE

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources,
gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of thiscollection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson
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1. AGENCY USE ONLY (Leave blank)

2. REPORT DATE

3. REPORT TYPE AND DATES COVEREDTechnical Memorandum

November 1992
4. TITLE AND SUBTITLE

5. FUNDING NUMBERS

Computer Program for Calculating and Fitting Thermodynamic Functions
WU–505–62–52–00

6. AUTHOR(S)

Bonnie J. McBride and Sanford Gordon
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)8. PERFORMING ORGANIZATIONREPORT NUMBER

National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135 – 3191

E–5894

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)10. SPONSORING/MONITORINGAGENCY REPORT NUMBER

National Aeronautics and Space Administration
Washington, DC 20546– 0001

NASA RP–1271

11. SUPPLEMENTARY NOTESBonnie J. McBride, NASA Lewis Research Center. Sanford Gordon, Sanford Gordon and Associates under contract to
Sverdrup Technology, Inc., Lewis Research Center Group, 2001 Aerospace Parkway, Brook Park, Ohio 44142 (workfunded by NASA Contract NAS3–25266). Responsible person, Bonnie J. McBride, 216–433–5870.
12a. DISTRIBUTION/AVAILABILITY STATEMENT

12b. DISTRIBUTION CODE

Unclassified - Unlimited
Subject Categories: 77
Available electronically at http://gltrs.grc.nasa.gov/GLTRSThis publication is available from the NASA Center for AeroSpace Information, 301–621–0390.
13. ABSTRACT (Maximum 200 words)

A computer program is described which (1) calculates thermodynamic functions (heat capacity, enthalpy, entropy, and freeenergy) for several optional forms of the partition function, (2) fits these functions to empirical equations by means of aleast-squares fit, and (3) calculates, as a function of temperature, heats of formation and equilibrium constants. The
program provides several methods for calculating ideal gas properties. For monatomic gases, three methods are given
which differ in the technique used for truncating the partition function. For diatomic and polyatomic molecules, fivemethods are given which differ in the corrections to the rigid-rotator harmonic-oscillator approximation. A method for
estimating thermodynamic functions for some species is also given.

14. SUBJECT TERMS

15. NUMBER OF PAGES

Thermochemical properties; Thermodynamic properties; Computational chemistry; Computer
programs; Diatomic molecules; Monatomic molecules; Polyatomic molecules; Molecular ions;
Statistical mechanics; Ideal gas
17. SECURITY CLASSIFICATIONOF REPORT

18. SECURITY CLASSIFICATION
OF THIS PAGE

Unclassified

Unclassified

NSN 7540-01-280-5500

19. SECURITY CLASSIFICATION
OF ABSTRACT

92
16. PRICE CODE

A05
20. LIMITATION OF ABSTRACT

Unclassified
Standard Form 298 (Rev. 2-89)
Prescribed by ANSI Std. Z39-18
298-102