(D.1)

APPENDIX A. Description of the rotor program, iar95.exe.

The "internal axis rotor" program, iar95.exe, has been written in the C

programming language to ca lculate rotational transition energies and intensities

betwe en one or two states each having a rotational Hamiltonian of the gene ral form,

The program calculates transition intensities between the eigenstates of Eq. (D.1)

following the formalism developed in Appendix B. Furthermore, the program use s no

symmetry to obtain the eigenvalues and eigenvectors of Eq (D.1) and does not impose

any selec tion rules on the ca lculation of transition intensities. The re ason for this

approach is a result of the relaxation of the selection rules that occur with the symmetry

reduction of the Hamiltonian as discussed in Ref. 2. The program also allows for

inertial axis rotation defined in terms of the Euler angles, , , and of one or both

states prior to diagona lization of the Hamiltonian matrix. Rotational perturbations

arising from inertial axis reorientation are thereby treatable when only one state's Euler

angle(s) are non-zero. When the Euler angles in both states are identical but non-zero,

non-principal methods (internal axis methods) are applicable and provide a useful and

convenient method for the treatment of perturbations terms like those given in Eq. (D.1)

that do not lie along the principal axes. The program operates in five phases.

Phase I is the parameter input and assigned line input phase.

Phase II is applie d twice, once for each state, and calculates the Hamiltonian

matrix for each J block. This consists of the matrix elements for all operators in Eq.

(D.1) having non-zero parameter va lues. Operators for which g = c in Eq. (D.1) are

treated as purely imaginary elements. Each matrix is diagona lized to give the

eigenvalues and eigenvectors which are then saved to file with the corresp onding

quantum numbers. The eigenvectors also are used to calculate the derivatives of the

expectation values of each operator in Eq. (D.1) with respect to its corresponding

parameter. These also are saved to file to be used later in a least squares analysis phase

(Phase 4). When the internal axis method is employed, the derivatives with respect to

A, B, and C are back-transformed to the principal axis derivatives to eliminate from the

least squares fit the additional (and unnecessary) cross term parameters.

Having the eigenvectors (real and possible imaginary), quantum numbers and

derivatives for each eigenvalue in each elec tronic state, Phase III calculates the

transition intensities between the levels of each state according to the selection rules

J = -1 (P), 0 (Q) and +1 (R) in the sequence R(0), P(1), Q(1), R(1), @@@ Q(Jmax). The

eigenvalues, eigenvectors, quantum numbers (JKaKc) and derivatives of each J block

for each state are first read from files. Intensities between all permutations of the K

sublevels within the value of the Korder are then calculated. The a-, b- and c-type sums

are performed individually and the band type components are scaled according to the
transition moment projection factors calculated in Phase I. The band type components

are then summed, squared (squared modulus when complex) and multiplied by a

Boltzmann factor. The quantum numbe rs of the calculated line are compared with

those observed. When a match is found or the calculated line intensity exceeds a

predefined minimum intensity cutoff, the observed and calculated transition energies,

intensity, associated quantum numbers and band type are saved to disk. The sum of

all such lines constitutes the final line set.

When no linear least squares analysis is desired, Phase IV reads the line set and

orders all lines ac cording to the calculated transition ene rgies and writes out a

formatted lineset for input into the analysis program, jb95.exe. The program then

terminates.

Phase V performs a linear least squares fit analysis (LSF) of the adjustable

parameters (specified on input) in order to minimize the sum of the obse rved minus

calculated energy differences. The phase operates in two nested cycles. The outer

cycle (slowest varying) calls Phases II and III repeatedly until the cycle count specified

on input is exceeded. Exact energies and derivatives are therefore used in the LSF

analysis based on the best fit pa rame ters from the previous cycle. The inne r cyc le

utilizes the old de rivatives and new parameters to obtain new but approximate

calculated energies. The new energy differences (OMC) are then used to determine

whether additional assigned lines will be acc epted in the next inner cycle. If no

additional lines are accepted based on the rejection level specified on input, the inner

cycle terminates.

Phase V terminates with an error if a) the number of fitted parameters exceeds

the number of observed lines accepted in the fit; b) linear dependence is found when

solving the system of equations; or c) a negative A, B or C parameter is generated.

Otherwise Phase V logs the best fit parameters and standa rd deviation of each

parameter as well as the overall OMC standard deviation for all accepted lines.

Phase III is called on termination of Phase V to calculate transition energies

based on the old derivatives and new parameters. The line set is ordered and written

out in a format for input to the analysis program, jb95.exe.
(B.7)

(B.8)

(B.5)

(B.6)

(5.17)

(5.18)

(5.19)

(5.20)

APPENDIX B. Matrix elements and transition intensity calculation used in iar95.exe.

Hamiltonian matrix elements

The symmetric rotor functions, *JK , provide a convenient ba sis set for the

Hamiltonian given in Eq. D.1. The matrix elements that form the Hamiltonian matrix

are given by2

Transition intensities

In isotropic magne tic field free space , the intensity, I, of a given rovibronic line

may be written as

where gN is the nuclear spin weighting factor. S is the line strength factor given by

where JKaKc are the a symmetric rotor wavefunctions labeled with the total angular

momentum quantum number J and the prolate and oblate symmetric top quantum

numbers Ka and Kc. μ

^

 is the elec tric dipole moment operator and the sum is over a ll

magnetic sublevels, M, of both states. S may be redefined in terms of the space-fixed

Z component of μ

^

 as

which becomes
(5.21)

(5.22)

(5.23)

(5.24)

(5.25)

when the dipole moment is expressed in spherical tensor form and referenced to the

molecular fixed frame. The eigenfunctions of the rotational Hamiltonian may always

be expanded in a basis of symmetric top functions, *JKM , or in terms of the rotation

matrices, D

J

M

*

K

, by

Substitution of Eq. (5.21) into Eq. (5.20) gives

where we have used the property that

and the Wigner 3-J (W3J) symbol relation

Rearranging Eq. (5.22) gives

Here, we have used the symmetry properties of the W3J symbols and the orthogonality

relation
(5.26)

(5.27)

(5.28)

(5.29)

(5.30)

(5.31)

(5.32)

Finally, we express Eq. (5.25) in terms of the Clebs ch-Gordan coefficients using

yielding 

Terms only contribute to the sum in Eq. (5.28) when K - K = q.

The Ca rtesian component proje ctions of the dipole moment operator are given

in terms of the spherical tensor forms appearing in Eq. (5.28) as

6

As an example, consider a dipole moment lying in the xz plane and having a orientation

angle, TM with respect to z. Then, μ^ x

 = μ^ sin TM and μ^ z

 = μ^ cos TM, and for an R

branch transition (J - J = +1), the line strength is obtained from
(E.2)

(E.3)

(E.4)

(E.5)

If the TM vector lies along the x axis, the cos TM term in Eq. (5.32) vanishes. If it lies

along the z axis, the sin TM term vanishes. Additionally, when the eigenvector

coefficients c appearing in Eq. (5.32) are obtained from diagona lization of a rigid rotor

Hamiltonian matrix, the selection rules guarantee that at least one of these two terms

will vanish when the sums are performed over K for a given transition. Both terms

and their relative signs become important only when the symmetry of the rotational

Hamiltonian is reduced to C2 or C1. When complex (real and imaginary) Hamiltonian

matrices are diagonalized, separate sums are performed over the real and imaginary

eigenvector coefficients. The line strength is obta ined from the squared modulus of the

real and imaginary summed values. 

Linear least squares analysis

The linear least squa res fitting algorithm used to fit N parameters of the rotational

Hamiltonian (Eq. D.1) to the observed transition energies, E

obs, is based on a "chisquared" minimization procedure where 2

 is defined as

where E'

i

 and E"i

 are the upper and lower calculated state energies obtained from

diagonalization Eq. (D.1) for each state. It is convenient to reexpress E'

i

 and E"i in

terms of its parameters and derivatives as

for all M' and M" terms in Eq. (D.1) where aj

 are the parameters A, B, C, D or E and

are linear functions of the energy, E. Substitution of Eq. (E.3) into Eq. (E.2) gives

where E

ori is defined as a0

. In order to evaluate , we make use of a relation first

introduced by Feynman1,

where are the e igenfunctions of Eq. (D.1) expressed in a symmetric

top basis.
(E.6)

(E.7)

The parameters, ak

, are desired such that the derivative of 2 with respec t to a ll

ak is zero, i.e.,

for all j = M' and M" parameters and giving a M' + M" + 1 set of equations

in unknown coefficients, ak

. Reversing the summation in Eq. (E.6) gives the normal

equations. The normal equations are solved for the parameters, ak, by a standard

technique such as LU decomposition and ba cksubstitution also known as singular value

decomposition.2
APPENDIX C. Rotor program, iar95.exe, sample input file and parameter

descr iption.

################################################################################

# IAR INPUT FILE : VERSION 2.0 #

################################################################################

#-------------------------------------------------------------------------------

# COMMENT LINE (< 200 CHARACTERS WITH NEW LINE END):

 2-METHYL NAPHTHALENE - E LINES

#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------

# OUTPUT FILENAME (EXTENSIONS WILL BE ADDED):

 2mne

#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------

# ASSIGNMENT FILENAME:

 2mne.asn

#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------

# J & K MAXIMUM OF ASSIGNED LINES TO FIT:

 -1 -1

#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------

# MAXIMUM J TO CALCULATE:

 30

#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------

# GROUND STATE A, B AND C ROTATIONAL CONSTANTS:

 2.80370062e+03 8.22797124e+02 6.38859058e+02

#-------------------------------------------------------------------------------

# GROUND STATE PHI, THETA AND CHI EULER ANGLES (UHU-1 CCW+):

 0.000000 0.000000 0.000000

#-------------------------------------------------------------------------------

# GROUND STATE FIT INDICATORS: 0|1=OFF|ON

 1 1 1

#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------

# GROUND STATE STATUS OF CONSTANTS:

 1 0 1

#-------------------------------------------------------------------------------

# GROUND STATE <PX>(B), <PY>(C) & <PZ>(A) CONSTANTS:

 8.00039176e+00 0.00000000e+00 6.91689529e+01

#-------------------------------------------------------------------------------

# GROUND STATE FIT INDICATORS: 0|1=OFF|ON

 1 0 1

#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------

# GROUND STATE STATUS OF CONSTANTS:

 0 0 0

#-------------------------------------------------------------------------------

# GROUND STATE <PXPY + PYPX>, <PXPZ + PZPX> & <PYPZ + PZPX> CONSTANTS:

 0.00000000e+00 0.00000000e+00 0.00000000e+00

#-------------------------------------------------------------------------------
# GROUND STATE FIT INDICATORS: 0|1=OFF|ON

 0 0 0

#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------

# GROUND STATE STATUS OF CONSTANTS:

 0 0 1

#-------------------------------------------------------------------------------

# GROUND STATE <DK>, <DJK> & <DJ> WATSON D DISTORTION CONSTANTS:

 0.00000000e+00 0.00000000e+00 1.43369769e-05

#-------------------------------------------------------------------------------

# GROUND STATE FIT INDICATORS: 0|1=OFF|ON

 0 0 1

#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------

# GROUND STATE STATUS OF CONSTANTS:

 0 0 1

#-------------------------------------------------------------------------------

# GROUND STATE <dK> & <dJ> WATSON D DISTORTION & <PZ**3> CONSTANTS:

 0.00000000e+00 0.00000000e+00 4.27435378e-03

#-------------------------------------------------------------------------------

# GROUND STATE FIT INDICATORS: 0|1=OFF|ON

 0 0 1

#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------

# EXCITED STATE A, B AND C ROTATIONAL CONSTANTS:

 2.72978104e+03 8.14588554e+02 6.30288152e+02

#-------------------------------------------------------------------------------

# EXCITED STATE PHI, THETA AND CHI EULER ANGLES (UHU-1 CCW+):

 0.000000 0.000000 0.000000

#-------------------------------------------------------------------------------

# EXCITED STATE FIT INDICATORS: 0|1=OFF|ON

 1 1 1

#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------

# EXCITED STATE STATUS OF CONSTANTS:

 1 0 1

#-------------------------------------------------------------------------------

# EXCITED STATE <PX>(B), <PY>(C) & <PZ>(A) CONSTANTS:

 4.56960401e+01 0.00000000e+00 4.07424568e+02

#-------------------------------------------------------------------------------

# EXCITED STATE FIT INDICATORS: 0|1=OFF|ON

 1 0 1

#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------

# EXCITED STATE STATUS OF CONSTANTS:

 0 0 0

#-------------------------------------------------------------------------------

# EXCITED STATE <PXPY + PYPX>, <PXPZ + PZPX> & <PYPZ + PZPX> CONSTANTS:

 0.00000000e+00 0.00000000e+00 0.00000000e+00

#-------------------------------------------------------------------------------

# EXCITED STATE FIT INDICATORS: 0|1=OFF|ON

 0 0 0

#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------
# EXCITED STATE STATUS OF CONSTANTS:

 0 0 1

#-------------------------------------------------------------------------------

# EXCITED STATE <DK>, <DJK> & <DJ> WATSON D DISTORTION CONSTANTS:

 0.00000000e+00 0.00000000e+00 2.89808193e-05

#-------------------------------------------------------------------------------

# EXCITED STATE FIT INDICATORS: 0|1=OFF|ON

 0 0 1

#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------

# EXCITED STATE STATUS OF CONSTANTS:

 0 0 1

#-------------------------------------------------------------------------------

# EXCITED STATE <dK> & <dJ> WATSON D DISTORTION & <PZ**3> CONSTANTS:

 0.00000000e+00 0.00000000e+00 -5.21773343e-02

#-------------------------------------------------------------------------------

# EXCITED STATE FIT INDICATORS: 0|1=OFF|ON

 0 0 1

#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------

# ORIGIN FREQUENCY AND FIT INDICATOR: 0|1=FIXED|FIT

 3.34473572e+05

 1

#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------

# TRANSITION MOMENT METHOD & REFERENCE FRAME: 0|1=ANG|%INT & 0|1=GND|EXE FRAME

 0 0

#-------------------------------------------------------------------------------

# TRANSITION MOMENT (CCW+): TM MAG/THETA/CHI FROM A | %INT ON A(Z) & B(X) & C(Y)

 1.000000 50.000000 0.000000 

#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------

# DELTA K ORDER & AMPLITUDE STATUS: 1|3|5=ORDER & 0|1=AMP STATUS OFF|ON

 3 0

#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------

# TEMPERATURE IN KELVIN (TO MHZ) & INTENSITY CUTOFF: 3.0 & 0.01

 9.000000 0.050000

#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------

# OUTPUT FORMAT INDICATOR & ERG & ITN SCALARS & FSR: 0|1=JB FORMAT OFF|ON

 1 0.01 1.00 599.504000

#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------

# PARITY STAT & GND & EXE KaKc PARITY PRODUCTS: Y|N=OFF|ON & E|O & E|O

 N E O

#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------

# LS FIT EXACT CYCLES & APPROX & REJ LEVEL: 0(-1)|1=OFF|ON & 1|.. & 1|..

 1 1 200.000000

#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------

# LOWER & UPPER EIGENVALUES & EIGENVECTORS LOGGED: 0|.. TO -1|.. & 0|.. TO -1|..

 0 -3
 0 -3

#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------

# DEBUG PRINT STATUS: 0|1=OFF|ON

 0

#-------------------------------------------------------------------------------

The program, iar95.exe, is fully thre e-dimensional for both Hamiltonian rotations

in one or two states and for spe cification of transition moment (TM) orientations. The

program also includes specification of the Watson D distortion parameters which can

be fit in rotated frames with the disadvantage that their meaning is obscure. Tests have

been done by direct comparison with output from ASYROT and BLZYROT. The

outputs from these three programs a re in good agre ement as long as the conventions

given below are adhered to. The sign conventions us ed in BLZYROT are the same

ones used here. See NOTE files in directories 'asy_iar_distortion' and 'blz_iar_axissw'

for actual test runs and further explana tion of output from these programs. Some

comments about fitting strategies are included in these notes.

This is an example input file for the program iar for UNIX or iar95.exe for

Windows95. This file is read by the rotor program in several different ways.

1. iar95 <RETURN>

 input file ?

You are prompted for the input file name after the program is started. ASCII files like

outfile.dat and the outfile.log file are the only survivors. NOTE: a new input file will

be created called 'outfile'.in where outfile is the output base filename parameter given

as an input parameter below.

2. iar95 input file

Entered as a command line argument. Both ASCII and JB binary files survive.

3. iar95 1.0

 iar95 1.0 input file

This entry form is for backward compatibility with old input files used with iar. The

new input file created is version 2.0 and may then be modified. Note that the new input

file format is more informative with comment lines that are ignored by iar95.exe.

Comment lines always begin with a # sign. However, while parameter entry is still in

a free format style, all parameters entries must exist.

A description of the parameters in the above input file are as follows:
----------------------------------------------------------------------------------------------------

2-METHYL NAPHTHALENE - E LINES

A line for comments. Text must be less that 200 characters and must end with a

newline character.

2mne

This is the base filename of all output. Files that will be overwritten include:

'outfile'.in is the new input file format with updated constants from the fit. 

 'outfile'.log contains a log of the various pha ses and outputs of the program including

the fit phases.

'outfile'.a gives a listing of the calculated lines in the ASCII forma t: band type, three

upper, three lower state quantum numbers, simulated intensity, observed

and calculated frequencies.

'outfile'.dat gives a listing of the calculated lines in the lines.dat format.

'outfile'.f binary file containing expt. and calc. freq, intensity and band type.

'outfile'.q binary file containing quantum numbers of calculated lines.

'outfile'.p binary file containing paramete r listing.

'outfile'.m binary file containing quick reference line positions. (older versions).

2mne.asn

The name of an ASCII file that contains the band type, the three excited, three ground

assigned quantum numbers and observed frequency used in the fitting phase. An

example follows: 

A 10 1 10 9 1 9 13370.8116

//

The end of the assigned line set must have the line //. When simultaneous fits of

UV/MW data are desired, the UV lineset ending with // line should be followed by the

MW data set ending with // line. The UV and microwave weighting factors are

specified after the // line at the end of the file.

-1 -1

These two parameters de termine the maximum J and K respec tively to use from the

assigned line set. -1 signals to use all lines.

30

Maximum value of J to calculate for each state.

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

2.80370062e+03 8.22797124e+02 6.38859058e+02
Values of rotational constants for the lower sta te: A(Z), B(X), C(Y)

0.000000 0.000000 0.000000 

Values of Euler angles used to rotate the Hamiltonian operator prior to diagonalization.

The angles are , , and in degrees. Positive angles refer to counterclockwise

rotation of the Hamiltonian or EQUIVALENTLY, CLOCKWISE rotation of the

coordinate system (axis system). For example, to rota te the Hamiltonian axis

counterclockwise in the ab plane (about c) by 1.2 degrees, this line would be

0.000000 1.2000000 0.000000

to rotate the Hamiltonian counterclockwise in the bc plane (about a) by 1.2 degrees,

this line would be

1.200000 0.000000 0.000000 

to rotate the Hamiltonian counterclockwise in the ac plane (about b) by 1.2 degrees,

this line would be

90.000000 1.2000000 -90.000000 

AXIS SWITCHING CASE - To model axis switching effects, the Euler angle(s) for

only one state should be non-z ero. A positive angle of rotation in the upper state will

cause a counterclockwise rotation of the Hamiltonian or equivalently, a CLOCKWISE

rotation of the upper inertial axes into the lower state principal axis system about the

axis specified. Positive angles for counterclockwise rotation is the convention used to

specify both TM moment orientations and axis switching angles in reference to the

COORDINATE SYSTEM. Therefore, switching angles will have the opposite sign to

that specified above. See below for a description of the reference frame for the TM

angle. 

INTERNAL AXIS ROTATION - In general, this program can be used to rotate the

Hamiltonians in both states. If the same angles are used, for example, in order to

simplify treatments of perturbations, the Euler angle(s) for both state s should be the

same or axis switching effects will be present.

1 1 1

Least squares analysis variation indic ators. Parameters are held fixed when set to zero.

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

1 0 1 

Indicates that the perturbation term below is non-zero.
8.00039176e+00 0.00000000e+00 6.91689529e+01

Values of perturbation constants D used to trea t Coriolis interactions making use of the

linear operators DbPb (DxPx), DcPc (DyPy) and DaPa (DzPz), respectively. Note that the

term Pc

(Py

) is imaginary and increases the memory required and lengthens the time of

the calculation.

1 0 1 

Least squares analysis variation indicators. Parameters are held fixed when set to zero.

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

0 0 0 

Indicates that the perturbation term below is non-zero.

0.000000 0.000000 0.000000 

Values of perturbation constants E used for the product operators PiPj where i not equal

j: EbcPbPc

 (ExyPxPy

), EcaPcPa

 (EyzPyPz

) and EbaPbPa

 (ExzPxPz

), respectively. Note that

terms with Pc(Py) are imaginary and increases the memory required and lengthens the

time of the calculation.

0 0 0 

Least squares analysis variation indicators. Parameters are held fixed when set to zero.

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

0 0 1 

Indicates that the perturbation term below is non-zero.

0.00000000e+00 0.00000000e+00 1.43369769e-05

Values of Watson's centrifugal distortion constants K

, JK and J

 ( J

[J(J+1)] 2)

0 0 1 

Least squares analysis variation indicators. Parameters are held fixed when set to zero.

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

0 0 1 

Indicates that the perturbation term below is non-zero.

0.00000000e+00 0.00000000e+00 4.27435378e-03

Values of the Watson's centrifugal distortion (A REDUCTION) constants K

 and J

and the internal rota tion FPa

3

 (FPz

3

) terms.

0 0 1 

Least squares analysis variation indicators. Parameters are held fixed when set to zero.
----------------------------------------------------------------------------------------------------

2.72978104e+03 8.14588554e+02 6.30288152e+02

0.000000 0.000000 0.000000 

1 1 1 

1 0 1 

4.56960401e+01 0.00000000e+00 4.07424568e+02

1 0 1 

0 0 0 

0.000000 0.000000 0.000000 

0 0 0 

0 0 1 

0.00000000e+00 0.00000000e+00 2.89808193e-05

0 0 1 

0 0 1 

0.00000000e+00 0.00000000e+00 -5.21773343e-02

0 0 1 

Values of the corresponding parameters for the upper state. When band origin is set

to exactly zero, pure rotationa l (microwave) transitions are assumed and these upper

state values are ignored except when doing simultaneous UV/MW fits. 

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

3.34473572e+05

Value of the band origin. Since double precision is now used, all digits can be retained

e.g. 950334472.353405 may be used as the origin frequency in MHz. When set to zero,

pure rotational (microwave ) transitions are a ssumed and the upper state parameters are

ignored. 

1

Least squares analysis variation indicator. Parameter is held fixed when set to zero.

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

0 0

1.000000 50.000000 0.000000 

Transition moment orientation can now be specified in one of two different ways using

the factors in the second line depending on value of parameter 1 on the first line. If

parameter 1 set to 0, the first value is the magnitude of the TM and the last two values
are angles in degree s. The first angle is the amount of rotation in the ab plane (like

Euler angle ) with positive values for counte rclockwise rotation as is the convention.

The second angle is the angle of rotation about the a axis relative to the b axis with the

same positive angles for CCW rotation convention. Examples:

a 1.0 0.0 0.0

b 1.0 90.0 0.0

c 1.0 90.0 90.0

ab 1.0 TM ANGLE 0.0

ac 1.0 TM ANGLE 90.0

bc 1.0 90.0 TM ANGLE

abc (33.3/33.3/33.3) 1.0 54.73561 45.0

The second method is used if the first parameter on first line is 1. The three values on

the second line are the (%)TM intensity components on the a, b and c axis,

respec tively. Note tha t these are the TM components and not the components. Signs

should be included if necessary as with axis switching. These numbers a re consistent

with BLZYROT.

Note that by inc reasing the magnitude parameter using method 1 or the percentages

using method 2, the intensities of the transitions printed out are scaled by this s ame

amount. The second parameter on line 1 is the reference frame for the TM. Usually this

is the ground state in which case the parameter value should be ze ro. If set to 1 the

coordinate frame from which the TM is measured is that of the excited state.

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

3 0

K order to calculate and the line intensity indicator =0 (or for amplitudes =1).

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

9.000000 0.050000

Temperature of band in Kelvin when rota tiona l constants a re in M Hz. Sca le

appropriate ly when different units such as cm-1 is used. The second parame ter is the

intensity cutoff factor.

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

1 0.01 1.00 599.504000

Factors for compatibility with an old unix version (MASSCOMP) of the jb program.

The first parameter when set to 0 indicates that frequencies and intensities files are

written out as normal without modification. The first parameter when set to 1 indicates

that the input a ssigned line set and binary and asc ii output files are to be used in

conjunction with jb. For the binary files, all frequencies will be converted to integers
in the binary files after multiplication by the 1.0e3 and all intensities will be converted

to short after multiplication by 1.0e3. For the lines.dat forma tted output file, all

frequencies will be multiplied by the second factor (0.01) and all intensities will be

multiplied by the third fac tor (1.0) before being written out in asc ii form. This is to

maintain compatibility with the assigned line file and to prevent overflow in JB. The

assigned line set must ALREADY have all frequencies multiplied by the second factor

(0.01) as is usual for assigned line sets us ed with ASYROT. The fourth factor is the

FSR of the reference cavity and is used to create quick reference binary file (.m) also

used by jb. Also, the ASCII file written out has the same form of a lines.dat file

produced by ASYROT and BLZYROT.

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

N E O

Parity selection status indicator. N means ignore parity when calculating transition

intensities and the next two labe ls are meaningless (but necessary). If status is Y, then

E and O determine which transitions are kept based on the ground and exc ited state

overall K parities, respectively. If E(O) is used then only when Ka+Kc

 is even (odd) will

the transition be printed. This condition must be true in both states, i.e. for the Y E O

combination (a-type band), transitions will be saved only when both Ka+Kc

 ground is

even and Ka+Kc excited is odd. Note that Wang transformation of the rotational

Hamiltonian is not applied in this program and therefore quantum labels may be come

switched for degenera te levels. This results in a mislabeling of the eigenvec tors and

the absenc e of transitions in the output when option Y is used above. N should be used

in these case s. Mis-labeled transitions will occur only for degenerate levels (of little

consequence since the correct label is obvious) or when pe rturbations be come large

enough to change the normal ordering of the asymmetric top energy levels. This latter

condition can lead to problems during least squares fitting of assigned lines especia lly

in the initial phases where constants change by "large" amounts. BEWARE! 

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

1 1 200.000000

Factors used in the least squares analysis using SVD algorithms. The first parameter

is the number of exact ene rgy cycles to perform. The constants in ea ch iteration are the

previous cycle's best fit parameters and are the ones used for rediagonalization of the

full Hamiltonians. When set to -1 (or 0), no LSA is done and a simulated line se t is

printed based on the initial parameters (0 will save additional derivative files which are

used by jb). The second parameter is the number of approximate cycles performed for

each exact cycle. In combination with the rejection level given as the third parameter,

assigned lines are accepted/rejected based on calculated energies obtained from the

new parameters but old derivatives. The rejection level is in units of the rotational

constants used in the least squares analysis.
1. R. P. Feynman, Phys. Rev. 56, 340 (1939).

2. W. H. Press, B. P. Flannery, S. A. Teukulsky and W. T. Vettering, Numerical

Recipes. The Art of Scientific Computing (Cambridge University Press, New York,

1989).

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

0 -3

0 -3

These parameters are used to print to the log file the eigen energies and eigen vectors

between J = 0 and J = -3 for the ground and excited states, respectively. In this case

nothing is printed since J initial is larger than J final.

0

This factor is for debugging purposes. It should always be set to 0 unless you want a

great dea l of information about eve ry operation in this program. This information is

printed to the standard output.

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

REFERENCES

1. Held, A, Champion, B. B. and D. W. Pratt, J. Chem. Phys. 95, 8732 (1991).

2. Plusquellic, D. F. and Pratt D. W., J. Chem. Phys. 97, 8970 (1992).