This class of compounds was chosen for two reasons. First, the

recent work of Eggert and       *ga
               Djerassl  has yielded a detailed set of

predictive rules for the acyclic amines. Secondly, for a given number

of Carbon atoms, a saturated, acyclic amine has decidedly more

structural possibilities than most other simple types of acyclic organic
compounds (for example, stereochemistry aside, there are nearly 15
million CZO-amines, but only about 6 million CPO-alcohols),ll and thus

the structural analysis of amines represents a particularly challenging

problem.

II.  DEFINITION OF THE PROBLEM

  A fully proton-decoupled, natural-abundance CMR spectrum'

typically consists of a number of sharp peaks representing the resonance

frequencies, in the applied magnetic field, of the various types of

Carbon atoms present in the sample.  A standard compound, commonly TMS,

is usually included in the sample to provide a reference frequency, and

the peak positions, or chemical shifts, are measured as fractional

deviations from this reference, in parts per million (ppm). Previous

investigations have shown that the shift of a particular Carbon is

determined by its hybridization and local environment, and thus each

shift contains some structural information.  There are a few ranges of

shifts which are characteristic of certain functional groups, such as

C=O or C=C, but aliphatic Carbons in most molecules lie in a broad


-4-

spectral region from which detailed structural information cannot be

extracted readily.

   For acyclic amines, 9a and a few other types of compounds, 9b-k

there exist predictive rules which allow one to calculate the spectrum

of a compound whose structure is known, with a typical accuracy of about

1-2 ppm in a total range of roughly 100 ppm. For these classes, the

structure-identification problem could in principle be solved via the

generation of all possible structures of a particular type (say, acyclic

amines with a particular number of Carbon atoms), the prediction of

their spectra, and the comparison of these predictions with the observed

spectrum. In fact, Sasaki et al.6b
                              --   have used this procedure in the

automated identification of a few small alkanes.  For large molecules,

though, the number of possible isomers can be overwhelming, and even a

very efficient computer program could not carry out such an analysis in

a reasonable length of time.

  Program AMINE is designed to accomplish the same goal, but in a

much more efficient manner.  It takes, as its only input data, an

observed CMR spectrum, the number of Carbons in the amine, and a

goodness-of-fit criterion.  The observed spectrum consists of a list of
shifts, c=(ol,..., on), measured in ppm relative to TMS. Each of
these corresponds to one or more Carbons in the sample molecule. Under

favorable circumstances, 12 it is possible to determine the number of

Carbons corresponding to each observed shift (this will be called the
tally of the shift) once the relative peak intensities and the


-5-

empirical formula are known.  If the tally of a shift is known to be at

least 2, 3, etc., then the shift is entered in duplicate, triplicate,

etc. in the observed-shift list.  These tallies are not necessary to

the program's operation, but even if they are underestimated, they can
add considerably to the speed and accuracy of the analysis.  The number

of Carbons,  N C' in the amine must be greater than, or equal to, the

number of shifts in the observed spectrum, Generally, NC cannot be
determined from the CMR spectrum, but must be obtained from some other

analytical method such as mass spectroscopy or elemental analysis.  The

goodness-of-fit criterion, DELTA, which is used in the comparison of 0
to the predicted spectra of molecules or molecular fragments, represents
the maximum expected error in the predictive rules. The amine rules are

derived, in part, from the alkane rules of Lindeman and Adams, 9d biho

note that 95 percent of the studied alkanes have predicted shifts within

1.5 ppm of the observed values.  A similar situation exists for the

amines, so a value of DELTA = 1.5 ppm has been used in most of this

work.

The goal of the program is to find all acyclic, NC-Carbon amines
whose predicted spectra satisfy the following two criteria:  a) Every

predicted peak must lie within DELTA of one of the observed peaks; and
b) Within this limit, the predicted shifts must be assignable to the

observed ones in such a way that all of the latter are accounted for.

III.  OVERVIEW OF PROGRAM OPERATION


-6-

  The operation of program AMINE can best be viewed in terms of four

interconnected processes; structure generation, pruning, filtering, and

spectrum matching.  The STRUCTURE GENERATOR builds a pool of

increasingly large and complex alkyl chain-ends, and eventually uses

these to construct amine molecules.  It relies heavily upon the PRUNER

to cull from the growing pool any chains which are inconsistent with the

observed spectrum , and similarly upon the FILTER to test entire amine

molecules.  The FILTER also takes care of outputting the acceptable

solution structures, and ranking them according to how well they fit the

observations.  Both the FILTER and the PRUNER use the spectrum MATCHER,

which is responsible for the actual comparison of predicted and observed

spectra.  Each of these processes will be discussed in detail, below.

IV. STRUCTURE GENERATION

  The structure generation scheme used in this study, which is

related to the enumeration algorithm of Henze and Blair, 13 is

applicable only to saturated, acyclic, monofunctional compounds.  It is

an efficient approach from the standpoint of CMR structural analysis

because it rapidly generates substructures which contain a relatively

large number of "predictable" Carbons Q. e., those near the ends of
alkyl chains), and thus many of these substructures may be ruled out

early in the analysis as being inconsistent with the observed data.


                        -7-

  At any point in the generation, the STRUCTURE GENERATOR contains a

pool of monovalent alkyl radicals which, through pruning (see below)
have been found to be consistent with the observed CMR spectrum. The
pool initially contains only the -CH3 radical. By attaching one or
more of these pool members.(along with an appropriate number of hydrogen
atoms) to a central Carbon, it constructs new radicals, each of which is

passed to the PRUNER for testing.  Any that agree with the observed

spectrum are included in the pool, and are subsequently used to

construct larger chains.  In the final step of the analysis, the

STRUCTURE GENERATOR similarly attaches alkyl groups to a central

Nitrogen, constructing amine molecules of the proper empirical formula.

These it passes to the FILTER for final testing and ranking. At all

stages of the generation, tests are made which insure that no radical or

amine is considered twice.

As will be discussed below, a given alkyl radical actually

undergoes several different

corresponding to a distinct

might exist.  The STRUCTURE

tests during pruning, with each test

chemical environment in which the chain-end

GENERATOR keeps a record of these tests for

each pool member, and constantly checks that it is using the radicals in

a consistent fashion.  If, for example, the PRUNER finds that the ethyl

group is consistent with the observed spectrum only if it is attached to

Nitrogen in a secondary amine, the STRUCTURE GENERATOR will never

construct an n-propyl group, set-butyl group, or any other radical which

contains an ethyl group connected to Carbon.  Neither will it generate

/--. -


-8-

primary or tertiary amines with !-ethyl groups.

V.  PRUNING

  The PRUNER is the real heart of program AMINE. It is responsible

for keeping the growing chain-end pool to a manageable size by weeding
out alkyl radicals which are inconsistent with the observed spectrum.

In testing a particular chain-end, R, shown schematically in Figure 1,

the basic question considered by the PRUNER is: "Of all possible sets

of CMR shifts which R could produce, is at least one consistent with the

observed spectrum?"  Actually, the question is somewhat more complex,

but this provides a good starting point.

Now, according to the predictive rules, 9a a Carbon's shift is

determined by the structure which surrounds it, up to four bonds away.

Further, the effect of a first-row atom which is four bonds removed does

not depend upon whether that atom is Carbon or Nitrogen.  Thus, because

X in Figure 1 must contain at least one such atom (namely Nitrogen), the
shifts of Cs and any Carbons "below" it are completely predictable and

independent of the internal structure of X. The shifts of the remaining
Carbons, Cd, Cp and C4, depend to varying degrees upon the structure

of X, with C, being the most sensitive.

  By investigating all possible X structures to a "depth" of four
atoms (measured from the R-X bond), the PRUNER could generate an

exhaustive list of spectra that R might produce, testing each for


-9-

inconsistency with the observed one.  Usually, though, X contains enough

atoms that there are several hundred of these "depth-4" structures, and

the above approach proves to be rather cumbersome. Instead, the PRUNER

considers only "depth-3" expansions of X, for which C 8 and all Carbons

below it are predictable.  The shift of &is simply ignored, even when
a reasonable estimate of its value might be made. This simplification

cuts the number of unique X substructures to, at most, 94.

   There are two factors which can reduce this number still further.

First, some of the substructures may contain too many (or few) Carbons

to be consistent with the known atom-count of X. Secondly, there are

many cases in which a single predicted spectrum for R may result from

two or more related X's.  This situation arises because, according to

the predictive rules, 9a the shifts of certain types of Carbons

(specifically, those which are four or more bonds from Nitrogen, or
three if the degree of the amine is known) are not sensitive to the type

or distribution of first-row atoms which are four bonds away, but only

to their number. Thus, in the computation of the shift of Co,

  CH?
-x = -CH( C
   CH3

is equivalent to three other structures:


-lO-

  CHcL
-x = -CH(      CH2-C
    N , -CH(      CH2-C
   CH3    CH2-C ' -CH(
               CH2-N

All four may be considered as a single entity, which can be represented

as:

-x = -CH{'-  2 (the no. of non-H atoms)
      C-

  Once such a grouping of X substructures has been done, there

remain, at most, 69 cases for the PRUNER to consider. These are

summarized in Table 1, where they are further grouped into fifteen
classes according to a) the type of atom directly attached to R, b) the

degree of that atom and c) if that atom is Carbon, and is attached to

Nitrogen, the degree of the amine. The actual  purpose of the PRUNER is

to consider each of these classes, determining whether at least one

class member gives R a predicted spectrum cons istent w ith the observed

one, and to return the results of the fifteen class-tests to the

STRUCTURE GENERATOR.

  The efficiency of this class-by-class investigation can be greatly

improved by the inclusion of a hierarchy of pre-tests, each of which is

aimed at excluding one or more classes at once.  For example, classes


-ll-

l-12 in Table 1 all have one common feature: The atom to which R is

attached is Carbon.  Thus, as a pre-test for all twelve classes, the

PRUNER treats X as a Carbon whose neighbors are unknown (schematically,

X= C-?) and predicts as much of the spectrum of R as possible. If

these predictions do not match the observations, it bypasses all further

consideration of classes l-12 and proceeds with the X = N-? pre-test for

classes 13-15.  Otherwise, it consider-s a number of more detailed

pre-tests, each corresponding to a possible set of neighbors to the

central Carbon in X = C-?.  The actual hierarchy is outlined in Figure

2.  In each of the pre-tests, the local environment of either Cp or CT
is known to a depth of only three atoms, and hence the corresponding

shift cannot be predicted precisely.  In most of these cases, the PRUNER

can derive upper and lower limits for the shift from the predictive

rules.  These limits, which define an estimated shift, encompass a

relatively small spectral region (O-5 ppm) because the shift of a Carbon

is usually not very sensitive to atoms which are four bonds away.  Even

though the estimated shifts are not exact, they convey useful

information to the MATCHER, and thus increase the overall program

efficiency.

VI.  FILTERING

In the final stages of the analysis, the STRUCTURE GENERATOR

constructs amine molecules with NC Carbons by attaching to a central


                         -12-
Nitrogen, one or more alkyl chains which have survived the pruning

process.  These amines are passed to the FILTER, which is responsible
for calculating their total CMR spectra and, via the MATCHER, comparing
these predictions with the observations. If an amine passes the test,
the FILTER writes out the structure along with the predicted shifts. It
then repeats the spectral comparison using progressively smaller values
of DELTA until it finds the smallest value, DELMIN, for which a match

still exists.  In the event that several solution amines result from a
particular run of AMINE, these DELMIN values can be helpful in ranking
the candidates according to how well they fit the observed spectrum.

VII.  SPECTRUM MATCHING

  Eventually, the pruning and filtering processes reduce to problems
in spectrum matching.  Suppose the MATCHER receives for testing a list

of m predicted shifts, some of which may be represented by small
spectral regions rather than exact values.  Now, the predictive rules

are not precise, so each shift is actually associated with a range of
acceptable values (given the generic symbol r) whose size is controlled

by the input parameter DELTA.  This parameter measures the maximum
tolerable disagreement between predicted and observed shifts, so the
range for a shift, S, extends from S+DELTA to S-DELTA, while that for an
estimated shift, bounded above and below by Su and Sl, extends from
Su+DELTA to Sl-DELTA.  It should be noted that, in the latter case,


-13-

there are really two factors which contribute to the breadth of the

range.  One is the basic imprecision in the predictive rules, while the

other arises because the PRUNER, in its pre-tests, sometimes calculates

shifts for Carbons whose environment is not completely known.  The

spectrum-matching algorithm, though, makes no distinction between these;

It only "knows" that a predicted spectrum consists of a list of ranges.
This list will be written as r-=(rI,r2,...,rm), with Ui and li as,
respectively, the upper and lower bounds for the range ri.

The nature of the observed spectrum, ~=(01,02,...,on), has been

discussed in section II.  The MATCHER takes these n shifts to be exact,

because any estimated uncertainty (usually on the order of 0.1 ppm) in

their measurement may be included in the tolerance DELTA. It is the

task of the MATCHER to ascertain whether c could be a subspectrum of
0, or if m=N, (NC being the number of Carbons in the amine), whether
r could be interpreted as 0.

  If, for a range ri, there exists an observed shift oj such that
uir"j>l i % then it will be said that ri can be assiqned to oj.
The simplest test of agreement between r and 0 involves checking that
each ri in c can be assigned to at least one o. in 0.
                                   J      This test does

not consider the important condition that, eventually, all shifts in 0

must be used, and therefore a stronger test can be defined.

  If every Carbon in the molecule gives a different observed shift,

or if an analysis of peak intensity data gives the tally of each peak,
then &NC.  In this case, it is clear that no two predicted shifts can


                        -14-
be assigned to the same oj.  Thus,,referring to Figure 3, r does not
match o even though the simple test is not violated, because  r
      -                        I and
r3 must both be assigned to 02.  In more complicated cases, each of
several ri's may be assignable to two or more o.'s, and vice versa,
                                   J
so the application of this test in an efficient manner can present

difficulties.  Fortunately, simple matching theory, 14a an outgrowth of
the mathematical field of graph theory, provides a general method (see
MATCHING ALGORITHM, below) of finding the maximum number, M, of ranges
which can be assigned to the elements of 0 without duplication.
Clearly c cannot match 0 if this number is less than m.

  There may be cases, though, in which complete tally information is

unavailable, which means that the number of observed shifts, n, is
smaller than the number of Carbons, NC.  In such cases, there are
(NC-n) "extra" shifts which lie,somewhere beneath the n observed ones,

but there is no way of determining where they belong. It is still

possible to strengthen the simple test, but here, the additional

constraint is that the predicted spectrum, once assigned, can have no
more than (NC-n) "extra" peaks, either.  If the simple test is passed,
then every ri can be assigned to at least one 0.. However, M is the
                                   3
maximum number of ranges which can be assigned to 0 without
duplication, so (m-M) must be the number of "extra" ranges in L.  The

condition that strengthens the simple test here, then, is
(m-M)-(NC-n). Because M cannot exceed m, this condition reduces to
the previous one (m=M) when n=Nc.


-15-

  The above spectrum-matching scheme is useful not only in the

current study, but for general cases in which a set of predicted CMR

shifts of variable uncertainty is to be compared with an observed

spectrum with, perhaps, incomplete intensity information.

VIII.  MATCHING ALGORITHM

The algorithm for determining M is related to the so-called

Hungarian method 14b of simple matching, but takes advantage of certain

special features of the spectrum-matching problem.  It may be described

briefly as follows: Begin with M=O and process the oj's in algebraic
order, beginning with the largest. For each Oj, scan the ranges ri
looking for those which satisfy Ui>Oj~li, but which have not yet
been assigned. If there are none, proceed to the next Oj. If there is
just one, assign it to o.,

J  increment M by 1 and proceed to the next

Oj*  If there are several, assign the one with the largest lower

limit (li) t0 Oj, increment M by 1 and proceed to the next 0..
                                             J

It is possible to prove that this gives the maximum matching

between c and 0, but a presentation of our proof is beyond the scope

of this paper.

IX.  RESULTS

Program AMINE has been implemented on the IBM 360/67 and DEC PC?-10


                        -16-

computers.  Any mention of timing ,in the following discussion refers to
total execution time (central processor time plus "wait time") on the

former machine. 15  The program requires about 35 thousand words of

storage.  A sample of the program's output is shown in Figure 4.

  The only large set of amine CMR spectra available in the literature

is that given by Eggert and Djerassi, 9a who used it in the derivation

of predictive rules.  The set consists of 102 amine spectra, including

both shifts and tallies.  Three of these spectra correspond to

diastereomeric mixtures, and these are not suitable for testing AMINE,

because the program assumes that the input spectrum corresponds to a

pure compound.  Neither is tridodecylamine because it exceeds the

maximum number of Carbons (currently 24) allowed by the program.  The

remaining 98 amines were used in the testing of the program.

  Some experimentation indicated that DELTA=1.5 ppm was small enough

for efficient and selective program operation, yet large enough that

about 95% of the test cases gave the correct solution among the output

structures.  Increasing DELTA by 50% to 2.25 ppm slowed the program by a

factor of 2-4, but AMINE always obtained the correct structure with this

higher DELTA value.  Generally, shift tallies were found to be

unnecessary for amines containing fifteen or fewer Carbons, but for

larger molecules, the analyses proved to be excessively costly unless

all of the Carbons were identified in the observed spectrum.

  With DELTA=1.5 ppm, and using tallies for the amines with sixteen

or more Carbons, the program obtained only one answer, the correct one,

;c; ,.


-17-

for the 88 amines listed in Table 2.  The six cases summarized in Table

3 gave from two to seven solutions, with the correct structure ranked

(see section VI.) first or tied I6 for first.  For three of these six,

the inclusion of tallies ruled out the incorrect answers. Four amines

gave no solutions with DELTA=1.5 ppm.  These were rerun using DELTfi=2.25

ppm, and tallies were included to offset the longer running-times. fis

indicated in Table 4, three of these runs gave only the correct answer,

while the fourth yielded two equally ranked solutions, including the

correct one.

  These analyses required from 0.02 to 100 seconds of computer time,

with a typical lo- or ll-Carbon amine using about 1-2 seconds.  In none

of the runs was an incorrect solution obtained without the accompanying

correct one, and in only four cases was it necessary to use the larger

DELTA value.  The results for the eight amines containing sixteen or

more Carbons are especially encouraging:  In a reasonable length of

time, the program was able to select the correct structure, along with

very few others, from an "isomer space' containing from about 300,000
(for Nc=16) to about 700,000,000 (for Nc=24) members."

   The above results are biased to some extent because the amines used

for testing the program are the same ones used by Eggert and Djerassi in

the predictive-rule formation.  As a test of the generality of the

program, analyses have been run on the spectra of four "unknown" amines

which do not appear in the original list. The results of these tests

cases are summarized in Table 5.  The spectra of the two 13-Carbon


-I8-

amines were analyzed using DELTA=1.5 ppm, and no attempt was made to

include tallies.  Only the correct structure was obtained in these

cases.  For the two 20-Carbon amines, tallies were measured under

special experimental conditions (see below). With DELTA=1.5 ppm, one of

these gave two equally ranked structures, while the other gave none. A

rerun of the second case with DELTA=2.25 ppm yielded five solutions with

the correct one ranked as tied for second. This is the only case in

which the ranking procedure favored an incorrect answer over the correct

one, but here, as in most of the other multiple-result runs, the

incorrect structures are sufficiently different from the correct one

that they should be distinguishable by mass-spectroscopic techniques.

X.  CONCLUDING COMMENTS

  Two major conclusions result from this study. First, the CMR

spectrum of an acyclic amine appears to be highly characteristic of the

structure of the amine.  For example, only one of the nearly 15
million11 structural isomers of C20H43N gives a predicted spectrum
which matches the observed spectrum of N-butyldi(2-ethylhexyl)amine.

Thus it can be concluded that.CMR data do indeed contain a tremendous

amount of structural information.  Secondly, it has been found that

efficient methods for extracting this information exist, and can be

implemented on the digital computer.

There is no reason to believe that these conclusions are peculiar


                        -19-

to the acyclic amines.  The computational techniques outlined in this

paper can read ily be generalized to other classes of saturated, acyclic,

monofunctional compounds:  To do so for a particular class, one needs to

obtain an accurate set of predictive rules, and, perhaps, to modify the

pruning process slightly to account for special features of those rules.

Such rules already exist for alkanes 9c,d , alkenesge,          9b
                               and alcohols ,

and as research in CMR spectroscopy progresses, further sets should

become available.  Extensions to polyfunctional and/or cyclic classes

would also require more sophisticated structure-generation methods, but

these are available. 3,6a,17

  In short, it appears that the computerized analysis of CMR spectra

holds great promise as an accurate and selective tool in the

identification of unknown compounds.

XI.  EXPERIMENTAL

  The four "unknown" amines were prepared, and their proton

noise-decoupled CMR spectra obtained, using previously described

techniques. 9a  The spectra of the two 20-Carbon amines were also run in

the presence of chromium acetylacetonate, and the integrated intensities

from these were used to determine the peak tallies. 18  The observed

shifts for the four amines are given below, in ppm downfield of internal

TIklS .  The estimated uncertainty in these shifts is 0.1 ppm. For the two

20-Carbon amines, tallies are included in parentheses.

?-L-I


-2o-

N-(3-methylbutyl)-2-ethylhexylamine;53.6, 48.6, 39.8, 39.6,

31.7, 29.3, 26.3, 24.8, 23.2, 22.8, 14.1, 11.0.

N-(3-methylbutyl)-1,5-dimethylhexylamine;53.5, 45.6, 39.9,

39.4, 37.8, 28.1, 26.4, 24.0, 22.7, 20.6.

N-(2-ethylhexyl)-N-(3-methylbutyl)heptylamine;59.6(l),
55.0(l), 53.1(l), 38.1(l), 36.8(l), 32.3(l), 31.8(l),
29.7(l), 29.4(l), 27.9(2), 26.5(l), 24.9(l), 23.6(2),

23.0(2), 14.3(2), 11.0(l)

N-pentyl-N-(3,3-dimethylbutyl)-3,5,5-trimethylhexylamine;
54.5(l), 52.5(l), 51.9(l), 50.1(l), 40.9(l), 31.1(l),
30.2(3), 30.0(l), 29.8(l), 29.7(3), 27.7(2), 22.9(2),

14.1(l).

XII.  ACKNOWLEDGEMENTS

  Thanks are due to Hanne Eggert for preparing the "unknown" amines

and obtaining their spectra, and to Larry Masinter together with Drs. N.

S. Sridharan and Bruce Buchanan for their helpful discussion and

criticism of this work.  The financial support for this project provided

by the National Institutes of Health (grant RR-612) is gratefully

/Q i .


-21-

acknowledged.


-22-

References

1.

2.

3.

4.

5.

6.

7.

8.

9.

For part X, see D. H. Smith, 8. G. Buchanan, W. C. White,
E. A. Feigenbaum, J. Lederberg, and C. Djerassi, submitted
for publication in Tetrahedron.

National Institutes of Health postdoctoral Fellow, 1972-
1973.

(a) B. G. Buchanan, A. M. Duffield, and A. V. Robertson in
"Mass Spectroscopy:  Techniques and Applications," ed. G.
W. A. Milne, Wiley and Sons, New York, 1971, p. 121;
(b) D. H. Smith, B. G. Buchanan, R. S. Engelmore, A. M.
Duffield, A. Yeo, E. A. Feigenbaum, J. Lederberg, and
C. Djerassi, 2. Amer. Chem. Sot., 1972, 94, 5962, and
previous papers i'nhe%ies.

A. Buchs, A. M. Duffield, G. Schroll, C. Djerassi, A. B.
Delfino, B. G. Buchanan, G. L. Sutherland, E. A. Feigenbaum,
and J. Lederberg, 3. Amer. Chem. Sot., 1970, 92-, 6831.
                       ---

(a) H. S. Herze, R. A. Hites, and K. B. Biemann, Anal. Chem.,
                                                      --
1971, 43, 681;

(b) L. R. Crawford and D. J. Morrison,\ibid., 1971, 43, 1790;
(c) D. H. Smith, ibid., 1972, 44, 536; -
(d) P. C. Jurs, ibid., 1971, &x1812, and references cited
therein.

(a) S.-I. Sasaki, Y. Kudo, S. Ochiai, and H. Abe, Mikro-
chimica Actapien], 1971, 726;
0-1. Sasaki , S. Ochiai, Y. Hirota, and Y. Kudo, Japan
Analyst, 1972, 21, 916.

H. Abe and S.-I. Sasaki, The Science Reports of the Tohoku
                                                  --
University, Series 1_, 1972, 55-, 63.

For a general discussion of CMR spectroscopy, see "Carbon-13
Nuclear Magnetic Resonance for Organic Chemists," G. C. Levy
and G. L. Nelson, Wiley-Interscience, New York, 1972.

(a) H. Eggert and C. Djerassi, J. Amer. Chem. Sot., in press;
(b) J. D. Roberts, F. J. Weiger5, J. I. Kroschfiz, and
H. J. Reich, ibid., 1970, 92-, 1338;
(c) D. M. Grant and E. G. Paul, ibid., 1964, 86, 2984;
(d) L. P. Lindeman and J. Q. Adams, Anal. Chem., 1971, 9,
1245;
(e) D. E'. Dorman, M. Jautelat, and J. D. Roberts, J. Org.
Chem., 1971, 36, 2757;


-23-

10.  Copies of the program, along with sample input decks, may be

obtained from the authors.

11.

These isomer counts were computed using the enumeration
algorithm of Henze and Blair, Reference 13.

12.

13.

G. N. La Mar, 2. Amer. Chem. Sot., 1971, 93, 1040.
                   P-m

H. R. Henze and C. M. Blair, 2. Amer. Chem. Sot., 1931, 53,
3042 and 3077.                     ---

14.

(a) "The Theory of Graphs and its Applications," C. Berge,
Wiley and Sons, New York, 1964, p. 92;
(b) ibid., p. 99.

15.

On the PDP-10, the program runs more slow1 by a factor
of about four (central processor time only 3 .

16.

Two structures are considered to be tied when their DELMIN
values differ by 0.1 ppm or less.

17.

Exhaustive, irredundant methods for the generation of
cyclic structures have recently been developed by L. M.
Masinter and N. S. Sridharan as part of our Heuristic
DENDRAL project.  A manuscript describing their work is
in preparation.

18.

S. Barcza and N. Engstrom, 3. Amer. Chem. Sot., 1972, 94,
                                 --m          -
1762.

(f) D. K. Dalling and D. M. Grant, 3. Amer. Chem. Sot., 1967,
89, 6612;                                 ---
E) M. Cristl, H. 3. Reich, and J. D. Roberts, ibid., 1971,

$3; 3463;

Dorman, S. J. Angyal, and J. D. Roberts, ibid.,
1351;
Crandall and S. A. Sojka, ibid., 1972, 94, 5084;
Woolfenden and D. M. Grantxid., 1966788, 1496;
Weigert and J. D. Roberts, ib;i., 1970, 92,
references cited therein.

P- 7/


Table 1.  The Substructures X Considered by the PRUNER.

Class "Depth 3" X structure(s) ' Class "Depth 3" X structure(s)

R-CH2-C- }1,2,3           13

R-CH2-NH2               14

R-CH2-NH-C

P

4 R,,,,(;

5

R-CH(;- 1,2,...,6
-1

6

R-CH(NH2
C- )0,1,2,3

7

8

R-CH( NH-C
C- )0,1,2,3          15

    C
R-CH( NLC

   C- } 0,1,2,3

9

10

11

12

R-C& 1,2,...,9
  C- l

  NH-C
R-C+- 0,1,...,6
  C- l

R-NH2
R-NH-C- )0,1,2,3

R-N(;- -1 0,1,5,6

( C
R-N(;; C
    3

R-N( CH2-C
CH2-C

R-N( CHLZ:

  CH C
F


Table 2.  Cases for which AMINE obtained only the correct structure
     using DELTA = 1.5 ppm and, except as noted, no tallies.

Amine (prefix only)

methyl
ethyl
wwl
isopropyl
trimethyl
butvl
see-butyl
isobutyl
tert-butyl
diethyl
pentyl
1-methylbutyl
2-methylbutyl
3-methylbutyl
2,2-dimethylpropyl
N-methyl-set-butyl
N-methyl-tert-butyl
N-methyldiethyl
hexyl
1,3-dimethylbutyl
1,2,2-trimethylpropyl
2,2-dimethylbutyl
dipropyl
diisopropyl
N-ethylbutyl
N-ethyl-se&butyl
triethvl
N,N-dihethyl-set-butyl
N,N-dimethyl-6$t-butyl
heptyl -
l-methylhexyl
1-ethylpentyl
1,3-dimethylpentyl
N-methylhexyl
N-isopropylbutyl
N-isopropyl-set-butyl
octyl
1-methylheptyl
2-ethylhexyl
1,5-dimethylhexyl
1,1,3,3-tetramethylbutyl
dibutyl
diisobutyl
N-ethylhexyl
K,N-dimethylhexyl
N,N-diethylbutyl
N,N-diethyl-set-butyl

,Amine (prefix only)

N-ethyldiisopropyl
nonyl
N-propylhexyl
N-set-butylpentyl
N-set-butyl-3-methylbutyl
N-tert-butyl-3-methylbutyl
N-methyl-1,1,3,3-tetramethyl-
   butyl
tripropyl
decyl
dipentyl
N-butylhexyl
N-tert-butylhexyl
N-set-butyl-3,3-dimethylbutyl
divmethylbutyl)
N-ethyldibutyl
N-ethyldibutyl
N,N-diisopropylbutyl
N-pentylhexyl
N-butyl-1-methylhexyl
N-pentyl-1,3-dimethylbutyl
N-(3,3-dimethylbutyl)pentyl
N-butyl-1-ethylpentyl
N-methyl-N-butylhexyl
N-propyldibutyl
N-isopropyldibutyl
N-(1,3-dimethylbutyl)hexyl
tributyl
N-ethyldipentyl
N-tert-butyldibutyl
N,N-dibutyl-3-methylbutyl
N,N-dibutylhexyl
N,N-dibutyl-3,3-dimethylbutyl
N-set-butyldipentyl
N,N-dipentyl-1-methylpentyl
tripentyl
tri(3-methylbutyl)

Using tallies:

di(2-ethylhexyl)
N,N-dipentyl-1,3-dimethylbutyl
N,N-dibutyl-1,1,3,3-tetramethyl-
  butyl
trihexyl
N-butyldi(2-ethylhexyl)


Table 3.  Cases for which AMINE obtained two or more structures
     using DELTA = 1.5 ppm and, except as noted, no tallies.

Amine (prefix only)

dihexyl

Solutions (prefix only)

dihexyl
N-pentylheptyl a

Rank

tied
tied

N-pentyl-1,1,3,3-tetra-     N-pentyl-1,1,3,3-tetra-        1
         methylbutyl            methylbutyl
               N-tert-butyl-l,l-dimethyl-
                    heptyla   2

N-(l-ethylpentyl)-l-propyl-  N-(l-ethylpentyl)-l-propyl-   tied
            butyl               butyl
              N-(l-ethylbutyl)-l-propyl-    tied
                             pentyl

N,N-dibutylheptyl

N,N-dibutylheptyl
N-butyl-N-pentylhexyla

:

dioctylb

dioctyl                 tied
N-heptylnonyl             tied
N-hexyldecyl             tied

trioctylb

trioctyl
N-heptyl-N-octylnonyl
N,N-diheptyldecyl
N-hexyl dinonly
N-hexyl-N-octyldecyl
N-hexyl-N-heptylundecyl
N,N-dihexyldodecyl

tied
tied
tied
tied
tied
tied
tied

a) The use of tallies excludes these structures.
b) Tallies were used in these runs.


Table 4. ",;:;; for which AMINE found no structures using
         = 1.5 ppm.  The correct solutions appeared
     when DELTA was increased to 2.25 ppm and tallies
      were included.          i

l-isopropylhexylamine
N-pentyl-1,2,2-trimethylpropylaminea
N-butyl-N-(1,2,2-trimethylpropyl)pentylamine

N-butyl-N-pentyl(l,l,3,3-tetramethylbutyl)amine

a) A second structure, equally ranked, was found in this
   case:  N-propyl-N-(1,2,2-trimethypropyl)hexylamine,