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3902 J. Am. Chem. SOC. 1985, 107, 3902-
the mechanisms were already known or limited to two alternatives,
and calculations using the larger basis sets have been further
limited to very small molecules. To be useful as a general chemical
tool, it must be possible to study rather large systems in detail.
This can require an enormous amount of computation.
A striking feature of the results in Table I11 is the relatively
small difference between the errors given by the 3-21G and 6-31G*
models and between the ones given by the three semiempirical
procedures. The accuracies of all seem indeed to be limited by
some common factor. Thermal energy seems the obvious can-
didate. As noted above, nearly all ab initio studies of reactions
have been based on the assumption that the thermal energy of
a molecule is an additive function of the atoms in it, so that a heat
of reaction or activation can be equated to the corresponding
differeme in total energy between the reactants and the products
or the transition state. The same assumption is made tacitly in
our semiempirical methods, where allowance for thermal energy
is included via the parametrization, so it applies generally to the
results in Table 111. Better results could undoubtedly be obtained
by making specific allowance for the thermal energy, using
partition functions constructed from calculated vibration fre-
quencies, etc..
One last point of interest should be noted. By using eq 5 in
reverse, ab initio energies of molecules can be estimated from their
experimental heats of formation, with an average error of only
fO.O1 au. This could be useful in the case of larger molecules
where calculations by the better ab initio methods would be
prohibitively expensive. Since these are believed to give energies
reasonably close to the H F limit, an indication of the latter could
be obtained simply, and at no cost, in this way. Such information
would provide a useful indication of the level of accuracy of ab
initio procedures relative to Hartree-Fock.
Acknowledgment. This work was supported by the Air Force
Office of Scientific Research (Contract No. F49620-83-C-0024),
the Robert A. Welch Foundation (Grant No. F-126), and the
National Science Foundation (Grant CHE82- 17948). The cal-
culations were carried out using a DEC VAX 11-780 computer
purchased with funds provided by the National Science Foundation
(Grant CHE78-03213) and The University of Texas at Austin.
AM1: A New General Purpose Quantum Mechanical
Molecular Model’
Michael J. S. Dewar,* Eve G. Zoebisch, Eamonn F. Healy, and James J. P. Stewart
Contributionfrom the Department of Chemistry, The University of Texas at Austin,
Austin, Texas 78712. Received October 29, 1984
Abstract: A new parametric quantum mechanical molecular model, AM1 (Austin Model l), based on the NDDO approximation,
is described. In it the major weaknesses of MNDO, in particular failure to reproduce hydrogen bonds, have been overcome
without any increase in computing time. Results for 167 molecules are reported. Parameters are currently available for C,
H, 0, and N.
Introduction
The purpose of the work reported in this series of papers’ has
been the development of a quantitative quantum mechanical
molecular model for chemists to use as an aid to experiment in
their own research, in particular in studies of chemical reactions
and reaction mechanisms. To be useful in this connection, such
a procedure must be not only sufficiently accurate but also ap-
plicable to the molecules in which chemists are directly interested
rather than confined to simple models. These requirements
eliminated, and still eliminate, a b initio procedures because such
procedures are too inaccurate and/or require far too much com-
puting time.’ Our approach has accordingly been to use an
approximation simple enough for the desired calculations to be
feasible, using currently available computers, and to upgrade the
accuracy of the results by introducing parameters that can be
adjusted to fit the results to experiment. In this way we have been
able to develop * two effective models, MIND0/33 and MNDO:
which are being widely weds5 As the preceding paper’ shows,
the results from MIND0/3 and MNDO are generally comparable
with those from ab initio methods that require at least 1000 times
more computing time.
(1) Part 76 of a series of papers reporting the development and use of
quantum mechanical molecular models. For part 75, see: Dewar, M. J. S.;
Storch, D. M. J. Am. Chem. Soc., preceding paper in this issue.
(2) Dewar, M. J. S. J. Mol. Struct. 1983, 100, 41.
(3) Bingham, R. C.; Dewar, M. J. S.; Lo, D. H. J. Am. Chem. SOC. 1975, 97, 1285, 1294, 1302, 1307.
(4) Dewar, M. J. S.; Thiel, W. J. Am. Chem. SOC. 1977, 99, 4899, 4907.
(5) A total of 623 papers reporting MNDO calculations have been listed in Chemical Abstracts since 1980.
It should be emphasized that even M I N D 0 / 3 and MNDO are
too slow for general use in chemistry, using currently available
computers. Calculations of reaction mechanisms, using standard
computers such as the DEC VAX 11-780, require excessive
amounts of computer time for systems containing more than a
dozen “heavy” atoms (Le., other than hydrogen). While much
larger systems can be treated using “state-of-the-art” computers,
such as the CDC 205 or CRAY, this does not reduce the cost of
the calculations, because while these are several hundred times
faster than a VAX, the cost of computing time is also greater by
an almost equally large factor. A 100-fold increase in the speed
of computers, with no increase in the cost of computing time, will
be needed to enable our procedures to achieve their full potential,
particularly in projected applications to biochemistry and or-
ganometallic chemistry.
A major problem in studying reactions by any current theo-
retical model is the lack of experimental data for the intermediate
sections of potential surfaces and for the geometries of transition
states. Calculations for these consequently involve the extrapo-
lation of an empirical6 procedure into areas where it has not been,
and indeed cannot be, tested. Such an extrapolation is safer, the
better the performance of the method in question in all areas where
it can be tested. Confidence in a semiempirical procedure is
moreover strengthened by demonstrations of its ability to reproduce
experimental results unrelated to those used in determining the
parameters in it. One of the major assets of M I N D 0 / 3 and
(6) The errors in energies calculated even by “state-of-the-art” ab initio methods are enormous by chemical standards, far too large for any conclusions to be drawn a priori from the results; see ref 1.
0 1985 American Chemical Society
New General Purpose Quantum Mechanical Molecular Model
M N D O was their demonstrated ability to reproduce all
ground-state properties’ of molecules of all kinds,15 including
properties and types of molecules not used in parametrizing them.
MIND0/3 has proved very effective in studies of a wide variety
of hydrocarbons.18 Problems arise, however, in the case of
molecules containing heteroatoms because of the neglect of
one-center overlap in the INDO approximation on which MIN-
D 0 / 3 is based. These problems are avoided in MNDO but at
the expense of other ~eaknesses,~in particular failure to reproduce
hydrogen bonds, energies that are too positive for crowded
molecules (e.g., neopentane) and too negative for ones containing
four-membered rings, and activation energies that tend to be too
large.
After several years of effort we have finally been able to develop
a “third generation” treatment in which these errors have been
largely corrected. In view of the terminological confusion that
has arisen between our procedures and conventional semiempirical
ones which, while using the same basic approximations (CNDO,
INDO, etc.), are grossly inaccurate, we decided to adopt ar.
entirely different name for the new procedure, Le., Austin Model
1 (AM1). While AM1 has as yet been parametrized only for the
“organic” elements (CHON), no problems should arise in ex-
tending it to other ”MNDO” elements. Parameters for these will
be reported in due course.
Development of AM
Extensive earlier attempts to correct the errors in MNDO,
indicated above, convinced us that they mostly had a common
cause, Le., a tendency to overestimate repulsions between atoms
when at ca. their van der Waals distance apart. The obvious way
to deal with this was to modify the core repulsion function4 (CRF)
in MNDO. Since extensive attempts to find a suitable function
of some other type failed, we decided to use a brute force approach,
modifying the existing function by additional Gaussian terms.
Now that we know the optimum form of the function, we hope
in later versions to approximate it by one with fewer parameters.
We believe that AM1, in its present form, probably represents
about the best that can be achieved using the NDDO approxi-
mation as a basis, without specific allowance for the contributions
of thermal energy. The C R F in it is as follows:
CRF(AB) = zAzByss[l + F(A) + F(B)J
where
~ ~~~~ ~ (7) Properties reproduced by MNDO include heats of formation: molec- ular g e ~ m e t r i e s , ~dipole moments: ionization e n e r g i e ~ , ~electron affinities,* p~larizabilities,~molecular vibration frequencies,’O thermodynamic proper- ties,” kinetic isotope effects,12properties of polymers,” and ESCA chemical shifts. (8) Dewar, M. J. S.; Rzepa, H. S. J. Am. Chem. Soc. 1978, 100, 784.
(9) Dewar, M. J. S.; Yamaguchi, Y.; Suck, S. H. Chem. Phys. Lett. 1978,
(10) Dewar, M. J. S.; Ford, G. P.; McKee, M. L.; Rzepa, H. S.;Thiel, W.; Yamaguchi, Y. J. Mol. Struct. 1978, 43, 135. (1 1) Numerous calculations have shown that the results from MNDO are at least as good as those from MIND0/3. For the latter, see: Dewar, M. J. S.; Ford, G. P. J. Am. Chem. SOC. 1977, 99, 7822.
(12) Brown, S. B.; Dewar, M. J. S.; Ford, G. P.; Nelson, D J.; Rzepa, H.
S. J. Am. Chem. Sor. 1978, 100, 7832.
(13) (a) Dewar, M. J. S.; Yamaguchi, Y.; Suck, S. H. Chem. Phys. 1979,
43, 145. (b) Dewar, M. J. S.; Stewart, J. J. P., work in course of publication.
(14) Rzepa, H. S., unpublished work.
(15) While both MIND0/3 and MNDO were parametrized using data exclusively derived from normal closed-shell neutral molecules, they reproduce the properties of ion^,'^^^^^ carbenes,’~~and ‘nonclassical” species (boron hydrides16 and carboranesl’). (16) Dewar, M. J. S.; McKee, M. L. Inorg. Chem. 1978, 17, 1569.
(17) Dewar, M. J. S.; McKee, M. L. Inorg. Chem. 1980, 19, 2662.
(18) MIND0/3 also reproduces the energies of “nonclassical” carbocations
surprisingly effectively. See: Dewar, M. J. S.; Rzepa, H. S. J. Am. Chem.
SOC. 1977, 99, 7432.
J. Am. Chem. SOC., Vol. 107, No. 13, 1985 3903
Table I. AM1 Parameters
element
parameter H C N 0
Us, -11.396427 -52.028658 -71.860000 -97.
a 2.882 324 2.648 274 2.947 286 4.455 371 Kl 0.122796 0.01 1355 0.025251 0. K2 0.005 090 0.045 924 0.028 953 0.081 430 K3 -0.018 336 -0.020061 -0.005 806 K4 -0.001 260 Ll 5.000 000 5.000 000 5.000 000 5.000 000 L2 5.000000 5.000000 5.000000 7.
L4 5.000^000
MI 1.200 000 1.600 000 1.500000 0.847 918
M 2 1.800000 1.850000 2.100000 1.
M 3 2.iOOOOO 2.050000 2.
M4 2.650^000
UP,
i-s i-P
P,
P P
L3 2.000000 5.000000 2.
The symbolism is the same as that in M N D 0. 4 The values of
the L parameters (which determine the widths of the Gaussians)
were not critical so a common value was used for most of them.
They were not included in the overall optimization. The M and
K parameters were all optimized. Note that the Gaussian terms,
like the others in the CRF, refer to individual atoms, not pairs
of atoms.
In MNDO, parameters were determined first for hydrocarbons
(C, H), and other elements were then added one at a time. We
had to do this because the number of molecules that could be
included in the basis set for parametrization was limited by the
computing time required. De~elopment’~of a greatly improved
optimization procedure has made possible the use of a much larger
basis set, allowing parameters for C, H, 0, and N to be optimized
in a single operation with a basis set which included some CHON
species.
Two strategies were used to modify the C R F and reduce ex-
cessive interatomic repulsions at large separations. In the first,
one or more attractive Gaussians were added to compensate the
excessive repulsions directly, centered in the region where the
repulsions were excessive. In the second, repulsive Gaussians were
centered at smaller internuclear separations, leading to an overall
reduction of the main term in the expression for the core repulsion
and hence reducing the repulsion at larger internuclear distances.
In the case of carbon, hydrogen, and nitrogen, both types of
Gaussian were included, while only repulsive Gaussians were
needed for oxygen. Attempts to use only repulsive Gaussians for
the other elements led to poorer results while use of attractive
Gaussians alone led to no improvement over MNDO.
This kind of modification is by no means subtle, and indeed
Burstein and Isaev20have recently described a similar modification
of MNDO which accommodates hydrogen bonds, specific extra
Gaussian terms being added for the pairs of atoms forming such
bonds. Such ad hoc additions of terms could of course be made
to correct errors in MNDO for any specific interactions in any
molecule or molecules but only at the expense of undermining its
validity as a general molecular model. For reasons indicated above,
a procedure of this kind can be useful in chemistry only if the same
parameters are used throughout, without reference to the structures
of the individual molecules to which it is being applied.
It should perhaps be emphasized that the development of an
effective treatment of this kind is not^ a trivial matter. Parame-
trization is still a purely empirical affair. All our attempts to
develop theories that might help in the choice of parametric
functions and parameters have failed. In the present study, each
choice of Gaussians had to be tested by a complete reparame-
(19) Stewart, J. J. P., unpublished work.
(20) Burstein, K. Ya.; Isaev, A. N., Theor. Chim. Acta 1984, 64, 397.
New General Purpose Quantum Mechanical Molecular Model
Table 111. Comparison of Mean Absolute Errors for AMI, MNDO,
and MIND0/
no. of
com- MINDO/
average error in: pounds AM1 MNDO 3
heats of formation (kcal/mol)
(a) hydrocarbons 58 5.07 5.87 9.
(b) species containing N 80 5.88 6.64 11.
and/or 0
dipole moments (D)
(a) hydrocarbons 11 0.17 0.25 0.
(b) species containing N 46 0.26 0.32 0.
and/or 0
ionization energies (eV)
(a) hydrocarbons 22 0.29 0.39 0.
(b) species containing N 29 0.40 0.55 1.
and/or 0
Parameters
As indicated above, the formalism used in AM1 is essentially
the same as in MNDO, with the exception of the CRF. The
one-center electron repulsion integrals (gij, hij) remain unchanged,
having the values assigned by Oleari.,I The parameters optimized
were Us,, U , [,, Jb, B,, and B,, and the parameters (Kx,CY, and M x involver in the C R F (see above).
The value of a model is not related to the number of parameters
used nor to the results for molecules in the parameterization basis
set. Instead we are interested in its ability to correctly handle
new situations, chemical systems which are not in the data set
used to develop and test the model. With this idea in mind we
carried out a selective grid search22of the parameter hypersurface
to find what we now believe to be the global minimum. Part of
the improvement in AM1 over MNDO is due to the fact that a
better minimum was found, corresponding in particular to different
orbital exponents, which have a large effect on activation barriers,
and to the ratios of the B parameters for s and p AOs, which
appear to control the bond angles. Since the results for oxygen
and nitrogen were little affected by changes in U,,, we set them at the Oleari2' values. Likewise B, and B , for oxygen were set
equal to ensure good bond angles for oxygen compounds.
Results and Discussion A. Heats of Formation of Neutral Closed-Shell Molecules.
Table I1 compares with experiment the heats of formation of the
138 molecules included in our standard tests. The third and fourth
columns compare the errors in heats of formation from two ab
initio models derived in the preceding paper.' The results from
MNDO and AM1 are summarized in Table I11 which shows the
average (unsigned) errors for the 58 hydrocarbons and 80 mol-
ecules containing nitrogen and/or oxygen.
Note that the AM1 errors for neopentane and tert-butylamine
are all much less than those from MNDO. Clearly there has been
a major improvement in the treatment of crowded molecules.
Similar remarks apply to molecules containing four-membered
rings, where the AM1 values are now reasonable. The im-
provement is dramatic in the case of cubane.
The only major AM1 errors for hydrocarbons are for fulvene
and bicyclobutane, both of which resisted attempts to eliminate
them. The results for n-paraffins indicate that the CHI increment
is in error by ca. -1.9 kcal/mol. AM1 performs well for olefins
and acetylenes, being much better than MNDO in the case of
conjugated acetylenes. Cyclopentane and cyclohexane are both
too stable, as would be expected in view of the too negative CH,
increment.
The AM1 values for the nitrogen compounds are, overall,
somewhat better than those from MNDO. The AM1 error for
pyrrole is larger than in MNDO. However, the AM 1 error for
Table I lists the final values of the parameters.
(21) Oleari, L.; DiSipio, L.; DeMichelis, G. Mol. Phys. 1966, 10, 97.
(22) Zoebisch, E. G. Ph.D. Dissertation, The University of Texas at Austin
(in preparation).
J. Am. Chem. Soc.. Vol. 107, No. 13, 1985 3905
Table IV. Comparison with Experiment of AM1 and MNDO Heats
of Formation (Mf; kcal/mol) for Cations
Mi error
cation obsd" AM1 AM1 MNDO
methyl cation
ethyl cation (classical)
2-propyl cation
fer!-butyl cation
ethylene radical cation
allyl cation
tropylium
benzyl cation
NH4+
CH2NH2+
OH3+
HCO+
CH2=OHt
NO,*
NOi 237 228 -9 -
"For references, see: Dewar, M. J. S. ; Thiel, W. J. Am. Chem. SOC.
Table V. Heats of Formation (AH?; kcal/mol) for Neutral Radicals
AHi error
radical expt' AM1 AM1 MNDO
"For references, see: Dewar, M. J. S. ; Thiel, W. J. Am. Chem. SOC.
pyridazine is less, and the errors for pyrimidine and pyrazine much
less, than in MNDO. Simple nitrates are also reproduced better
by AM1 while the error for methyl isocyanide, although large,
is also much less than in MNDO.
The AM 1 errors for oxygen-containing compounds are some-
what larger than those for nitrogen-containing ones or hydro-
carbons, as was also the case in MNDO. Singlet oxygen ('Ag 0,)
is much too stable and carbon monoxide much too unstable.
Clearly AM1, like MNDO, has problems with diatomic molecules
(see also NJ. The error in ozone is, however, much less, suggesting
that AM 1, unlike MIND0/3 or MNDO, may be useful in studies
of the mechanism of ozonization. Note in this connection the
excellent results for peroxides. The error for carbon dioxide, while
large, is much less than in MNDO although maleic anhydride
is worse.
Turning now to molecules containing both nitrogen and oxygen,
AM1 is seen to represent a very real improvement over MNDO,
though the errors are still rather large. While MNDO gave a
value for the heat of isomerization of methyl nitrite to nitro-
methane that was in error by 41.8 kcal/mol, this has been reduced
in AM1 to 23.7 kcal/mol. The correction of nonbonded repulsions
also shows itself in the geometries of nitrobenzene and benz-
aldehyde, both of which are (correctly) predicted to be planar by
AM1. MNDO predicted the substituents to be orthogonal to the
ring, presumably through overestimation of the repulsions between
oxygen and the ortho hydrogen atoms.
B. Cations. Table IV shows similar comparisons with ex-
periment of heats of formation calculated for a number of cations,
using AM1 and MNDO. The AM1 values are clearly better.
AM1 does, like MNDO, fail to make the T complex form of the
ethyl cation more stable than the classical one. However, the error
3906 J. Am. Chem. SOC.,Vol. 107, No. 13, 1985 Dewar et al.
Table VI. Heats of Formation (AHr; kcal/mol) for Anions
AHI
anion expta AM 1 error
C H 3 0 - -36.0 -38.8 -2.
C2HSO- -47.5 -45.8 -1.
C6HsO- -40.5 -41.0 -0. HCOO- -106.6 -1 10.0 3. CHSCOO- -122.5 -1 16.0 6. CH3NH- 30.5 33.1 2.
(1-pyrrole)- 19.5 28.1 8. NCCH2 24.1 30.8 6.
(CH3)2N- 24.7 22.4 -2.
02NCH2- -26.4 -29.2 -2.
HO- -33.2 -14.1 19.
CSHS- 21.3 25.2 3.
a Bartmess, J. E.; McIver, R. T., Jr. In “Gas Phase Ion Chemistry”;
Academic Press: New York, 1979; Vol. 11.
Table VII. Calculated Heats of Reaction for Formation of
Hydrogen-Bonded and van der Waals Adducts
donor/acceptor AH donor/acceptor AH
CH30H/HzO -2.7 C,HSN/H20 -2. HIO/CHIOH -5.0 H C O O H / N H , -2. H2O/C02 -2.5 H C O O H / H C O O H -6. H 2 0 / C H 2 0 -3.4 NH2CHO/NH2CHO -7.
NH3/H20 -2.7 C 0 2 / C 0 2 0.
H 2 0 / H 2 0 -3.3 CH,/CH, -0.
Table VIII. Rotational and Inversion Barriers (kcal/mol)
barrier error
molecule obsd“ AM1 AM1 M N D O ethylene 65.0 65.93 0.9 -2. ethane 2.9 1.25 -1.7 -1. methylamine 2.0 1.29 -0.7 -0. methanol 1.1 1.04 -0.1 -0. HO-OH (cis) 7.0 6.90 0.0 -0. HO-OH (trans) 1.1 0.09 -1.0 -1. formamide -20 10. n-butane (gauche) 0.8 0.73 -0. n-butane (eclipsed) 4-6 3. nitrobenzene 6. NH, (inversion) 6 4.24 2
OFor references, see: Dewar, M.J.S.; Thiel, W. J. Am. Chem. SOC.
is less than that in MNDO and indeed is similar to that given by t h e 4-31G ab initio model (7.3 kcal/molZ3). C. Radicals. T a b l e V shows similar comparisons with ex- periment of heats of formation for radicals. Here AM1 is clearly m u c h superior t o MNDO. W h i l e t h e errors for N O and NO2, and for t h e corresponding cations, a r e still large, these were t o be expected, given the poor results for other diatomic molecules and given that C 0 2 is isoelectronic with NO2+. D. Anions. T a b l e V I compares heats of formation calculated by AM1 for a variety of anions with experiment. The agreement is very good except for HO-, w h e r e t h e AM1 value is far too positive, a n d t h e 1-pyrrolyl anion, w h e r e t h e error reflects t h a t
(14 k c a l / m o l ) for pyrrole.
MNDO likewise gave a h e a t of f o r m a t i o n for HO- t h a t was m u c h too positive.24 T h e error was attributed, undoubtedly correctly, t o the failure of our procedures to allow for orbital
expansion in a t o m s carrying large negative charges. It h a s been
found25 t h a t ab initio methods reproduce t h e energies of anions
~ ~~ ~~ ~ ~
(23) (a) Pople, J. A. Inr. J. Mass Specrrom. Ion Phys. 1976, 17, 1. (b)
Lathan, W. A.; Curtis, L. A,; Hehre, W. J.; Lisle, J. B.; Pople, J. A. Prog.
Phys. Org. Chem. 1974, 1 1 , 1.
(24) Dewar, M. J. S.; Rzepa, H. S. J. Am. Chem. Soc. 1978, 100, 784.
(25) (a) Chandrasekhar, J.; Andrade, J. G.; Schleyer, P. v. R. J. Am. Chem. SOC. 1981, 103, 5609. (b) Spitznagel, G. W.; Clark, T.; Chandra-
sekhar, J.; Schleyer, P. v. R. J. Comput. Chem. 1982, 3, 363.
Table IX. First Ionization Potentials ( I P eV) IP error molecule expt, AM1 AM1 M N D O hydrogen methane ethane ethylene acetylene propane
prop en e
ProPYne allene isobutane trans-l,3-butadiene diacetylene neopentane cyclopropane cyclopropene cyclobutane cyclobutene cyclopentene cyclopentadiene benzene toluene naphthalene nitrogen ammonia methylamine dimethy lamine trimethylamine eth ylidenimine pyrrole pyridine hydrogen cyanide acetonitrile acrylonitrile propynenitrile cyanogen ozone water methanol dimethyl ether oxirane furan carbon monoxide carbon dioxide formaldehyde acetaldehyde acetone ketene propenoaldehyde glyoxal (trans) formic acid
12.10b
10.07’
11.00b
11 .OO’
9.45‘ 8.93’
12.7Sb
0.57 1 .oo 0.76 0. 0.44 0. -0.70 -0. -0.57 -0. -0.11 0. 0.51 0. 0.95 1. -0.04 -0. 0.58 0. 0.07 0. 0.31 0. methyl formate 11.02 11.57 0.55 0.
a Except where noted: Siegbahn, K.; Allison, D. A.; Allison, J. H. In
“Handbook of Spectroscopy”, Robinson, J. W., Ed; CRC Press:
Cleveland Ohio, 1974; Vol. I, Section B. bFor references, see: Dewar,
M. J. S.; Thiel, W. J. Am. Chem. SOC. 1977 99, 4907.
only if diffuse AOs are included in t h e basis set. U s e of a split basis set is likewise essential in calculations for cations to allow for orbital shrinkage with positive charge. .Indeed, it seems
surprising a t first sight t h a t t h e results f r o m MNDO a n d AM
for ions of b o t h signs are normally so good, given t h a t t h e pa- rameters in both treatment were determined solely from d a t a for n e u t r a l molecules a n d given t h a t no provision is made in either for c h a n g e s in AOs with a t o m i c charge. However, t h e charges on atoms in neutral organic molecules c a n be quite large, judging by results both from AM1 or MNDO and from a b initio methods. The scheme used in MNDO a n d AM1 can evidently accomodate
itself to such situations. Problems arise only when the c h a r g e on
an a t o m approaches unity. N o t e t h a t even a methyl g r o u p is sufficient to relieve t h e situation, the AM1 heat of formation for CH30- agreeing well with experiment. I n it the calculated formal
c h a r g e o n oxygen is 0.76.
E. Hydrogen Bonds. Table VI1 shows calculated (AM1) heats
3908 J. Am. Chem. SOC., Vol. 107. No. 13, (^1985) Dewar et al.
Table XII. Bond Lengths (XU, A), Bond Angles (XYZ, deg), and Dihedral Angles (WXYZ, deg) molecule geometrical parameters, calcd (obsd)“ H l H H 0.667 (0.742) CH4 CH 1.112 (1.094) C2H C 2 H 4 C’H C3Hs (a)
CC 1.501 (1.536), CH 1.117 (1.091), HCC 110.7 (110.9)
CC 1.325 (1.339). CH 1.098 (1.086), HCC 122.7 (121.2)
CC 1.195 (1.203), CH 1.061 (1.060)
CC 1.507 (1.526), C’H4 1.117 (1.089) C’H’ 1.117 (1.094), C2H71.123 (1.096), C’C’C’ 111.8 (112.4), H7C2H8107.0 (106.1),
H4C’C2110.42 (111.8), HSC’H6108.2 (107.3), C2CiHSH6121.4 (126.4)
1.119 (1.098). C’C2C’ 123.9 (124.3), H4CiC2122.5 (121.5), HSC’C2 122.8 (120.5), H6C2Ci 121.3 (119.0), H7C’C2 111.9 (111.2)
H2C=CHCH3 (a) (^) C’C2 1.331 (1.336), C2C31.478 (1.496), C’H4 1.097 (1.081), C1H5 1.098 (1.091), C2H6 1.103 (1.090), C3H71.117 (1.109), C3H
HC=CCH CH,C=CH
n-C4Hio i-C4Hlo
H8C’H9 108.0 (106.2). C2C’H8H9 120.0 (126.0)
C‘C’ 1.197 (1.206), C2C’ 1.427 (1.459), C’H 1.060 (1.056), C’H 1.121 (1,105). C2C3H 110.5 (110.2)
C’C2 1.510 (1.533), C’C’ 1.514 (1.539), C’C2C’ 111.6 (112.8)
CC 1.514 (1.525), CCC 110.7 (111.2)
H,C=C=CH, CC 1.298 (1.308), CH 1.100 (1.087), HCH 115.4 (118.2)
CH,CH=CHCH’
H2C=C(CH3)
H$=CHCH=CH
C’C2 1.475 (1.508), C2C’ 1.336 (1.347), C’C2C’ 123.96 (123.8)
C’C2 1.336 (1.330), C2C’ 1.483 (1.508), C’C2C3 122.4 (122.4)
C’C2 1.334 (1.341), C2C31.451 (1.463), C’C’C’ 123.5 (123.3)
HJCC=CCH,
HC=CCH=CH
HC=CC=CH
C (C H 3 ) 4
cyclopropane
cycI op r op en e
cyclobutane cyclobutadiene cyclopentane cyclopentadiene (a) fulvene cyclohexane cyclohexene benzene bicyclobutane spiropentane housane (a) norbornane norbornadiene naphthalene N NH
HN(CHJ N(CH3)’ azirane pyrrole
pyridine
HCN
CHgNH
CH’CN
CHZ=CHCN
NCCN
CH,NC (a) HzNNH CH2N 0 2 0 3 H2O H CH,OH (a)
(CHd2O furan
CH3C0’02H
HCOOCH
N
HO’N
C’C2 1.425 (1.444), C2C31.198 (1.213), C’H 1.121 (1.115), HC’C2 110.6 (110.7)
C’C2 1.198 (1.208), C2C’ 1.409 (1.431), C’C4 1.336 (1.341), C2C3C4124.3 (123.1)
C’C2 1.198 (1.205). C2C3 1.357 (1.376), C’H 1.060 (1.046)
CC 1.521 (1.539), CH 1.116 (1.120), HCC 110.3 (110.0)
CC 1.501 (1.510), CH 1.104 (1.089), HCH 111.7 (115.1)
C’C2 1.317 (1.296), C2C31.490 (1.509), C’H 1.069 (1.072). C’H 1.106 (1.088), HC’C2 151.9 (149.9), HC’H 111.5 (114.6)
CC 1.545 (1.548), CH 1.109 (1.133), HCH 109.6 (108.1), CCCC 0.0 (153.0)
C’H 1.080 (1.083), C3H 1.109 (1.094), HC‘C’ 136.3 (133.5), HC’H 110.6 (109.2), C1C4HH131.7 (135.8)
CC 1.521 (1.546), CH 1.116 (1.114), HCC 110.3 (111.7)
C’C2 1.359 (1.342), C2C3 1.471 (1.469), C’C’ 1.509 (1.509)
C’C2 1.483 (1.470), C2C3 1.363 (1.355), C’C4 1.477 (1.476), C’C6 1.332 (1.349)
CC 1.515 (1.536), CH 1.121 (1.121), CCC 111.3 (111.4). HCH 107.4 (107.5), CCCC 55.1 (54.9)
C’C2 1.334 (1.335), C2C31.485 (1.504), C3C4 1.517 (1.515), C4Cs 1.514 (1.550), CiC2C4Cs14.0 (28.3) CC 1.395 (1.397), CH 1.100 (1.084) C’C2 1.510 (1.498), C’C’ 1.494 (1.497), C’H 1.080 (1.071), C’H, 1.105 (1.093), C2H,, 1.104 (1.093), C2C’C’C4 122.0 (121.7) C’C2 1.480 (1.469), C2C’ 1.507 (1.519), C2 1.105 (1.091), HC2H 112.5 (118.4), C3C2H 145.7 (148.3) C’C2 1.536 (1.528), C2C3 1.557 (1.565). CiC4 1.541 (1.536), C’C’ 1.505 (1.507). CJC4C1Cz114.6 (116.7) C’C2 1.542 (1.539), C2C3 1.540 (1.557). C’C7 1.550 (1.560). C’C7C494.3 (93.1), C6C1C4C3112.0 (113.1) C’C’ 1.531 (1.535), C’C’ 1.354 (1.343), C’C’ 1.576 (1.573), C’C2C492.7 (94.1), C6C’C4C’ 112.5 (115.6) C’C2 1.373 (1.364), C2C3 1.416 (1~415),C’C9 1.422 (1.421), C9Clo 1.421 (1.418) N N (1.094) N H 0.998 (1.012), HNH 109.0 (106.7) CN 1.432 (1.474), N H 1.004 (l.Oll), HNC 111.3 (112.0), HNH 109.0 (105.9) CN 1.437 (1.426), N H 1.003 (1.019), CNC 114.6 (112.2), HNC 109.0 (108.9), HNCC 126.3 (125.4) CN 1.447 (1.451), CNC 112.8 (110.9) CN 1.455 (1.475), CC 1.495 (1.481), N H 1.002 (1.016), HNCC 106.5 (112.5) N’C2 1.391 (1.370), C2C31.401 (1.382), C’C4 1.436 (1.417), N’H 0.984 (0.996), C2H 1.089 (1.076), C’H 1.085 (1.077), H2CC 130.0 (130.8), HC’C’ 126.8 (125.5) C2N’ 1.347 (1.338), C2C’ 1.408 (1.394), C3C4 1.396 (1.392), C2H 1.047 (1.086), C’H 1.096 (1.082), C4H 1.100 (1.081), C6N’C 117.6 (lI6.9), N’C’C’ 123.4 (123.8), C2C3C4118.3 (118.5), C’C4C’ 118.9 (118.4), HC2C’ 120.8 (120.2), HC’C’ 120.5 (120.1) CN 1.160 (1.154), CH 1.069 (1.063) CN 1.163 (1.157), CC 1.440 (1.458), CH 1.120 (1.104), HCC 110.1 (109.5) C’C’ 1.334 (1.339). C2C3 1.420 (1.426), C’N 1.164 (1.164), C’C2C3 123.2 (122.6) CN 1.162 (1.154), CC 1.384 (1.389) CiN2 1.395 (1.424), N2C3 1.181 (1,166), C’H 1.125 (l,lOl), HC’N2 110.1 (109.1) NN 1.379 (1.449), N H 1.014 (1.022), H N N 107.2 (112.0), H N H 105.8 (106.0), HNNH 61.9 (90.0) CN 1.294 (1.32). N N 1.139 (1.12). CH 1.099 (1.08), HCH 121.2 (127) 00 1.087 (1.216) 00 1.160 (1.278), 000 120.9 (116.8) OH 0.962 (0.957), HOH 103.4 (104.5) 00 1.300 (1.475), OH 0.983 (0.950), HOO 105.9 (94.8), HOOH 128.3 (119.8) C’O’ 1.410 (1.425), 0 2 H 30.964 (0.945), C’H4 1.119 (1.094), C‘HJ 1.119 (1.094), C’02H’ 107.2 (108.5), H4C’02 105.1 (107.0),
CO 1.417 (1.410). COC 112.9 (111.7) O’C2 1.397 (1.362). C2C31.397 (1.361). C’C4 1.447 (1.431), C2H 1.085 (1.075), C’H 1.086 (1.077). HC20’ 114.3 (115.9), HC3C 125.5 (128.0) CO 1.171 (1.128) CO 1.189 (1.162) CO 1.228 (1.208), CH 1.110 (1.116), HCH 115.6 (116.5) C’C2 1.489 (1,501). C 2 0 1.231 (1,216). C2H 1.117 (1,114). C’C’O 123.5 (123.9), C’C2H 115.3 (117.5) CC 1.495 (1.507), CO 1.236 (1.222), CCC 115.5 (117.2) C’C2 1.307 (1.314), C’O 1.193 (1.161), C’H 1.095 (1.085), HC’H 117.2 (122.6) CO 1.229 (1.207). CC 1.508 (1.525), CH 1.111 (1.116), OCC 121.0 (121.2), HCC 115.9 (112.2) CO’ 1.230 (1.202), C 0 2 1.356 (1.343), 0 2 H 0.972 (0.927), CH 1.103 (1.097), O’C02 117.6 (124.9), C02H 110.6 (106.3), HCO’
CC 1.486 (1.520), CO 1.234 (1.214), CO 1.365 (1.364), OH 0.971 (0.97), CCO 129.4 (126.6), CCO 114.0 (110.6), COH 110.
O’C2 1.230 (1.200), C’O’ 1.364 (1.334), 0 3 C 41.429 (1.437), O’C203119.1 (125.9), C203C4117.3 (114.8) N N 1.128 (1.126), NO 1.175 (1.186) NO2 1.157 (1.163), NO’ 1.319 (1.433), O’H 0.974 (0.954), O ’ N 0 2 112.6 (110.7), N 0 2 H 107.0 (102.1)
HSCiH6110.1 (108.6), 02C’HSH6119.5 (129.8)
New General Purpose Quantum Mechanical Molecular Model (^) J. A m. Chem. Soc., Vol. 107, No. 13, 1985 3909
Table XI1 (Continued) molecule geometrical parameters, calcd (obsd)’
HON02(a) N O ’ 1.186 (1.1991, N O 2 1.195 (1.211), N O 3 1.334 (1.406), 03H0.983 (0.964). 01N02129.1 (113.9), O W 0 3 116.4 (115,9), N03H109.
H 2 N C H 0 (a) C N 1.365 (1.376), C O 1.242 (1.193), C H 3 1.117 (1,102). NH’ 0.990 (1.014), NH2 0.986 (1.002), H ’ N C O 0.1 ( - 7 ) , H 2 N C H 30. (-12) ‘For numbering of atoms and references, see: Dewar, M. J. S. ; Thiel, W. J. Am. Chem. SOC. 1977 99, 4907.
Table XIII. Heats of Activation (kcalimol)
heat of activation
reaction obsd AM 1 MNDO MIND0/
CH,. t CH,=CHCH, .+ CH,CH,CHCH, 7.4b 1.31 13.5 7.
(CH,),CH. (C) 3.99 18.0 12.
CH; t CH,CH, + CH4 + C,H; 11“ 11.96 27.2 6. :CHCH, +CH,=CH, 1-3 14.92 21.8 0.
CH; + HC=CH + CH,CH=CH, 7.7a 6.83 16.7 7.
40 F 6e 61.57 9 0 63.
32.9f 36.
a Kerr, J. A.; Parsonage, M. J. “Evaluated Kinetic Data o n Gas Phase Addition Reactions; Reactions of Atoms and Radicals with Alkenes,
10% of total product.
Alkynes, and Aromatic Compounds”; Butterworths: London, 1972.
probably low, d u e to neglect of tunneling. Ab initio estimates range from 6.6 to 11.5. e Kwart, H.; Latimare, hl. C. J. A m. Chem. SOC.
1971, 93, 3770. (a) Cooper, W.; Walters, W. D. Ibid. 1958, 80, 4220. (b) Carr, R. W.; Walters, W. D. J. Phys. Chem. 1965, 6 9 , 1073.
results are again better, as the average errors listed in Table I
show.
Cvetzanovic, R. J. ; Irwin, R. S. J. Chem. PJiys. 1967,46, 1694.
This value (Baughcum, S. L.; Smith, 2. ; Wilson, E. B.; Duerst, R. W. J. A m. Clrern. SOC. 1984,106, 2260) is
AM1 value compares quite well with that (35.8 kcal/mol) from
a recent “state-of-the-art” calculation by Schaefer et aL2’
I. Molecular Geometries. Table XI1 shows the geometries
calculated by AM1 for the 138 molecules used in our extended
tests, together with experimental values where available. The
agreement with experiment is generally satisfactory.
J. Activation Energies of Some Simple Reactions. While no
systematic attempt has yet been made to test the ability of AM
to predict reaction paths, calculations have been carried out for
some simple reactions, most of them ones where M N D O gave
activation energies that were much too large. While these errors
were formerly thought to be due to the overestimation of repulsions
in MNDO, it now appears that they were due largely to selection
of a less-than-optimal minimum on the parameter hypersurface;
see above. In any case AM1 certainly gives better results, in
particular for hydrogen abstraction by radicals from paraffins,
olefins, or acetylenes, or for addition of radicals to multiple bonds;
see Table XIII. Similar comments apply to reactions involving
intramolecular migration of hydrogen. Here, however, the errors
in AM1 are also quite large. Problems arise here because the
experimental barriers are probably too large, owing to neglect of
tunnelling. However, it does appear that the AM1 values, while
less than the MNDO ones, are still too large. The other reaction,
the conrotatory opening of cyclobutene to butadiene, is interesting
in that ab initio models give activation energies that are much
too large unless allowance is made for electron correlatiomZ6 The
Conclusions
As the tests reported here indicate, AM1 seems to represent
To a very real improvement over MNDO, with no increase in the
computing time needed. The specific failings in MNDO have been
at least moderated while the average error for molecules of other
kinds has also been reduced. The main gains are the ability of
AM1 to reproduce hydrogen bonds and the promise of better
estimates of activation energies for reactions. We hope soon to
have AM1 parameters available for the other elements already
parameterized in MNDO.
Acknowledgment. This work was supported by the Air Force
Office of Scientific Research (Contract No. F49620-83-C-0024),
the Robert A. Welch Foundation (Grant No. F-126), and the
National Science Foundation (Grant CHE82-17948). The cal-
culations were carried out using a DEC VAX 11-780 computer
purchased with funds provided by the National Science Foundation
(Grant CHE78-03213) and The University of Texas at Austin.
Registry No. C, 7440-44-0; H atom, 12385-13-6; 0 atom, 17778-80-2;
N atom, 17778-88-0.
(26) Hsu, K.; Buenker, R. J.; Peyerimhoff, S. D. J. Am. Chem. SOC. 1971,
(27) Breulet, J.; Schaefer, H. F., 111 J. Am. Chem. SOC. 1984, 106, 1221.
