A New General Purpose Quantum Mechanical

A New General Purpose Quantum Mechanical

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3902 J. Am. Chem. SOC. 1985, 107, 3902-3909 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 1. 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 HF 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 1-780 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

Contribution from 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, ab 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, MIND0/3 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, 9, 489, 4907. (5) A total of 623 papers reporting MNDO calculations have been listed in Chemical Abstracts since 1980.

0002-7863/85/1507-3902$01.50/0

It should be emphasized that even MIND0/3 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 1-780, 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 MIND0/3 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

0 1985 American Chemical Society

New General Purpose Quantum Mechanical Molecular Model

MNDO 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-

D0/3 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 AM1

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 CRF 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 ge~metries,~ dipole moments: ionization energie~,~ electron affinities,* p~larizabilities,~ molecular vibration frequencies,’O thermodynamic proper- ties,” kinetic isotope effects,12 properties of polymers,” and ESCA chemical shifts.14 (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, 59, 54 1.

(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, 9, 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, 9, 7432.

J. Am. Chem. SOC., Vol. 107, No. 13, 1985 3903

Table I. AM1 Parameters element parameter H C N 0

Us, -1.396427 -52.028658 -71.860000 -97.830000 -39.614239 -57.167 581 -78.262380 1.188 078 1.808 665 2.3 15 410 3.108 032 1.685116 2.157940 2.524039 -6.173787 -15.715783 -20.299 110 -29.272773

-7.719283 -18.238 6 -29.272773 a 2.882 324 2.648 274 2.947 286 4.455 371 Kl 0.122796 0.01 1355 0.025251 0.280962 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 5.0 0 5.0 0 5.0 0 5.0 0

L2 5.0 5.0 5.0 7.0

L4 5.0 0 MI 1.200 0 1.600 0 1.50 0.847 918

M2 1.800000 1.850000 2.100000 1.445071 M3 2.iOOOOO 2.050000 2.400000

M4 2.650 0

L3 2.0 5.0 2.0

The symbolism is the same as that in MND0.4 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 CRF 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 Isaev20 have 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.

3904 J. Am. Chem. SOC., Vol. 107, No. 13, 1985 Dewar et al. Table 1. Comparison with Experiment of Heats of Formation (AHf; kcal/mol) Calculated for Closed-Shell Molecules by Various Procedures molecule hydrogen methane ethane ethylene acetylene propane propene

ProPYne allene n-butane isobutane but-1-ene trans-2-butene cis-2-butene isobutene

1,2-butadiene trans- 1,3-butadiene 1-butyne 2-butyne vinylacetylene diacetylene n-pentane neopentane trans- 1,3-pentadiene cis- 1,3-pentadiene 1,4-pentadiene cyclopropane cis-dimeth ylcyclopropane cyclopropene 1 methylcyclopropene 1,2-dimethyIcyclopropene methylenecyclopropane cyclobutane cyclobutene, C, 1,2-dimethylcyclobutene methylenecyclobutane cyclopentane cyclopentene cyclopentadiene fulvene cyclohexane

cyclohexene 1,3-~yclohexadiene benzene toluene ethylbenzene styrene cycloheptatriene bicyclobutane spiropentane bicyclopropyl bicyclo[2.1 .O]pentane norborane norbornadiene bicyclo[2.2.2]octane naphthalene adamantane cubane nitrogen ammonia methylamine dimethylamine trimethylamine ethylamine n-propylamine isopropylamine tert-butylamine acetaldehyde imine

(Parte 1 de 4)

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