Several modifications that have been made to the NDDO core-core interaction term and to the method of parameter optimization are described. These changes have resulted in a more complete parameter optimization, called PM6, which has, in turn, allowed 70 elements to be parameterized. The average unsigned error (AUE) between calculated and reference heats of formation for 4,492 species was 8.0 kcal mol−1. For the subset of 1,373 compounds involving only the elements H, C, N, O, F, P, S, Cl, and Br, the PM6 AUE was 4.4 kcal mol−1. The equivalent AUE for other methods were: RM1: 5.0, B3LYP 6–31G*: 5.2, PM5: 5.7, PM3: 6.3, HF 6–31G*: 7.4, and AM1: 10.0 kcal mol−1. Several long-standing faults in AM1 and PM3 have been corrected and significant improvements have been made in the prediction of geometries.

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Optimization of parameters for semiempirical methods V: modification of NDDO approximations and application to 70 elements.

It is demonstrated that semiempirical methods give electrostatic potential (ESP) derived atomic point charges that are in reasonable agreement with ab initio ESP charges. Furthermore, we find that MNDO ESP charges are superior to AM1 ESP charges in correlating with ESP charges derived from the 6-31G* basis set. Thus, it is possible to obtain 6-31G* quality point charges by simply scaling MNDO ESP charges. The charges are scaled in a linear (y = Mx) manner to conserve charge. In this way researchers desiring to carry out force field simulations or minimizations can obtain charges by using MNDO, which requires much less computer time than the corresponding 6-31G* calculation.

Atomic charges derived from semiempirical methods

The approximate self‐consistent molecular orbital theory with complete neglect of differential overlap (CNDO) presented in earlier papers has been modified in two ways. (a) Atomic matrix elements are chosen empirically using data on both atomic ionization potentials and electron affinities. (b) Certain penetration‐type terms, which led to excess bonding between formally nonbonded atoms in the previous treatment, have been omitted. The new method (denoted by CNDO/2) has been applied to symmetrical triatomic (AB2) and tetratomic (AB3) molecules, for a range of bond angles. The theory leads to calculated equilibrium angles, dipole moments, and bending force constants which are in reasonable agreement with experimental values in most cases.

Approximate Self‐Consistent Molecular Orbital Theory. III. CNDO Results for AB2 and AB3 Systems

An LCAO-MO-SCF-CI model along the lines introduced by Del Bene and Jaffe is developed that is capable of reproducing the better identified observed spectra of nitrogen heterocycles with a rms error of ∼ 1000 cm−1. The model is applied to the spectra of pyrrole, benzene, pyridine, the diazines, symmetric triazine and symmetric tetrazine. The benzene and pyridine spectra are reproduced nearly exactly. The band observed in pyrrole at ∼ 6.5 eV is calculated as two bands at ∼ 6.5 eV, but they are assigned π→σ
* and not π→π. No evidence is found for the low lying 1
B
2g
 in pyrazine, reported at ∼ 30400 cm−1 in pure crystals. The lowest excited singlet of sym. triazine is calculated as 1
E″ (n→π
*), not 1
A″2 (n→π), in agreement with a recent interpretation of Fischer and Small. Several bands are reassigned, and the electronic nature of the transitions discussed. Naphthalene and quinoxaline are examined to insure that no large drift of results are met with molecules of other sizes. Comparison of eigenvalues with molecular ionization potentials is made. Here the numerical agreement appears satisfactory for the first few ionization potentials only.

An intermediate neglect of differential overlap technique for spectroscopy: Pyrrole and the azines

Modern semiempirical methods are of sufficient accuracy when used in the modeling of molecules of the same type as used as reference data in the parameterization. Outside that subset, however, there is an abundance of evidence that these methods are of very limited utility. In an attempt to expand the range of applicability, a new method called PM7 has been developed. PM7 was parameterized using experimental and high-level ab initio reference data, augmented by a new type of reference data intended to better define the structure of parameter space. The resulting method was tested by modeling crystal structures and heats of formation of solids. Two changes were made to the set of approximations: a modification was made to improve the description of noncovalent interactions, and two minor errors in the NDDO formalism were rectified. Average unsigned errors (AUEs) in geometry and ΔHf for PM7 were reduced relative to PM6; for simple gas-phase organic systems, the AUE in bond lengths decreased by about 5 % and the AUE in ΔHf decreased by about 10 %; for organic solids, the AUE in ΔHf dropped by 60 % and the reduction was 33.3 % for geometries. A two-step process (PM7-TS) for calculating the heights of activation barriers has been developed. Using PM7-TS, the AUE in the barrier heights for simple organic reactions was decreased from values of 12.6 kcal/mol-1 in PM6 and 10.8 kcal/mol-1 in PM7 to 3.8 kcal/mol-1. The origins of the errors in NDDO methods have been examined, and were found to be attributable to inadequate and inaccurate reference data. This conclusion provides insight into how these methods can be improved.

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Optimization of parameters for semiempirical methods VI: more modifications to the NDDO approximations and re-optimization of parameters.

A general discussion of approximate methods for obtaining self‐consistent molecular orbitals for all valence electrons of large molecules is presented. It is shown that the procedure of neglecting differential overlap in electron‐interaction integrals (familiar in π‐electron theory) without further adjustment may lead to results which are not invariant to simple transformations of the atomic orbital basis set such as rotation of axes or replacement of s, p orbitals by hybrids. The behavior of approximate methods in this context is examined in detail and two schemes are found which are invariant to transformations among atomic orbitals on a given atom. One of these (the simpler but more approximate) involves the complete neglect of differential overlap (CNDO) in all basis sets connected by such transformations. The other involves the neglect of diatomic differential overlap (NDDO) only, that is only products of orbitals on different atoms being neglected in the electron‐repulsion integrals.

D. P. Santry

Papers

Approximate Self-Consistent Molecular Orbital Theory. I. Invariant Procedures