MNDO/AM1‐type parameters for twelve elements have been optimized using a newly developed method for optimizing parameters for semiempirical methods. With the new method, MNDO‐PM3, the average difference between the predicted heats of formation and experimental values for 657 compounds is 7.8 kcal/mol, and for 106 hypervalent compounds, 13.6 kcal/mol. For MNDO the equivalent differences are 13.9 and 75.8 kcal/mol, while those for AM1, in which MNDO parameters are used for aluminum, phosphorus, and sulfur, are 12.7 and 83.1 kcal/mol, respectively. Average errors for ionization potentials, bond angles, and dipole moments are intermediate between those for MNDO and AM1, while errors in bond lengths are slightly reduced.

Optimization of parameters for semiempirical methods II. Applications

Before we start, we need a working definition for MOPAC. The following description has been used many times to describe MOPAC: MOPAC is a general-purpose, semiempirical molecular orbital program for the study of chemical reactions involving molecules, ions, and linear polymers. It implements the semiempirical Hamiltonians MNDO, AM 1, MINDO/3, and MNDOPM3, and combir_es the calculations of vibrational spectra, thermodynamic quantities, isotopic substitution effects, and force constants in a fully integrated program. Elements parameterized at the MNDO level include H, Li, Be, B, C, N, O, F, A1, Si, P, S, C1, Ge, Br, Sn, Hg, Pb, and I; at the PM3 level the elements H, C, N, O, F, A1, Si, P, S, C1, Br, and I are available. Within the electronic part of the calculation, molecular and localized orbitals, excited states up to sextets, chemical bond indices, charges, etc. are computed. Both intrinsic and dynamic reaction coordinates can be calculated. A transition-state location routine and two transition-state optimizing routines are available for studying chemical reactions.

MOPAC: A semiempirical molecular orbital program

A combined quantum mechanical (QM) and molecular mechanical (MM) potential has been developed for the study of reactions in condensed phases. For the quantum mechanical calculations semiempirical methods of the MNDO and AM1 type are used, while the molecular mechanics part is treated with the CHARMM force field. Specific prescriptions are given for the interactions between the QM and MM portions of the system; cases in which the QM and MM methodology is applied to parts of the same molecule or to different molecules are considered. The details of the method and a range of test calculations, including comparisons with ab initio and experimental results, are given. It is found that in many cases satisfactory results are obtained. However, there are limitations to this type of approach, some of which arise from the AM1 or MNDO methods themselves and others from the present QM/MM implementation. This suggests that it is important to test the applicability of the method to each particular case prior to its use. Possible areas of improvement in the methodology are discussed.

A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations

Using a recently developed procedure for optimizing parameters for semiempirical methods,1 PM3 has been extended to a total of 28 elements. Average ΔHf errors for the newly parameterized elements are Be: 8.6, Mg: 8.4, Zn: 5.8, Ga: 14.9, Ge: 11.4, As: 8.5, Se: 11.1, Cd: 2.6, In: 11.3, Sn: 9.0, Sb: 13.7, Te: 11.3, Hg: 6.8, Tl: 6.5, Pb: 7.4, and Bi: 10.9 kcal/mol. For some elements the paucity of data has resulted in a method, which, while highly accurate, is likely to be only poorly predictive.

Optimization of parameters for semiempirical methods. III. Extension of PM3 to Be, Mg, Zn, Ga, Ge, As, Se, Cd, In, Sn, Sb, Te, Hg, Tl, Pb, and Bi

The extension of the MNDO formalism to d orbitals is outlined. MNDO/d parameters are reported for Na, Mg, Al, Si, P, S, Cl, Br, I, Zn, Cd, and Hg. According to extensive test calculations covering more than 600 molecules and several properties, MNDO/d provides significant improvements over established semiempirical methods, especially for hypervalent compounds. The mean absolute error in MNDO/d heats of formation amounts to 5.4 kcal/mol for the complete validation set of 575 molecules and is identical for the subsets of 508 normal valent and 67 hypervalent compounds. In addition to the statistical evaluations, several specific applications are briefly discussed to illustrate the performance of MNDO/d in selected areas and to comment on problematic cases.

Extension of MNDO to d Orbitals: Parameters and Results for the Second-Row Elements and for the Zinc Group

Revised MNDO parameters for silicon

The energies of the lowest singlet (S1) and triplet (T1) states of 28 molecules have been calculated by the “half-electron” (MNDO-HE) and spin-unrestricted (UMNDO) versions of MNDO. While most of the calculated values are too negative, because of overestimation of the correlation energy in MNDO-HE and UMNDO, the errors are systematic and depend in an understandable way on the nature of the molecular orbitals (MOS) involved. When appropriate corrections are applied, the calculated energies agree with experiment almost as well as they do for ground states. This justifies the use of MNDO-HE or UMNDO for studies of excited state processes.

James E. Friedheim

Papers

Revised MNDO parameters for silicon

Calculation of energies of excited states using MNDO

Studies of chemical problems using quantum mechanical molecular models. Part 72. Stannylenes: an MNDO investigation