Extension of the PM3 Method on s,p,d Basis. Test Calculations on Organochromium Compounds

A model for estimation of the two-electron interaction in molecules is proposed. It is based on the bipolar expansion of the Ohno potential which is considered as a universal effective potential of the two-electron interaction. It allows to estimate efficiently the two-electron fockian terms taking into implicit account the dynamic electron correlation. The formulas obtained do not depend explicitly on the orbital quantum number of the basis AO’s, and this approach may be used to extend the semiempirical NDDO-type methods to the s,p,d basis. In this work, this approach was applied to the semiempirical PM3 model, and the test calculations were performed on organochromium compounds, taking into explicit account the chromium d orbitals. The calculated thermodynamic, structural, and electron properties of above 30 organochromium compounds of different classes (sandwich complexes, carbonyls, nytrosyls, and mixed derivatives) stay in good agreement with the experimental data. Advances in theory of semiempirical quantum chemical methods of MNDO type (MNDO, AM1, PM3) 1-3 are wellknown now. However, the taking into explicit account the transition metal d AO’s to treat the structure and reactivity of the organometal compounds (OMC) is an actually unresolved problem in the framework of these methods. One of the questions consists of the semiempirical estimation of two-center, two-electron integrals over the Slater’s s,p,d basis. Such a semiempirical procedure must not be the ordinary method of their approximation but must keep track of the dynamic electron correlation and the sufficient noncompleteness of the basis set. Within the MNDO-type methods the “point charge model” 4 is used for the estimation of the two-center, two-electron integrals. The continuous electron distribution of the atom is presented by a set of separate point charges provided that the long-distance multipole moments of the atom are kept. Unfortunately, this approach cannot be simply extended to the arbitrary basis set (s,p,d,f,...). Recently, McCourt et al. 5 have applied the operator technique to generate the point charges in the more comprehensive case of s,p,d distributions. Unfortunately, the resulting integral expressions are too cumbersome and, moreover, are of the form of series with sign-alternating high-order terms which may cause instability of the algorithm. In 1992, Thiel and Voityuk 6,7 have proposed the modification of the point charge scheme to treat the hypervalent compounds with s,p,d basis (the MNDO/d method). Within the MNDO/d the small multipole moments of third and fourth order induced by the p,d and d,d electron distributions are ignored, and only the monopole, dipole, and quadrupole moments are taken into account. To preserve the rotational invariance of this procedure, additional relations have been imposed on the corresponding two-electron integrals. Unfortunately, the atom parameters of the transition metal atoms have not been reported so far for this method. It is doubtful that the point charge model is convenient to describe the complex electron distributions of transition metal atoms because of the large number of energetically near-valence states. The energy difference between these states is often of the order of the terms ignored in the point charge model or of the errors arising in going from the continuous electron distributions to the discrete charges. Moreover, this approach does not eliminate the problem of the extension to other basis sets (e.g., of s,p,d,f AO’s), and it generates a large number of atom parameters. Therefore, the point charge scheme is not employed in this work, and we suggest the use of another electron interaction model. It is not surprising that the dynamic electron correlation somewhat decreases the interaction between the electrons moving in the molecule. In other words, the interaction potential of correlated electrons is distinguished from the Coulomb interaction, and it is less in magnitude. This decrease may be represented as an increase of the effective interelectron distance, and the interaction of correlated electrons may be described by an effective interelectron potential. The ratio of this effective potential to the Coulomb potential is referred to here as a correlation function.