Criteria for the Construction of Good Self-Consistent-Field Molecular Orbital Wave Functions, and the Significance of LCAO-MO Population Analysis

Abstract

Criteria for the optimal choice of finite linear combinations of STO's (Slater‐type orbitals) adequate to closely approximate SCF (self‐consistent‐field) MO's are examined in the light of computations on HF and other molecules. First, however, some aspects of the AO (generalized Heitler—London) method are discussed. The concept of induced configuration mixing is proposed as a helpful way of thinking of the higher‐order interactions which carry the wave function from that of a ground‐state atom pair over toward an SCF‐MO form. The concept of valence polarization is suggested as preferable to and/or more general than that of hybridization. When, in the AO method, a molecule is formed from atoms, the AO's of the latter are valence polarized, and if the molecule is heteropolar, also Coulomb polarized. It is noted that both types of polarization are effected in part by the mixing in of highly shrunken excited AO's. The same concepts are applicable also in the MO method. In an optimal choice of a finite STO basis set for approximating SCF MO's, the principle of balanced truncation, including balanced polarization, should be used; that is to say, an equally generous (or parsimonious) set of primary and of polarizing STO's should be used for each atom, with due respect to the numbers and kinds of occupied AO's in the free atom. The use of flexibilized and polarized SCF AO's (modified SCF AO's, or MAO's) as equivalents to linear combinations of STO's is discussed. In these connections, problems of interpretation and recording of LCAO‐MO population analyses obtained using extended STO basis sets are critically examined. The inherent limitations on the meaning of charges on atoms in a molecule (or of degree of ionic character, or net ionicity) are discussed. It is shown with examples that unacceptable atomic charges are found from an LCAO‐MO population analysis made on SCF‐MO wave functions approximated using unbalanced STO sets, while acceptable results are obtained with judiciously balanced and sufficiently complete STO sets. Likewise, unbalanced STO basis sets can given unacceptable results for overlap populations. For example, with certain unbalanced sets, there are large apparent π overlap populations in HF and in LiF, where with well‐balanced sets a much smaller, but appreciable and probably genuine, amount of π bonding is indicated, confirming evidence from spectroscopic data in the case of diatomic hydrides. The effects of insufficiently complete and unbalanced STO sets on the computed dipole moments of SCF‐MO wave functions are discussed in terms of examples. These indicate that one may expect fairly accurate though slightly too large computed dipole moments for good SCF‐MO wave functions. They also indicate that improvement of the latter by limited configuration interaction may give computed values close to experimental values.