Electronic Population Analysis on LCAO-MO Molecular Wave Functions. III. Effects of Hybridization on Overlap and Gross AO Populations

The effects of AO hybridization on gross AO and overlap populations for LCAO-MO electron configurations are discussed in terms of some simple examples, using equations and graphs. The validity of ``gross AO populations'' as true measures of the population in various AOs is critically discussed. It is shown that the degree of hybridization in the AOs of an LCAO MO does not in general give the true amount of s or p character in the MO; this is given instead by the gross s or p population in the MO. Nevertheless, ``forced hybridization'' among the AOs, although not contributing to gross AO populations, leads to important negative contributions to overlap populations, hence to bond energies. For example, forced 2s—2p hybridization has the result that the total overlap population for two pairs of electrons occupying bonding σ LCAO MOs built from 2s and 2pσ AOs in a homopolar diatomic molecule is actually less than the sum of the overlap populations which one would have if one pair could be in an MO built from pure 2s AOs and the other in an MO built from pure 2pσ AOs. This sort of forced hybridization with resultant loss of bond strength may explain why double bonds seldom if ever consist of two σ bonds.