Orthonormal Sets of LCAO Molecular Orbitals for Second-Row Homopolar Diatomic Molecules

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Abstract
The forms of the LCAO MO's (molecular orbitals approximated by linear combinations of atomic orbitals) of any homopolar second‐row diatomic molecule are studied under the restriction that they shall form an orthogonal set. The requirement of orthogonality per se causes 1s−2s−2pσ hybridization (forced hybridization) among the AO's (atomic orbitals) used in constructing the LCAO's. Equations, tables, and figures are given showing how the degrees of hybridization in the members of mutually orthogonal sets of σg LCAO MO's, likewise of σu LCAO MO's, are related, as a function of two parameters: (a) assumed degree of hybridization in any one member of the set; (b) a parameter proportional to interatomic distance times effective nuclear charge. This is done using primarily Slater AO's, but the effect of using SCF (self‐consistent‐field) AO's is also studied. Assuming that overlap integrals are good measures of bond strengths, it is shown that the effect of forced hybridization is to diminish bond strengths. It is concluded that this bond‐weakening effect in LCAO MO valence theory is the counterpart of certain exchange repulsions which appear in the Heitler‐London valence bond theory, namely those between bonding electrons on one atom and electrons in different (either bonding or lone‐pair) AO's on the other atom. The procedure used promises to give a good measure of the strengths of inner shell‐outer shell interatomic repulsions; it tends to indicate that these are, in general, not large but not negligible. A paradox resulting from forced hybridization is touched on and more or less resolved; this paradox has to do with the method of counting the numbers of s and pσ electrons per atom in a molecule described by LCAO methods.

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