Increased Valence or Electronic Hypervalence for Symmetrical Three-Centre Molecular Orbital Configurations

centre molecular orbitals for a symmetrical Y–A–B type bonding unit with overlapping atomic orbitals y, a, and b, it is deduced that the maximum value for theA-atom valence, (VA =Vab +Vay), is (a) 4(3 − 2√2) = 0.6863 for the one-electron and five-electron configurations (1) = (ψ1)1 and (5) = (ψ1)2(ψ2)2(ψ3)1; (b) 8(3 − 2√2) = 1.3726 for the two-electron and four-electron configurations (2) = (ψ1)2 and (4) = (ψ1)2(ψ2)2; and (c) 4/3 for the three-electron configuration (3) = (ψ1)2(ψ2)1. Thus for each of the three-centre molecular orbital configurations, the A-atom can exhibit increased valence, or electronic hypervalence, relative to the valence for an A-atom in a two-centre molecular orbital configuration. When k1 = 0 for (1) and k3 = 0 for (5), the A-atom odd-electron charge is not equal to zero. This odd-electron charge is available for (fractional) electron-pair bonding to a fourth atom X, to give an additional contribution, Va, to the valence. The resulting maximum value for the A-atom valence (VA = V ab + Vay + Va) is equal to 1.2020 for each of (1) and (5). A-atom valencies are calculated for the three-centre bonding units for several molecules and ions. The expressions for VA = Vab + Vay were derived with atomic orbital overlap integrals omitted. The present paper shows how the theory is modified when these integrals are included