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

Abstract

With ψ1 = y + k1a + b, ψ2 = y – b, and ψ3 = y – k3a + b as Y–A and A–B bonding, non-bonding, and antibonding three-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 the A atom valence, (VA = Vab + Vay), is (a) 4(3 – 2√2) = 0.6863 for the one-electron and five-electron configurations Φ(1) = (ψ1)1 and Φ(5) = (ψ1)2ψ2)2(ψ3)1; (b) 8(3 – 2√2) = 1.3726 for the two-electron and four-electron configurations Φ(2) = (ψ1)2 and Φ(4) = (ψ1)2(ψ2)2; and (c) 4/3 for the three-electron configuration Φ(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 Φ(1) and k3 ≠ 0 for Φ(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 = Vab + Vay + Va) is equal to 1.2020 for each of Φ(1) and Φ(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.