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

Richard D. Harcourt

doi:10.1071/CH07189

RESEARCH ARTICLE

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

Richard D. Harcourt ^A

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^A School of Chemistry, University of Melbourne, VIC 3010, Australia. Email: r.harcourt@unimelb.edu.au

Australian Journal of Chemistry 60(9) 691-695 https://doi.org/10.1071/CH07189
Submitted: 6 June 2007 Accepted: 7 August 2007 Published: 11 September 2007

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, (V_A = V_ab + V_ay), 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, V_a, to the valence. The resulting maximum value for the A-atom valence (V_A = V_ab + V_ay + V_a) 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 V_A = V_ab + V_ay were derived with atomic orbital overlap integrals omitted. The present paper shows how the theory is modified when these integrals are included.

References

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

Abstract

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