Valence Bond and Molecular Orbital Descriptions of the Three-Electron Bond

Abstract

When two atomic orbitals are used to accommodate the electrons of the three-electron bond (or three-electron two-center bond), it is well-known that the valence bond (Ȧ·Ḃ ≡ ÄḂ ↔ ȦB̈) and molecular orbital (one antibonding + two bonding electrons) descriptions of this type of bond are equivalent, i.e. Ψ = Ψ(VB) = Ψ(MO). With three atomic spin orbitals to accommodate the electrons of ÄḂ, and three additional atomic spin orbitals to accommodate the electrons of ȦB̈, it is deduced that a wave function of the form Ψ = Ψ1(VB) + Ψ2(VB) = Ψ1(MO) + Ψ2(MO) may be constructed from each set of three atomic spin orbitals, for which the Ψ1 and Ψ2 are three-electron bond wave functions. The equivalence is illustrated via the results of some ab initio calculations for the ground states of H2- and He2+. For H2-, the use of canonical double-ζ molecular orbitals constructed from 1s‘ and 1s‘‘ atomic orbitals on each atomic center must lead to ionization of this anion to form H2 when the exponents of the diffuse (1s‘‘) orbital components of these molecular orbitals are energy-optimized.