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

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 = Ψ 1 (VB) + Ψ 2 (VB) = Ψ 1 (MO) + Ψ 2 (MO) may be constructed from each set of three atomic spin orbitals, for which the Ψ 1 and Ψ 2 are three-electron bond wave functions. The equivalence is illustrated via the results of some ab initio calculations for the ground states of H 2 - and He 2 + . For H 2 -, 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 H 2 when the exponents of the diffuse (1s‘‘) orbital components of these molecular orbitals are energy-optimized.