What is Physically Wrong with the Description of Odd-Electron Bonding by Hartree-Fock Theory? A Simple Nonempirical Remedy

The odd-electron (one and three) bond involves resonance between two charge-shift related structures, in both MO and VB theory. A physically correct description of odd-electron bonding should reflect the instantaneous response of the orbital size and shape to the charge fluctuation inherent in the odd-electron bonding. VB theory contains this response and involves charge-fluctuation-adapted orbitals in the resonance structures, resulting in reliable bond energies. In contrast, due to its constraints, the Hartree-Fock theory fails to represent this crucial feature of the odd-electron bond and generates thereby poor bond energies. A nonempirical remedy for this Hartree-Fock bias is proposed. This is the “Uniform Mean-Field Hartree—Fock” (UMHF) procedure which is based on the simple unrestricted Hartree-Fock method, but involves orbital occupancy constraints and correction of the resonance energies by non-empirical factors. The UMHF approach is tested on three-electron- and one-electron-bonded molecules and is shown to yield bonding energies in satisfactory agreement with more sophisticated calculations (up to and beyond fourth order of Moller—Plesset perturbation theory). The UMHF procedure is offered as a routine inexpensive tool for obtaining odd-electron bond energies for large molecules.