Self-Interaction Corrections Within the Fermi-Orbital-Based Formalism

Abstract

Abstract In this chapter, we suggest a recent modification to the self-interaction correction, which allows one to recast the self-interaction correction into a form that is explicitly invariant to unitary transformations and which is also size extensive. In addition to restoring unitary invariance and a correct asymptotic potential the formulation seems to provide classical electronic positions, or descriptors, which seem to be in accord with Lewis structures. By explicitly introducing the constraint of unitary invariance, it has been found that the accuracy of binding energies in simple molecules is improved compared to the uncorrected density functional. The improvement in binding energies seems to be especially pronounced for systems containing pi bonds. Further as for the case of the original self-interaction corrected formulation, the results show that the improvement of the occupied-orbital eigenvalues, based on comparison to experimental ionization potentials, is retained in this formulation. This chapter includes a discussion of recent results on small molecules and a complete derivation of the equations required to calculate the positions of the Fermi-orbital descriptors. In addition to molecules that are clearly composed of single, double, and triple bonds, we provide an example on the benzene molecule that yields orbitals that adequately describe the resonant character of this system.