Applications of Self-Interaction Correction to Localized States in Solids

Density Functional Theory provides an exact mapping of a many-body electron problem which occurs in solids onto a one-electron problem1. Instead of considering, for N interacting electrons in an external potential u(r), the 3N-dimensional Schrodinger equation for the wavefunction Ψ(r 1, r 2, r 3, r N ), DFT expresses this many-body problem in terms of the electronic density distribution n( r ) and a universal exchange and correlation functional of the density, E xc [n(r)].The task of solving the many-body problem is then reduced to finding sufficiently accurate expressions for E xc [n(r)] and then solving the relevant one-electron Schrodinger equation with an effective potential of which the exchange-correlation potential is a prominent part. Surprisingly, DFT has turned out to be a powerful and extremely successful scheme of calculating electronic properties of solids. This is owing to a simple and practical approximation for E xc [n(r)] , the local density approximation, where the exchange and correlation potential, is approximated by the exchange-correlation energy per particle, exc(n), of a homogeneous electron gas of density n.This simple function of density can be very precisely calculated and allows for an accurate determination of the ground state energies and charge densities of any system1.