Self-interaction correction to density-functional approximations
for many-electron systems
Phys. Rev. B, 23 (10):
5048-- (May 1981)Abstract
The exact density functional for the ground-state energy is strictly
self-interaction-free (i.e., orbitals demonstrably do not self-interact),
but many approximations to it, including the local-spin-density (LSD)
approximation for exchange and correlation, are not. We present two
related methods for the self-interaction correction (SIC) of any
density functional for the energy; correction of the self-consistent
one-electron potenial follows naturally from the variational principle.
Both methods are sanctioned by the Hohenberg-Kohn theorem. Although
the first method introduces an orbital-dependent single-particle
potential, the second involves a local potential as in the Kohn-Sham
scheme. We apply the first method to LSD and show that it properly
conserves the number content of the exchange-correlation hole, while
substantially improving the description of its shape. We apply this
method to a number of physical problems, where the uncorrected LSD
approach produces systematic errors. We find systematic improvements,
qualitative as well as quantitative, from this simple correction.
Benefits of SIC in atomic calculations include (i) improved values
for the total energy and for the separate exchange and correlation
pieces of it, (ii) accurate binding energies of negative ions, which
are wrongly unstable in LSD, (iii) more accurate electron densities,
(iv) orbital eigenvalues that closely approximate physical removal
energies, including relaxation, and (v) correct longrange behavior
of the potential and density. It appears that SIC can also remedy
the LSD underestimate of the band gaps in insulators (as shown by
numerical calculations for the rare-gas solids and CuCl), and the
LSD overestimate of the cohesive energies of transition metals. The
LSD spin splitting in atomic Ni and s-d interconfigurational energies
of transition elements are almost unchanged by SIC. We also discuss
the admissibility of fractional occupation numbers, and present a
parametrization of the electron-gas correlation energy at any density,
based on the recent results of Ceperley and Alder.
