CONSTRUCTION AND APPLICATION OF GRADIENT-EXPANSION APPROXIMATIONS FOR EXCHANGE ENERGY WITH SELF-INTERACTION CORRECTION

We observe that the expressions for the single-particle exchange-energy density ex and the orbital-dependent exchange potentials vx(i) diverge at the nodes of the single-particle densities when the self-interaction-correction (SIC) method is applied to the conventional expression for the exchange energy Ex in the gradient-expansion approximation (GEA). An expression for ExGEA is constructed that reduces to the conventional form in the slowly varying density limit and leads to convergent SIC expressions for ex and vx(i). When this gradient-expansion-approximation self-interaction-correction (GEASIC) functional is employed in the calculation of the total energy for atoms with closed subshells, the results are significantly closer to the Hartree-Fock results than those obtained from either the GEA or the local-spin-density self-interaction-correction (LSDSIC) approximation. Furthermore, when the recently derived value for the GEA constant, i.e., (10/7 of Shams value, is employed, the results are found to be further improved. In addition, we show that the construction of a single (i.e., orbital-independent) Kohn-Sham potential from these GEASIC potentials leads not only to accurate exchange-only total energies but to reasonably accurate results for Emax as compared to experimental ionization energies when the effect of correlation is included in the LSDSIC approximation. © 1990 The American Physical Society.