Self-consistent multiplicative constant method for the exchange energy in density-functional theory

We advance a self-consistent multiplicative constant (SCMC) method based on a local exchange potential that yields total, exchange, and atomization energies approaching quite closely, but at a much lower computational cost, those of the exact orbital-dependent exchange treatment [S. Ivanov, S. Hirata, and R. J. Bartlett, Phys. Rev. Lett. 83, 5455 (1999); A. Görling, ibid. 83, 5459 (1999)]. Application of the SCMC method to any approximate exchange energy functional permits us to remove the self-interaction correction from the latter as well as to restore its variational character. The SCMC method is implemented here using the following exchange energy functionals: local-density approximation, the Perdew-Wang 1991, Becke 1988, and the one-parameter hybrid Becke Lee-Yang-Parr functional. Calculations for atoms and diatomic molecules are presented. In addition, we prove that the exchange energy evaluated from the Kohn-Sham exchange-only determinant is an upper bound to the Hartree-Fock exchange energy.