| In the first part of the thesis, the exchange-correlation functional of Langreth and Mehl Physical Review B28, 1809 (1983) is generalized to include spin dependence. It is then applied to the calculation of ground-state and electron removal energies in atoms. The resulting correction increases the binding of core electrons, while decreasing the binding of outer electrons; in each case this correction has the correct sign and roughly the correct magnitude to compensate for the known errors in local (spin) density approximation (LDA). However, the extra overbinding of d electrons, relative to s electrons, is not reduced, at least within the central field approximation. A functional for the correlation energy alone is also given, for use in cases where the exchange part can be calculated exactly. In the second part of the thesis, a standard perturbation approach is used to calculate the contribution of the screened second order exchange interaction and the self-energy correction of same order to the nonlocal part of the exchange-correlation energy as a density functional. It is found when both local (LDA) and nonlocal terms are included, that the random phase approximation (RPA) is much better than expected. Evidence is presented that suggests for localized systems that the leading non-RPA terms in the LDA represent mostly a spurious self-interaction error which is removed when the nonlocal beyond-RPA terms are included. It is suggested that this error can be most simply avoided by just using the RPA alone for both the local and nonlocal contribution, as done in the simple approximation suggested by Langreth and Mehl. |
