Density-Functional Theory Studies of Correlation Energy Effects at Metallic Surfaces.

In this thesis we study the effects of correlation in the inhomogeneous electron gas at metallic surfaces. These studies are performed within the context of density-functional theory (DFT). Using accurate representations of the electronic density profile, we have estimated variationally the surface correlation energy of jellium metal. The accuracy of these estimates is founded in the assumption that the exchange -correlation energy functional of the density is approximated accurately by the wave-vector analysis method, and by the fact that the non-local exchange energy contributions are treated exactly. In contrast to the previously accepted conclusion that for surfaces correlation effects are as significant as exchange, our results indicate the ratio of these energies to lie between 34% - 97% over the metallic density range, the smaller ratios corresponding to the higher density metals. In this work we have also examined the local density (LDA) and gradient expansion approximations (GEA) (to O((DEL)('2))) for the correlation energy. We have demonstrated for realistic metal surface densities the cancellation of the errors in the LDA for exchange and correlation, and shown that the density profiles at surfaces would have to be unphysically slowly varying for the correlation energy GEA to converge. We have also studied the effects of correlation at surfaces by screening the exchange, and observe that the surface exchange energy for screened-Coulomb interaction decreases as the screening length is reduced. Thus, the more short-ranged the interaction, the easier it is to split the crystal in two. In addition we have derived the DFT first gradient correction coefficient in the GEA for the screened-Coulomb exchange energy, and shown it to be the same as that obtained within Hartree -Fock theory (HFT) for finite screening. This coefficient reduces to the DFT bare-Coulomb interaction value in the limit of no screening in which limit the HFT coefficient is singular. The GEA for the screened-Coulomb surface exchange energy in both HFT and DFT are also examined and both expansions shown not to converge to the exact values as a function of the density profile. An explanation for these surprising results is presented and suggestions made for future work based on the wave-vector method.