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Orbital Functionals in Time-Dependent Density-Functional Theory
(2007)
- The subject of this work are orbital functionals in density-functional theory (DFT). After a short introduction the basic ideas of static and time-dependent DFT are presented in Chap. 2. In this chapter the advantages and disadvantages of common approximations for the exchange-correlation (xc) functional are also discussed as well as the basic ideas behind orbital functionals. In the first part of Chap. 3 the ground-state formalism of the DFT for fractional particle numbers is recapitulated. In the second part the concept of fractional particle numbers is extended to time-dependent situations and physical consequences are discussed. In particular, it is shown that under certain conditions the time-dependent xc potential must change discontinuously whenever the particle number crosses an integer number. The subject of Chap. 4 is the static and time-dependent optimized effective potential equation. This integral equation must be solved to obtain the xc potential corresponding to an orbital-functional approximation for the xc functional. It is shown that the integral equation in the time-dependent case can be transformed into a set of coupled differential equations. Based on this set of differential equations an approximate solution for the xc potential is developed. In Chap. 5 the set of coupled differential equations obtained in Chap. 4 is studied from a numerical point of view. It turns out that instabilities spoil the exact numerical solution, however, the approximation developed in Chap. 4 is found to be stable and can be used to go beyond the commonly used Krieger-Li-Iafrate (KLI) approximation. Exact properties of the xc potential are studied in Chap. 6. In particular, it is shown that the widely used KLI approximation for the xc potential violates the Zero-Force theorem. As demonstrated in Chap. 6 this violation can render the whole approximate solution useless. In combination with the fact that the KLI approximation satisfies the Harmonic-Potential theorem this observation also shows that the xc potential obtained from the KLI approximation is not a functional derivative of some xc functional. In Chap. 7 and 8 the photoelectron spectra from small anionic sodium clusters are studied. In Chap. 7 the Kohn-Sham eigenvalues obtained from different approximations for the xc potential are compared to the experimental results. It is found that although the more weakly bound peaks are well reproduced in all approximations the more strongly bound peaks are not. In Chap. 8 the theoretical photoelectron spectra are extracted from the excitation energies of the clusters with one electron less. It is found that the general agreement between the experimental and theoretical spectra is considerably improved. Especially the more strongly bound parts of the spectra are reproduced much better. This result shows that even for sodium clusters effects beyond the independent-particle picture must be taken into account in the interpretation of photoelectron spectra.
