Multi-Configuration Kohn-Sham Methods with Orbital-Dependent Functionals

The main objectives of the present thesis are, firstly, to apply the effective exact-exchange Localized Hartree-Fock (LHF) method, an effective exact-exchange Kohn-Sham (KS) method, as potential remedy of systematic limitations of conventional KS approaches and, secondly, to develop, implement and apply a new multi-configuration optimized effective potential method based on the existing effective exact-exchange approach. The goal of the new method is to cover static correlation effects through orbital-dependent exchange-correlation functionals. In the first part (Chap. 2 and 3) of this thesis the foundations of the KS method and their systematic shortcomings are reviewed, different derivations of orbital-dependent exchange-correlation functionals are given, then the LHF method is recalled, and finally the new MCLHF (Multi-Configuration Localized Hartree-Fock) approach is derived. The second part of this thesis is, firstly, concerned with three different types of application (anions, HOMO-LUMO gaps of molecular chains, and linear polarizabilities of molecular model chains) of the LHF method. The focus was an investigation how systematic limitations of conventional exchange-correlation treatments can be overcome by using the effective exact-exchange method LHF. In Chap. 4 small and medium size negatively charged systems have been investigated. It has been shown that the exact treatment of the exchange energy improves the description of the electron structure of those systems due to the cancellation of the unphysical Coulomb self-interaction. As a result, the effective KS potential in the LHF approach is attractive enough to bind all electrons in anions, i.e., to yield, in contrast to approaches based on the local density or the generalized gradient approximation, stable anions. Chap. 5 is concerned with the systematic underestimation of HOMO-LUMO gaps and excitation energies for extended chain-like molecular systems in the framework of KS and TDDFT (time-dependent density-functional theory) methods. Different KS methods employing conventional exchange-correlation functionals and effective exact-exchange methods based on orbital-dependent functionals have been applied to carbon chains (polyynes and cumulenes). The role of the employed KS exchange-correlation potential and the exchange-correlation kernel in TDDFT calculations on the underestimation of excitation energies was investigated. It is found that for long polyynes the independent-particle model (HOMO-LUMO gap as zeroth-order approximation for the corresponding excitation energy) yields a better agreement with experimental excitation energies than excitation energies calculated using time-dependent DFT methods with conventional exchange-correlation kernels. In Chap. 6 the description of the electronic structure of hydrogen chain-like model systems in the presence of an external static electric field is reinvestigated. In contrast to Hartree-Fock (HF) methods or Hartree-Fock based perturbation theory methods, or coupled cluster methods conventional DFT methods fail completely in describing polarizabilities (alpha) and hyper-polarizabilities (beta, gamma, ...) of extended pi-electron systems. DFT dramatically overestimates these quantities. It is shown that orbital-dependent methods in the framework of LHF give much better results than conventional DFT methods but still deviate from full EXX/OEP and HF methods as well as from correlated HF-based methods. The admixture of correlation using conventional correlation functionals lowers only slightly the exchange-only results. The characteristic counteracting field potential of exact-exchange methods is also found in LHF. This potential is hindering the electron movement along the molecular chain against the applied external field and is responsible for lowering polarizabilities as compared to conventional DFT methods. Applications of the MCLHF approach representing a further main topic of this work are given in Chap. 7: The treatment of static correlation within a DFT framework. The MCLHF approach proved to be applicable not only in cases determined by two configurations, like the dissociation of hydrogen, but also in cases characterized by the interaction of more than two configurations, like the isomerization of cyclo-butadiene. In contrast to standard multi-configuration self-consistent field (MCSCF) methods and previous combinations of MCSCF procedures with density-functional theory, the MCOEP method yields well-defined physically meaningful orbitals and eigenvalue spectra. Finally, in Chap. 8, future prospects directly connected to the present work are discussed.