Ab initio description of double and charge transfer excitations: from solvable models to complex systems

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In the endeavor for an ab initio understanding of the electronic structures of complex physical systems, double and charge transfer excitations are both receiving increasing attention due to their possible technological relevance. The former are involved in many ultra-fast processes which are now experimentally accessible while the latter are believed to be essential in explaining complex processes involved in photosynthesis. The challenges to describe double and charge-transfer excitations within a density-functional framework are related since both require a functional which is non-local in space and time. Especially the non-locality in time, i.e. a frequency dependence, is missing from currently available functionals.Within this project we will develop a frequency-dependent density functional which will enable us to describe both double and charge-transfer excitations. Moreover, as an alternative approach we will employ reduced density-matrix functional theory, which has proven to be capable of solving many long-standing problems in density-functional theory. We will provide a stringent derivation of a time dependent version of reduced density-matrix functional theory and derive a functional of the density matrix appropriate for the description of charge-transfer and double excitations. The properties of all functionals will be derived from exact calculations for one and two-dimensional model systems where the interacting Schrödinger equation can be solved without approximations for a small number of particles.