Many-body methods in electron structure calculations of excited molecules: General
The central topic of our research activities is the development and application of Green's function or propagator methods for the treatment of (generalized) electronic excitations in molecules, comprising both (neutral) excitation as well as electron removal (ionization) and electron attachment processes. The propagator methods allow for a direct determination of excitation (or ionization/electron attachment) energies and spectral intensities, thus circumventing the necessity of deriving those quantities from separate computations for the ground and the excited states.
For a long time we have been pursuing a general approach referred to as algebraic- diagrammatic construction (ADC) which allows us to derive in a systematical way higher- order approximation (ADC(n)) schemes for the respective propagators and their physical information. The ADC approach is based on a specific reformulation of the respective propagator referred to as intermediate state representation (ISR). The comparison of the (algebraic) ISR representation (ADC form) with the original diagrammatic perturbation expansion of the propagator through a given order n of perturbation theory allows one to determine successively the ingredients of the ISR representation, that is, ADC secular matrix elements and (effective) transition amplitudes. The computational concept of the resulting ADC approximations is simple: It combines the eigenvalue problem of a hermitian secular (ADC) matrix with perturbation theory for the matrix elements. The eigenvalues are the excitation energies, while the transition moments are derived from the corresponding eigenvectors and the effective transition amplitudes.
The usefulness of the ADC methods is based on three basic properties: the perturbation expansions obtained for the secular matrix elements and effective amplitudes are regular, that is, they behave essentially like the Rayleigh-Schrödinger series for the ground-state energy and wave-function, respectively. The explicit configuration space (dimension) of the ADC secular problem needed for a certain level of approximation is smaller than those of a comparable configuration interaction (CI) treatment (compactness). The ADC secular equations are separable, that is, local excitations in a system of non-interacting fragments are strictly decoupled from non-local excitations. As a consequence of the separability property, the ADC results both for the energies and transition moments are size-consistent (size-intensive), which is a crucial condition for the applicability of the methods to large molecules.
The present status of the ADC methods for electronic excitation and ionization is briefly sketched in the paragraphs below.
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Electronic excitations in molecules
An adequate theoretical description of electronic excitations in molecules is a basic requirement for the understanding of photophysical and photochemical processes. In spite of the ongoing growth of computer capabilities and impressive methodological advances, the present state of the art here is much less satisfactory than in the treatment of the ground state, and it is still an urgent concern to improve existing computational schemes or to develop new methods.
Intermediate state representations
K-shell excitation and ionization of molecules