Applications of a non-perturbative many-body formalism to general open-shell atomic and molecular problems: calculation of the ground and the lowest π-π* singlet and triplet energies and the first ionization potential of trans-butadiene

Abstract In this paper we explore the feasibility of widening the scope of the non-perturbative open-shell many-body formalism recently developed by us [1], which utilizes an Ursell type of cluster expansion about certain starting wavefunctions spanning a model space. We show that, by generalizing the definition of the cluster expansion operator, we can incorporate into the model space (a) determinants differing widely in energy and (b) determinants differing in their number of electrons. This flexibility is useful for the calculation of difference energies of interest, like transition energies and ionization potentials of atomic and molecular systems. The generalized scheme has been tested on the 4π-electron problem trans-butadiene for which, by choosing a very general model space, we have calculated the energies of the ground, the lowest π-π* singlet and triplet and the first ionization potential by choosing a single composite cluster expansion operator for all states. Results for some more restricted choice of model spaces are also given. The agreement between the results of the present theory and that found from CI calculations, complete in the chosen basis, is excellent.