Correlation problem in open-shell atoms and molecules

Abstract In this paper we present a non-perturbative approach to the calculation of correlation energies of open-shell systems. The formulation utilizes an Ursell-type expansion about a multi-determinant starting wavefunction. We have proved a theorem which enables us to derive an effective hamiltonian for the system consisting entirely of linked terms. In the symmetry-degenerate case this effective hamiltonian acts within the subspace of a set of symmetry-degenerate functions, and generates the energy eigenvalues of the system. The present theory has been cast in a diagrammatic language which facilitates the analysis of the correlation problem. The workability of the theory has been tested on a 4 π electron problem, transbutadiene, for which we have calculated the lowest π-π* singlet and triplet energies. The agreement between the results of the present theory and that found from a full CI calculation is excellent. The desirable feature of the theory is that the effective hamiltonian is energy-independent. We have demonstrated the connection of the present theory with open-shell perturbation theories. We have also indicated a method for extending this theory to general open-shell systems.