Convergence studies of the effective valence shell Hamiltonian for correlation energies of the fluorine atom and its ions using third order quasidegenerate many-body perturbation theory

The effective valence shell Hamiltonian ℋv, is evaluated through third order quasidegenerate many-body perturbation theory (QDMBPT) for all 46 [2s,2p] valence states of F+7 through F−. The effects of independently varying the orbital basis set, the unperturbed Hamiltonian, and the definition of the valence shell are studied. A generalized of QDMBPT allows the separate evaluation of the many-electron effective integrals which are independent of the number and configuration of valence electrons; hence, one ℋv calculation yields all 46 state energies simultaneously. Methods for dealing wih quasidegeneracy problems associated with large valence shells are numerically tested and proven effective. Guidelines for ℋv calculations on more complicated systems are presented.