On the use of spin graphs for spin adapting many-body perturbation theory

In connection with spin adaptation in many-body perturbation theory, this paper reexamines the use of spin graphs in view of a Hugenholtz-like representation where both the orbital and the spin parts coexist. Together with the idea of essentially distinct diagrams, this representation leads to an economic handling of spin adaptation. As a side issue, the appropriate generalization of the Epstein–Nesbet partitioning for spin-adapted perturbation theory is obtained. Compact formulas up to fourth order of the ground-state energy, and up to third order for excitation energies and ionization potentials are given.