Modified potentials in many-body perturbation theory: Three-body and four-body contributions

Three-body and four-body contributions to the third-order diagrammatic perturbative energy expansion are evaluated for the electronic energy, using both the standard self-consistent-field potential V^N and a modified potential V^N-1 to determine the unoccupied states. The 21 Pad\'e approximants to the energy are constructed and first-order perturbative wave functions are inserted into the Rayleigh quotient to yield rigorous upper bounds for the energy. The results indicate that the standard V^N potential generates a more suitable virtual orbital basis for the calculations.