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 VN and a modified potential V^N-1 to determine the unoccupied states. The [2/1] 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 VN potential generates a more suitable virtual orbital basis for the calculations.
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Silver et al. (1977) studied this question.
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