The feasibility of many-body perturbation-theory (MBPT) calculations with hole and particle states expanded in a finite set of bound-type functions is investigated. The correlation energy of atomic beryllium is used as a test case. Particle states with negative and positive energy values are treated uniformly. We find that convergence of individual diagrams to better than ${10}^{-4\mathrm{}}$ a.u., and similar agreement with Kelly's numerical results can be obtained using basis sets composed of $9s$, $7p$, $5d$, and $4f$ Slater orbitals for intrashell correlation and a $10s8p6d4f$ set for the intershell effects. The total correlation energy calculated with these basis functions is in good agreement with experiment. These results indicate that MBPT calculations by the expansion method are indeed feasible. While this method may not be more convenient than the numerical approach for atomic systems, it should be useful for molecular calculations, where finding a suitable complete set of numerical orbitals presents difficult problems.

• Received 5 January 1972

DOI:https://doi.org/10.1103/PhysRevA.7.427