It was recently proposed to use variational functionals based on many-body perturbation theory for the calculation of the total energies of many-electron systems. The accuracy of such functionals depends on the degree of sophistication of the underlying perturbation expansions. An older such functional and a recently constructed functional, both at the level of the $\mathrm{GW}$ approximation (GWA), were tested on the electron gas with indeed very encouraging results. In the present work we test the older of these functionals on atoms and find correlation energies much better than those of the random-phase approximation but still definitely worse as compared to the case of the gas. Using the recent functional of two independent variables it becomes relatively easy to include second-order exchange effects not present in the GWA. In the atomic limit we find this to be very important and the correlation energies improve to an accuracy of 10–20 % when obtained from calculations much less demanding than those of, e.g., configuration-interaction expansions.

• Received 30 April 2003

DOI:https://doi.org/10.1103/PhysRevB.69.195102