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The isoelectronic series of Be, Ne and Si are investigated using avariational determination of the second-order density matrix. A semidefiniteprogram was developed that exploits all rotational and spin symmetries in theatomic system. We find that the method is capable of describing the strongstatic electron correlations due to the incipient degeneracy in the hydrogenicspectrum for increasing central charge. Apart from the ground-state energyvarious other properties are extracted from the variationally determinedsecond-order density matrix. The ionization energy is constructed using theextended Koopmans' theorem. The natural occupations are also studied, as wellas the correlated Hartree-Fock-like single particle energies. The exploitationof symmetry allows to study the basis set dependence and results are presentedfor correlation-consistent polarized valence double, triple and quadruple zetabasis sets.

Variational determination of the second-order density matrix for the isoelectronic series of beryllium, neon and silicon