The isoelectronic series of Be, Ne and Si are investigated using a
variational determination of the second-order density matrix. A semidefinite
program was developed that exploits all rotational and spin symmetries in the
atomic system. We find that the method is capable of describing the strong
static electron correlations due to the incipient degeneracy in the hydrogenic
spectrum for increasing central charge. Apart from the ground-state energy
various other properties are extracted from the variationally determined
second-order density matrix. The ionization energy is constructed using the
extended Koopmans' theorem. The natural occupations are also studied, as well
as the correlated Hartree-Fock-like single particle energies. The exploitation
of symmetry allows to study the basis set dependence and results are presented
for correlation-consistent polarized valence double, triple and quadruple zeta
basis sets.Comment: 19 pages, 7 figures, 3 tables v2: corrected typo in Eq. (52