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

TL;DR

This paper introduces a variational method using a semidefinite program to determine the second-order density matrix for the isoelectronic series of beryllium, neon, and silicon, effectively capturing strong electron correlations.

Contribution

The work develops a symmetry-exploiting variational approach to accurately describe electron correlations in atomic systems using the second-order density matrix.

Findings

Method accurately describes static electron correlations.

Ionization energies are computed via extended Koopmans' theorem.

Results show basis set dependence on correlation energies.

Abstract

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.