Conditions for describing triplet states in reduced density matrix functional theory

TL;DR

This paper establishes necessary conditions on the one-body reduced density matrix for representing triplet states in two-electron systems, and demonstrates their utility in improving triplet state calculations in reduced density matrix functional theory.

Contribution

It introduces specific occupation number conditions for triplet states and applies them to enhance the accuracy of triplet excitation calculations in RDMFT.

Findings

Conditions improve the quality of 1RDMs in calculations

Conditions can be used for systems with more than two electrons

Application of conditions yields more accurate triplet energies

Abstract

We consider necessary conditions for the one-body-reduced density matrix (1RDM) to correspond to a triplet wave-function of a two electron system. The conditions concern the occupation numbers and are different for the high spin projections, $S_z=\pm 1$, and the $S_z=0$ projection. Hence, they can be used to test if an approximate 1RDM functional yields the same energies for both projections. We employ these conditions in reduced density matrix functional theory calculations for the triplet excitations of two-electron systems. In addition, we propose that these conditions can be used in the calculation of triplet states of systems with more than two electrons by restricting the active space. We assess this procedure in calculations for a few atomic and molecular systems. We show that the quality of the optimal 1RDMs improves by applying the conditions in all the cases we studied.