Variational reduced-density-matrix method using three-particleN-representability conditions with application to many-electron molecules

Abstract

Molecular two-electron reduced density matrices (2-RDMs) are computed variationally without the many-electron wave function by constraining the 2-RDM with a set of three-particle $N$-representability conditions known as three-positivity conditions. These constraints restrict four distinct three-particle probability distributions, which can be defined for any $N$-particle system, to be nonnegative. The variational calculation of the 2-RDM with full three-positivity conditions is implemented with the first-order semidefinite programming algorithm [D.A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)]. We also derive and implement a generalization of the ${T}_{2}$ representability condition, which is a subset of the three-positivity conditions. Energies and 2-RDMs are computed for several molecules as well as the nitrogen molecule at both equilibrium and nonequilibrium geometries. The ground-state energies for nitrogen are within $0.0015\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ of the values from full configuration interaction at all internuclear distances.