Connection of an elementary class of parametric two-electron reduced-density-matrix methods to the coupled electron-pair approximations

Abstract

Parametric two-electron reduced-density-matrix (p-2RDM) methods have recently been shown to exhibit accuracies greater than coupled cluster with single and double substitutions (CCSD) at a lower computational cost. In this paper we derive an elementary class of parametric 2-RDM methods with connections to the coupled electron pair approximations (CEPA). Three parametric 2-RDM methods p-2RDM/n are presented that correspond to the CEPA/n family where n = 1, 2, 3. We isolate the function distinguishing the stationary condition of the parametric 2-RDM methods from the nonlinear equations of CEPA. Calculations of energies, geometries, and harmonic frequencies show that p-2RDM/n and CEPA/n are very similar for a variety of closed-shell systems. Finally, each of the p-2RDM/n methods is extended to satisfy particle–hole symmetry by the removal of exclusion principle violating terms in the virtual space. These extensions denoted p-2RDM′/n are shown to be essential for the proper dissociation of CH radical. Both p-2RDM/n and p-2RDM′/n form an elementary class of parametric 2-RDM methods with accuracy like CCSD; more general parametric 2-RDM methods [D.A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)] have an accuracy approaching CCSD with full triple excitations.