Parametric two-electron reduced-density-matrix (p-2RDM) methods have enjoyedmuch success in recent years; the methods have been shown to exhibit accuraciesgreater than coupled cluster with single and double substitutions (CCSD) forboth closed- and open-shell ground-state energies, properties, geometricparameters, and harmonic frequencies. The class of methods is herein discussedwithin the context of the coupled electron pair approximation (CEPA), andseveral CEPA-like topological factors are presented for use within the p-2RDMframework. The resulting p-2RDM/n methods can be viewed as a density-basedgeneralization of CEPA/n family that are numerically very similar totraditional CEPA methodologies. We cite the important distinction that theobtained energies represent stationary points, facilitating the efficientevaluation of properties and geometric derivatives. The p-2RDM/n formalism isgeneralized for an equal treatment of exclusion-principle-violating (EPV)diagrams that occur in the occupied and virtual spaces. One of these generaltopological factors is shown to be identical to that proposed by Kollmar [C.Kollmar, J. Chem. Phys. 125, 084108 (2006)], derived in an effort toapproximately enforce the D, Q, and G conditions for N-representability in hissize-extensive density matrix functional.
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