On the relationship between parametric two-electron reduced-density-matrix methods and the coupled electron pair approximation

TL;DR

This paper explores the connection between parametric two-electron reduced-density-matrix methods and the coupled electron pair approximation, introducing CEPA-like factors into the p-2RDM framework for improved accuracy and efficiency.

Contribution

It introduces CEPA-like topological factors into p-2RDM methods, creating a density-based generalization that aligns closely with traditional CEPA approaches and ensures stationary energies.

Findings

p-2RDM/n methods are similar to CEPA methodologies

Energies are stationary, aiding property and geometry calculations

Generalized treatment of EPV diagrams enhances accuracy

Abstract

Parametric two-electron reduced-density-matrix (p-2RDM) methods have enjoyed much success in recent years; the methods have been shown to exhibit accuracies greater than coupled cluster with single and double substitutions (CCSD) for both closed- and open-shell ground-state energies, properties, geometric parameters, and harmonic frequencies. The class of methods is herein discussed within the context of the coupled electron pair approximation (CEPA), and several CEPA-like topological factors are presented for use within the p-2RDM framework. The resulting p-2RDM/n methods can be viewed as a density-based generalization of CEPA/n family that are numerically very similar to traditional CEPA methodologies. We cite the important distinction that the obtained energies represent stationary points, facilitating the efficient evaluation of properties and geometric derivatives. The p-2RDM/n formalism is generalized for an equal treatment of exclusion-principle-violating (EPV) diagrams that occur in the occupied and virtual spaces. One of these general topological factors is shown to be identical to that proposed by Kollmar [C. Kollmar, J. Chem. Phys. 125, 084108 (2006)], derived in an effort to approximately enforce the D, Q, and G conditions for N-representability in his size-extensive density matrix functional.