Reduced density matrix functional theory from an ab initio seniority-zero wave function: Exact and approximate formulations along adiabatic connection paths

TL;DR

This paper introduces a new formulation of reduced density matrix functional theory based on an ab initio seniority-zero wave function, deriving an adiabatic connection approach to better describe electron correlation effects.

Contribution

It develops an exact and approximate framework for RDMFT using seniority-zero wave functions and introduces an adiabatic connection formula for higher-seniority density matrix functionals.

Findings

Curvature of the AC integrand indicates second-order perturbation theory is insufficient.

Multiple linear interpolations along the AC improve correlation descriptions.

Guidance for future higher-seniority density-matrix functional approximations.

Abstract

Currently, there is a growing interest in the development of a new hierarchy of methods based on the concept of seniority, which has been introduced quite recently in quantum chemistry. Despite the enormous potential of these methods, the accurate description of both dynamical and static correlation effects within a single and in-principle-exact approach remains a challenge. In this work, we propose an alternative formulation of reduced density-matrix functional theory (RDMFT) where the (one-electron reduced) density matrix is mapped onto an ab initio seniority-zero wave function. In this theory, the exact natural orbitals and their occupancies are determined self-consistently from an effective seniority-zero calculation. The latter involves a universal higher-seniority density matrix functional for which an adiabatic connection (AC) formula is derived and implemented under specific constraints that are related to the density matrix. The pronounced curvature of the (constrained) AC integrand, which is numerically observed in prototypical hydrogen chains and the Helium dimer, indicates that a description of higher-seniority correlations within second-order perturbation theory is inadequate in this context. Applying multiple linear interpolations along the AC or connecting second-order perturbation theory to a full-seniority treatment via Pad\'{e} approximants are better strategies. Such information is expected to serve as a guide in the future design of higher-seniority density-matrix functional approximations.