Density Matrices of Seniority-Zero Geminal Wavefunctions

TL;DR

This paper develops methods to evaluate density matrices of seniority-zero geminal wavefunctions, enabling accurate calculations for molecular dissociation and suggesting improvements for Richardson-Gaudin states.

Contribution

It introduces a new approach to compute density matrices for specific geminal wavefunctions, making previously intractable problems feasible for certain classes of states.

Findings

Density matrices can be computed efficiently for RG states, AGP, and strongly-orthogonal geminals.

Dissociation curves for hydrogen chains are near exact using these methods.

Incorrect results with ground state RG are potentially fixable with alternative RG states.

Abstract

Scalar products and density matrix elements of closed-shell pair geminal wavefunctions are evaluated directly in terms of the pair amplitudes, resulting in an analogue of Wick's theorem for fermions or bosons. This expression is in general intractable, but it is shown how it becomes feasible in three distinct ways for Richardson-Gaudin (RG) states, the antisymmetrized geminal power, and the antisymmetrized product of strongly-orthogonal geminals. Dissociation curves for hydrogen chains are computed with off-shell RG states and the antisymmetrized product of interacting geminals. Both are near exact suggesting that the incorrect results observed with ground state RG states are fixable using a different RG state.