Geminal theory within the seniority formalism and bi-variational principle

TL;DR

This paper reviews the mathematical structure of geminal wavefunctions in quantum chemistry, focusing on reducing computational costs and applying the bi-variational principle for better accuracy in electron pairing models.

Contribution

It introduces a bi-variational framework for geminal theory within the seniority formalism, addressing computational challenges and enhancing the theoretical foundation.

Findings

Reviewed recent methods to reduce permanent overlap calculations

Presented the bi-variational principle as a consistent computational framework

Connected geminal wavefunctions with chemical bonding concepts

Abstract

We present an overview of the mathematical structure of geminal theory within the seniority formalism and bi-variational principle. Named after the constellation, geminal wavefunctions provide the mean-field like representation of paired-electron wavefunctions in quantum chemistry, tying in with the Lewis picture of chemical bonding via electron pairs. Unfortunately, despite its mean-field product wave function description, the computational cost of computing geminal wavefunctions is dominated by the permanent overlaps with Slater determinant reference states. We review recent approaches to reduce the factorial scaling of the permanent, and present the bi-variational principle as a consistent framework for the projected Schr\"odinger Equation and the computation of reduced density matrices.