Geminal wavefunction models in chemistry

TL;DR

Geminal wavefunctions offer a compact way to model strong electron correlation, and recent advances have revitalized their role in electronic structure and quantum computing.

Contribution

The paper reviews recent developments, methodological innovations, and future directions of geminal wavefunctions in electronic structure and quantum computation.

Findings

Renewed interest due to computational and theoretical advances

Hybrid methods combining geminals with coupled-cluster theory

Emerging applications in quantum algorithms

Abstract

Geminal wavefunctions, introduced in the late 1950s, have long been recognized for their ability to compactly capture strong electron correlation. Despite their promise, they were historically overshadowed by more computationally efficient methods. Advances in both computational resources and theoretical frameworks have renewed interest in geminal-based approaches, particularly as researchers seek accurate yet tractable wavefunctions for complex electronic systems. Recent developments highlight their versatility: from serving as efficient starting points for correlated wavefunctions, to hybrid formulations that blend geminal concepts with coupled-cluster theory, to emerging applications in quantum algorithms where orbital-pairing provides a natural structure. In this mini-review, we summarize key advances in geminal wavefunction theory, with a focus on their modern resurgence, new methodological innovations, and potential directions for electronic structure theory and quantum computation.