Homotopy continuation methods for coupled-cluster theory in quantum chemistry

TL;DR

This paper reviews the application of homotopy continuation methods to solve coupled-cluster equations in quantum chemistry, highlighting recent mathematical developments and their potential for understanding multiple solutions.

Contribution

It provides an overview of recent mathematical approaches, including topological degree theory and algebraic tools, applied to homotopy methods in quantum chemistry.

Findings

Homotopy methods effectively analyze multiple solutions in coupled-cluster equations.

Recent mathematical tools enhance understanding of solution structures.

The review bridges applied mathematics and quantum chemistry techniques.

Abstract

Homotopy methods have proven to be a powerful tool for understanding the multitude of solutions provided by the coupled-cluster polynomial equations. This endeavor has been pioneered by quantum chemists that have undertaken both elaborate numerical as well as mathematical investigations. Recently, from the perspective of applied mathematics, new interest in these approaches has emerged using both topological degree theory and algebraically oriented tools. This article provides an overview of describing the latter development.