Accelerated coupled cluster calculations with Procrustes orbital interpolation

TL;DR

This paper introduces a Gaussian process-based algorithm that interpolates coupled cluster amplitudes across geometries, significantly reducing computational effort while maintaining chemical accuracy in quantum chemistry calculations.

Contribution

It presents a novel interpolation method using Gaussian processes and Procrustes orbital alignment to improve initial guesses for CCSD calculations, reducing computational scaling.

Findings

Achieves approximate CCSD energies with $O(N^5)$ scaling.

Provides better initial guesses than MP2 and previous geometry methods.

Reduces number of iterations needed for convergence.

Abstract

The coupled cluster method is considered a gold standard in quantum chemistry, reliably giving energies that are exact within chemical accuracy (1.6 mHartree). However, even in the CCSD approximation, where the cluster operator is truncated to include only single and double excitations, the method scales as $O(N^6)$ in the number of electrons, and the cluster operator needs to be solved for iteratively, increasing computation time. Inspired by eigenvector continuation, we present here an algorithm making use of Gaussian processes that provides an improved initial guess for the coupled cluster amplitudes. The cluster operator is written as a linear combination of sample cluster operators which are obtained at particular sample geometries. By reusing the cluster operators from previous calculations in that way, it is possible to obtain a start guess for the amplitudes that surpasses both MP2-guesses and "previous geometry"-guesses in terms of the number of necessary iterations. As this improved guess is very close to the exact cluster operator, it can be used directly to calculate the CCSD energy to chemical accuracy, giving approximate CCSD energies scaling as $O(N^5)$.