Cholesky decomposition in spin-free Dirac-Coulomb coupled-cluster calculations

TL;DR

This paper introduces a Cholesky decomposition-based method for spin-free Dirac-Coulomb coupled-cluster calculations, significantly reducing computational costs and enabling high-accuracy relativistic quantum chemistry computations.

Contribution

The authors develop a molecular-orbital based Cholesky decomposition algorithm that makes relativistic coupled-cluster calculations more computationally efficient and comparable to non-relativistic methods.

Findings

Reduced disk-space requirements for large-scale calculations.

Computational costs increased by less than 15% due to additional integrals and transformations.

Efficient calculations demonstrated on transition metal carbonyl molecules.

Abstract

We present an implementation for the use of Cholesky decomposition (CD) of two-electron integrals within the spin-free Dirac-Coulomb (SFDC) scheme that enables to perform high-accuracy coupled-cluster (CC) calculations at costs almost comparable to those of their non-relativistic counterparts. While for non-relativistic CC calculations atomic-orbital (AO) based algorithms, due to their significantly reduced disk-space requirements, are the key to efficient large-scale computations, such algorithms are less advantageous in the SFDC case due to their increased computational cost on that case. Here, molecular-orbital (MO) based algorithms exploiting the CD of the two-electron integrals allow to reduce disk-space requirements, and lead to computational cost in the CC step that are more or less the same as in the non-relativistic case. The only remaining overhead in a CD-SFDC-CC calculation are due to the need to compute additional two-electron integrals, the somewhat higher cost of the Hartree-Fock calculation in the SFDC case, and additional cost in the transformation of the Cholesky vectors from the AO to the MO representation. However, these additional costs typically amount to less than 5-15 % of the total wall time and are thus acceptable. We illustrate the efficiency of our CD scheme for SFDC-CC calculations on a series of illustrative calculations for the X(CO)$_4$ molecules with X = Ni, Pd, Pt.