Cholesky Decomposition in Spin-Free Dirac–Coulomb Coupled-Cluster Calculations

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 nonrelativistic counterparts. While for nonrelativistic 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 in that case. Here, molecular-orbital (MO)-based algorithms exploiting the CD of the two-electron integrals allow us to reduce disk-space requirements and lead to computational cost in the CC step that is more or less the same as in the nonrelativistic case. The only remaining overhead in a CD-SFDC-CC calculation is 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.