Cholesky Decomposition-Based Implementation of Relativistic Two-Component Coupled-Cluster Methods for Medium-Sized Molecules

Abstract

A Cholesky decomposition (CD)-based implementation of relativistic two-component coupled-cluster (CC) and equation-of-motion CC (EOM-CC) methods using an exact two-component Hamiltonian augmented with atomic-mean-field spin−orbit integrals (the X2CAMF scheme) is reported. The present CD-based implementation of X2CAMF-CC and EOM-CC methods employs atomic-orbital-based algorithms to avoid the construction of two-electron integrals and intermediates involving three and four virtual indices. Our CD-based implementation extends the applicability of X2CAMF-CC and EOM-CC methods to medium-sized molecules with the possibility to correlate around 1000 spinors. Benchmark calculations for uranium-containing small molecules were performed to assess the dependence of the CC results on the Cholesky threshold. A Cholesky threshold of 10 −4 is shown to be sufficient to maintain chemical accuracy. Example calculations to illustrate the capability of the CD-based relativistic CC methods are reported for the bond-dissociation energy of the uranium hexafluoride molecule, UF 6 , with up to quadruple-ζ basis sets, and the lowest excitation energy in the solvated uranyl ion [UO 2 2+ (H 2 O) 12 ].

Relativistic Exact Two-Component Coupled-Cluster Study of Molecular Sensitivity Factors for Nuclear Schiff Moments

“…The use of analytic relativistic coupled-cluster gradient techniques greatly expedites the calculations and enables routine black-box calculations of these parameters. Future work will extend the Cholesky-decomposition-based implementation for exact two-component coupled-cluster methods to analytic gradient calculations, aiming to further improve the computational efficiency by significantly reducing the storage requirement. This will enable routine calculations for molecular sensitivity factors in medium-sized molecules, which might be sufficient to cover the molecular species of interest to the search for the NSM interaction.…”

“…On the other hand, relativistic spin–orbit CC (SO–CC) methods − with variational treatments of spin–orbit coupling, including spinor-based relativistic CC methods, are computationally more expensive because of spin-symmetry breaking. While these methods were most often used in calculations of atoms and small molecules, recent algorithmic and implementational advances extend the applicability of SO–CC methods to larger molecules. ,− …”