A Comparison of Relativistic Coupled Cluster and Equation of Motion Coupled Cluster Quadratic Response Theory

TL;DR

This paper compares relativistic coupled cluster quadratic response theory (QR-CC) with equation of motion coupled cluster quadratic response theory (QR-EOMCC), analyzing their accuracy and differences for heavy elements and relativistic effects.

Contribution

It introduces an implementation of relativistic QR-CC and compares its performance with QR-EOMCC for various heavy element properties and relativistic effects.

Findings

QR-EOMCC yields different hyperpolarizabilities for heavy elements.

QR-EOMCC performs similarly to QR-CC for Verdet constants.

Relativistic effects significantly influence properties of heavy and superheavy elements.

Abstract

We present the implementation of relativistic coupled cluster quadratic response theory (QR-CC), following our development of relativistic equation of motion coupled cluster quadratic response theory (QR-EOMCC) [X. Yuan et al., J. Chem. Theory Comput. 2023, 19, 9248]. These codes, which can be used in combination with relativistic (2- and 4-component based) as well as non-relativistic Hamiltonians, are capable of treating both static and dynamic perturbations for electric and magnetic operators. We have employed this new implementation to revisit the calculation of static and frequency-dependent first hyperpolarizabilities of hydrogen halides (HX, X=F-Ts) and the Verdet constant of heavy noble gas atoms (Xe, Rn, Og) and of selected hydrogen halides (HF to HI), in order to investigate the differences and similarities of QR-CC and the more approximate QR-EOMCC. Furthermore, we have determined the relative importance of scalar relativistic effects and spin-orbit coupling to these properties, through a comparison of different Hamiltonians, and extended our calculations to superheavy element species (HTs for hyperpolarizabilities, Og for the Verdet constant). Our results show that as one moves towards the bottom of the periodic table, QR-EOMCC can yield rather different results (hyperpolarizabilities) or perform rather similarly (Verdet constant) to QR-CC. These results underscore the importance of further characterizing the performance of QR-EOMCC for heavy element systems.