Frequency-Dependent Quadratic Response Properties and Two-photon Absorption from Relativistic Equation-of-Motion Coupled Cluster Theory

TL;DR

This paper develops a relativistic quadratic response theory within the equation-of-motion coupled cluster framework, enabling detailed analysis of electronic response properties including hyperpolarizability, magneto-optical effects, and two-photon absorption in various atomic and molecular systems.

Contribution

The authors implement a general relativistic quadratic response theory based on EOM-CC, capable of handling both electric and magnetic perturbations, and compare it with non-relativistic methods for accuracy.

Findings

Accurate hyperpolarizability calculations for hydrogen halides.

Evaluation of Verdet constants highlighting relativistic effects.

Two-photon absorption cross-sections for ions relevant to optical clocks.

Abstract

We present the implementation of quadratic response theory based upon the relativistic equation-of-motion coupled cluster method. We showcase our implementation, whose generality allows us to consider both time-dependent and time-independent electric and magnetic perturbations, by considering the static and frequency-dependent hyperpolarizability of hydrogen halides (HX, X = F-At), providing a comprehensive insight into their electronic response characteristics. Additionally, we evaluated the Verdet constant for noble gases Xe and Rn, and discussed the relative importance of relativistic and electron correlation effects for these magneto-optical properties. Finally, we calculate the two-photon absorption cross-sections of transition ($ns^{1}S_{0}\to (n+1)s^{1}S_{0}$) of Ga$^{+}$, and In$^{+}$, which are suggested as candidates for new ion clocks. As our implementation allows for the use of non-relativistic Hamiltonians as well, we have compared our EOM-QRCC results to the QR-CC implementation in the DALTON code, and show that the differences between CC and EOMCC response are in general smaller than 5\% for the properties considered. Collectively, the results underscore the versatility of our implementation and its potential as a benchmark tool for other approximated models such as density functional theory for higher-order properties.