Perturbational treatment of spin-orbit coupling for generally applicable high-level multi-reference methods

TL;DR

This paper introduces an efficient perturbational method for incorporating spin-orbit coupling into high-level multi-reference quantum chemistry calculations, enabling more accurate and computationally feasible modeling of relativistic effects.

Contribution

The authors develop and implement a perturbational approach to spin-orbit coupling within multi-reference methods, compatible with existing high-level quantum chemistry frameworks, and validate its accuracy.

Findings

Validated against fully variational spin-orbit MRCISD calculations.

Allows for approximate analytic gradients for geometry optimization.

Provides a size-consistent and size-extensive treatment of spin-orbit effects.

Abstract

An efficient perturbational treatment of spin-orbit coupling within the framework of high-level multi-reference techniques has been implemented in the most recent version of the COLUMBUS quantum chemistry package, extending the existing fully variational two-component (2c) multi-reference configuration interaction singles and doubles (MRCISD) method. The proposed scheme follows related implementations of quasi-degenerate perturbation theory (QDPT) model space techniques. Our model space is built either from uncontracted, large-scale scalar relativistic MRCISD wavefunctions or based on the scalar-relativistic solutions of the linear-response-theory-based multi-configurational averaged quadratic coupled cluster method (LRT-MRAQCC). The latter approach allows for a consistent, approximatively size-consistent and size-extensive treatment of spin-orbit coupling. The approach is described in detail and compared to a number of related techniques. The inherent accuracy of the QDPT approach is validated by comparing cuts of the potential energy surfaces of acrolein and its S, Se, and Te analoga with the corresponding data obtained from matching fully variational spin-orbit MRCISD calculations. The conceptual availability of approximate analytic gradients with respect to geometrical displacements is an attractive feature of the 2c-QDPT-MRCISD and 2c-QDPT-LRT-MRAQCC methods for structure optimization and ab inito molecular dynamics simulations.