# Zeroth order regular approximation approach to electric dipole moment interactions of the electron

## TL;DR

This paper introduces a quasi-relativistic two-component computational approach using ZORA for efficient calculation of electron electric dipole moment interactions, validated against more complex relativistic methods on heavy diatomic molecules.

## Contribution

It presents a novel two-component method combining cGHF and cGKS within ZORA for accurate and efficient eEDM interaction calculations, reducing computational complexity.

## Key findings

- Method accurately reproduces relativistic four-component results.
- Purely relativistic effects are captured by the upper component treatment.
- Validated on molecules like RaF, BaF, YbF, and HgF.

## Abstract

A quasi-relativistic two-component approach for an efficient calculation of $\mathcal{P,T}$-odd interactions caused by a permanent electric dipole moment of the electron (eEDM) is presented. The approach uses a (two-component) complex generalized Hartree-Fock (cGHF) and a complex generalized Kohn-Sham (cGKS) scheme within the zeroth order regular approximation (ZORA). In applications to select heavy-elemental polar diatomic molecular radicals, which are promising candidates for an eEDM experiment, the method is compared to relativistic four-component electron-correlation calculations and confirms values for the effective electrical field acting on the unpaired electron for RaF, BaF, YbF and HgF. The calculations show that purely relativistic effects, involving only the lower component of the Dirac bi-spinor, are well described by treating only the upper component explicitly.