Electric-field gradients at the nuclei from all-electron, four-component relativistic density-functional theory using Gaussian-type orbitals

TL;DR

This paper develops a relativistic all-electron method using Gaussian orbitals to accurately compute electric field gradients at nuclei, especially for heavy elements, and applies it to various halides to improve nuclear quadrupole moment estimates.

Contribution

It introduces a four-component relativistic density-functional theory implementation for EFGs with Gaussian orbitals, enhancing accuracy for heavy-element compounds.

Findings

Relativistic effects significantly influence EFGs in heavy-element compounds.

The method provides a refined estimate of the nuclear quadrupole moment of 209Bi.

Results suggest revisiting experimental EFG data for bismuth oxyhalides.

Abstract

We present an all-electron, four-component relativistic implementation of electric field gradients (EFGs) at the nuclei using Gaussian-type orbitals and periodic boundary conditions. This allows us to include relativistic effects variationally, which is important for compounds containing heavy elements and for a property dependent the electronic structure close to the nuclei. The all-electron approach ensures an accurate treatment of both core and valence orbitals, as both are important in the evaluation of EFGs. Computational efficiency is achieved through the use of a recent implementation of density fitting in combination with quaternion algebra and restricted kinetic balance. We use the relativistic approach to calculate the EFGs in different arsenic, antimony and bismuth halides and oxyhalides, and explore the importance of relativistic effects on EFGs in solids and compare these with results obtained for molecular species. Our calculations contribute to establishing a reliable estimate for the nuclear quadrupole moment of 209Bi, for which our best estimate is -428(17) mb, in excellent agreement both with molecular data and a recent reevaluation of the nuclear quadrupole moment obtained from atomic data and ab initio calculations. Our results suggest that there is a need to revisit the experimental data for the EFGs of several bismuth oxyhalides.