Scalar relativistic effects with Multiwavelets: Implementation and benchmark

TL;DR

This paper presents an implementation of scalar relativistic effects using multiwavelets in quantum chemistry, demonstrating improved accuracy and error control in describing electrons near nuclei, validated through comparisons with established codes.

Contribution

The work extends the Multiwavelet-based code MRChem to include scalar relativistic effects via ZORA, providing a robust and adaptive approach for accurate quantum chemical calculations.

Findings

Validated implementation against numerical and plane-wave codes.

Achieved accurate total energies for selected elements and molecules.

Demonstrated the effectiveness of multiwavelets in describing nuclear regions.

Abstract

The importance of relativistic effects in quantum chemistry is widely recognized, not only for heavier elements but throughout the periodic table. At the same time, relativistic effect are strongest in the nuclear region, where the description of electrons through linear combination of atomic orbitals becomes more challenging. Furthermore, the choice of basis sets for heavier elements is limited compared to lighter elements where precise basis sets are available. Thanks to the framework of multiresolution analysis, multiwavelets provide an appealing alternative to overcome this challenge: they lead to robust error control and adaptive algorithms that automatically refine the basis set description until the desired precision is reached. This allows to achieve a proper description of the nuclear region. In this work we extended the Multiwavelet-based code MRChem to the scalar zero-order regular approximation (ZORA) framework. We validated our implementation comparing the total energies for a small set of elements and molecules. To confirm the validity of our implementation, we compared both against a radial numerical code for atoms and the plane-wave based code exciting.