Exploring Locality in Molecular Dirac-Coulomb-Breit Calculations: A Perspective.

The Dirac-Coulomb-Breit (DCB) operator is widely recognized for its ability to accurately capture relativistic effects and spin-physics in molecular calculations. However, due to its high computational cost, there is a need to develop low-scaling approximations without compromising accuracy. To tackle this challenge, it becomes essential to gain a deeper understanding of the DCB operator's behavior. This work aims to explore local integral approximations, shedding light on the locality of the parts of the charge-current distribution due to the small component. In particular, we propose an atomic Breit approximation that leverages an analysis of the behavior observed in a series of gold chains. Through benchmark studies of metal complexes, we evaluated the accuracy and performance of the proposed atomic Breit approximation. This work provides a comprehensive understanding of the behavior of the charge-current distribution in terms of its contributions from its AO basis constituents, facilitating the development of low-scaling methods that strike a balance between computational efficiency and accuracy.