Ab initio Calculations in Atoms, Molecules, and Solids, Treating Spin-Orbit Coupling and Electron Interaction on Equal Footing

Understanding the interplay between electron-electron interaction and spin-orbit coupling in molecules and materials is key to answering various fundamental and technological questions. An unbiased theoretical treatment requires that material specificity, electron correlation, and spin-orbit coupling (SOC) be captured accurately and on equal footing. We have incorporated explicit, non-perturbative treatment of spin-orbit coupling into ab initio auxiliary-field quantum Monte Carlo (AFQMC) calculations. The approach allows a general computational framework for molecular and bulk systems in which materials specificity, electron correlation, and spin-orbit coupling effects can be captured accurately, with favorable computational scaling versus system size. We adopt relativistic effective-core potentials which have been obtained by fitting to fully relativistic data and which have demonstrated a high degree of reliability and transferability in molecular systems. This results in a 2-component spin-coupled Hamiltonian, which is then treated by generalizing the ab initio AFQMC approach. We demonstrate the method by computing the electron affinity in Pb, the bond dissociation energy in Br₂ and I₂, and solid Bi.