  We incorporate 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 and on equal footing, 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 Br$_2$ and I$_2$, and solid Bi.
