  We present a recently developed projector quantum Monte Carlo method for
calculations of electronic structure in systems with spin-orbit interactions.
The method solves for many-body eigenstates in the presence of spin-orbit using
the fixed-phase approximation.The trial wave function is built from
two-component spinors and explicit Jastrow correlation factors while the core
electrons are eliminated by relativistic effective core potentials with
explicit spin-orbit terms. We apply this method to WO and W$_2$ molecules that
enable us to build multi-reference wave functions and analyze in detail the
impact of both electron correlations and of spin-orbit terms. These
developments open new opportunities for calculations of systems with
significant spin-orbit effects by many-body quantum Monte Carlo methods.
