  We investigate the inclusion of variable spins in electronic structure
quantum Monte Carlo, with a focus on diffusion Monte Carlo with Hamiltonians
that include spin-orbit interactions. Following our previous introduction of
fixed-phase spin-orbit diffusion Monte Carlo (FPSODMC), we thoroughly discuss
the details of the method and elaborate upon its technicalities. We present a
proof for an upper-bound property for complex nonlocal operators, which allows
for the implementation of T-moves to ensure the variational property. We
discuss the time step biases associated with our particular choice of spin
representation. Applications of the method are also presented for atomic and
molecular systems. We calculate the binding energies and geometry of the PbH
and Sn$_2$ molecules, as well as the electron affinities of the 6$p$ row
elements in close agreement with experiments.
