  We study several aspects of the recently introduced fixed-phase spin-orbit
diffusion Monte Carlo (FPSODMC) method, in particular, its relation to the
fixed-node method and its potential use as a general approach for electronic
structure calculations. We illustrate constructions of spinor-based wave
functions with the full space-spin symmetry without assigning up or down spin
labels to particular electrons, effectively "complexifying" even ordinary
real-valued wave functions. Interestingly, with proper choice of the simulation
parameters and spin variables, such fixed-phase calculations enable one to
reach also the fixed-node limit. The fixed-phase solution provides a
straightforward interpretation as the lowest bosonic state in a given effective
potential generated by the many-body approximate phase. In addition, the
divergences present at real wave function nodes are smoothed out to lower
dimensionality, decreasing thus the variation of sampled quantities and making
the sampling also more straightforward. We illustrate some of these properties
on calculations of selected first-row systems that recover the fixed-node
results with quantitatively similar levels of the corresponding biases. At the
same time, the fixed-phase approach opens new possibilities for more general
trial wave functions with further opportunities for increasing accuracy in
practical calculations.
