  We introduce a basis of counting functions that, by cleanly tessellating
three dimensional space, allows real space number counting Jastrow factors to
be straightforwardly applied to general molecular situations. By exerting
direct control over electron populations in local regions of space and encoding
pairwise correlations between these populations, these Jastrow factors allow
even very simple reference wave functions to adopt nodal surfaces well suited
to many strongly correlated settings. Being trivially compatible with
traditional Jastrow factors and diffusion Monte Carlo and having the same cubic
per-sample cost scaling as a single determinant trial function, these Jastrow
factors thus offer a powerful new route to the simultaneous capture of weak and
strong electron correlation effects in a wide variety of molecular and
materials settings. In multiple strongly correlated molecular examples, we show
that even when paired with the simplest possible single determinant reference,
these Jastrow factors allow quantum Monte Carlo to out-perform coupled cluster
theory and approach the accuracy of traditional multi-reference methods.
