  Accuracy of the fixed-node diffusion Monte Carlo (FN-DMC) depends on the node
location of the best available trial state $\Psi_T$. The practical FN-DMC
approaches available for large systems rely on compact yet effective $\Psi_T$s
containing explicitly correlated single Slater determinant (SD). However, SD
nodes may be better suited to one system than to another, which may possibly
lead to inaccurate FN-DMC energy differences. It remains a challenge, how to
estimate inequivalency or appropriateness of SDs. Here we use the differences
of a measure based on Euclidean distance between the natural orbital occupation
number (NOON) vector of the Slater determinant (SD) from the exact solution in
the NOON vector space, that can be viewed as a measure of SD inequivalency and
a measure of the expected degree of nondynamic-correlation-related bias in
FN-DMC energy differences. This is explored on a set of small noncovalent
complexes and covalent bond breaking of Si$_2$ vs. N$_2$. It turns out that
NOON-based measures well reflect the magnitude and sign of the bias present in
the data available, thus providing new insights to the nature of bias
cancellation in SD FN-DMC energy differences.
