  Growth in computational resources has lead to the application of real space
diffusion quantum Monte Carlo (DMC) to increasingly heavy elements. Although
generally assumed to be small, we find that when using standard techniques the
pseudopotential localization error can be large, on the order of an electron
volt for an isolated cerium atom. We formally show that localization error can
be reduced to zero with improvements to the Jastrow factor alone and we define
a metric of Jastrow sensitivity that may be useful in the design of
pseudopotentials. We employ an extrapolation scheme to extract the bare fixed
node energy and estimate the localization error in both the locality
approximation and the T-moves schemes for the Ce atom in charge states 3+ and
4+. The locality approximation exhibits the lowest Jastrow sensitivity and
generally smaller localization errors than T-moves, although the locality
approximation energy approaches the localization free limit from above/below
for the 3+/4+ charge state. We find that energy minimized Jastrow factors
including three-body electron-electron-ion terms are the most effective at
reducing localization error for both the locality approximation and T-moves.
Less complex or variance minimized Jastrows are generally less effective. Our
results suggest that further improvements to Jastrow factors and trial
wavefunction forms will be necessary to reduce localization errors to chemical
accuracy in calculations of heavy elements.
