  We analyze the problem of eliminating finite-size errors from quantum Monte
Carlo (QMC) energy data. We demonstrate that both (i) adding a recently
proposed [S. Chiesa et al., Phys. Rev. Lett. 97, 076404 (2006)] finite-size
correction to the Ewald energy and (ii) using the model periodic Coulomb (MPC)
interaction [L. M. Fraser et al., Phys. Rev. B 53, 1814 (1996); P. R. C. Kent
et al., Phys. Rev. B 59, 1917 (1999); A. J. Williamson et al., Phys. Rev. B 55,
4851 (1997)] are good solutions to the problem of removing finite-size effects
from the interaction energy in cubic systems, provided the exchange-correlation
(XC) hole has converged with respect to system size. However, we find that the
MPC interaction distorts the XC hole in finite systems, implying that the Ewald
interaction should be used to generate the configuration distribution. The
finite-size correction of Chiesa et al. is shown to be incomplete in systems of
low symmetry. Beyond-leading-order corrections to the kinetic energy are found
to be necessary at intermediate and high densities, and we investigate the
effect of adding such corrections to QMC data for the homogeneous electron gas.
We analyze finite-size errors in two-dimensional systems and show that the
leading-order behavior differs from that which has hitherto been supposed. We
compare the efficiency of different twist-averaging methods for reducing
single-particle finite-size errors and we examine the performance of various
finite-size extrapolation formulas. Finally, we investigate the system-size
scaling of biases in diffusion QMC.
