In the past, corrections for the CFSE in QMC simulations have been
applied using results for different simulation cell sizes and
extrapolating to the infinite cell size limit
[46, 33, 43, 47]. This empirical procedure is
very costly as it requires several calculations at increasingly large
system sizes. As mentioned in section 
, the CFSE
is approximately inversely proportional to the number of atoms in the
simulation cell. A reasonable approximation is
where N is the number of electrons in the system and 
is
defined as the radius of a sphere whose volume equals the volume per
electron so that
To obtain a value for 
in Eq.(), a series of
calculations is performed for different system sizes. This fitting
scheme is not very accurate when results for only 2 or 3 system sizes
are available, especially when the estimate for the CFSE is subject to
statistical noise at each system size.
