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Previous Methods of Removing Finite Size Effects


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 gif, 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 tex2html_wrap_inline7463 is defined as the radius of a sphere whose volume equals the volume per electron so that


To obtain a value for tex2html_wrap_inline7729 in Eq.(gif), 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.

Andrew Williamson
Tue Nov 19 17:11:34 GMT 1996