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Recent calculations using coupled cluster on solids have raised discussion ofusing a $N^{-1/3}$ power law to fit the correlation energy when extrapolatingto the thermodynamic limit, an approach which differs from the more commonlyused $N^{-1}$ power law which is (for example) often used by quantum MonteCarlo methods. In this paper, we present one way to reconcile these viewpoints.Coupled cluster doubles calculations were performed on uniform electron gasesreaching system sizes of $922$ electrons for an extremely wide range ofdensities ($0.1<r_s<100.0$) to study how the correlation energy approaches thethermodynamic limit. The data were corrected for basis set incompleteness errorand use a selected twist angle approach to mitigate finite size error fromshell filling effects. Analyzing these data, we initially find that a power lawof $N^{-1/3}$ appears to fit the data better than a $N^{-1}$ power law in thelarge system size limit. However, we provide an analysis of the transitionstructure factor showing that $N^{-1}$ still applies to large system sizes andthat the apparent $N^{-1/3}$ power law occurs only at low $N$.

Power laws used to extrapolate the coupled cluster correlation energy to the thermodynamic limit