Correction of Finite Size Errors in Many-body Electronic Structure Calculations

Finite-size (FS) effects are a major source of error in many-body (MB) electronic structure calculations of extended systems. Reducing FS errors is thus a key to broader applications of MB methods in real materials, and the subject has drawn considerable attention.\footnote{P. R. C. Kent \textit{et. al.}, Phys. Rev. B \textbf{59}, 1917 (1999); S. Chiesa \textit{et. al.} Phys. Rev. Lett. \textbf{97}, 076404 (2006).} We show that MB FS effects can be effectively included in a modified local density approximation calculation. A parametrization for the FS exchange-correlation functional is obtained. The method is simple and gives post-processing corrections that can be applied to any MB results. Conceptually, it gives a consistent framework for relating FS effects in MB and DFT calculations, which is important if the two methods are to be seamlessly interfaced to bridge length scales. Applications to a model insulator (P$_2$ in a supercell), to semiconducting Si, and to metallic Na show that the method delivers greatly improved FS corrections.\footnote{H.\,Kwee, S.\,Zhang and H.\,Krakauer (2007), preprint at http://arxiv.org/abs/0711.0921.}