S. Goedecker, INTEGRAL-REPRESENTATION OF THE FERMI DISTRIBUTION AND ITS APPLICATIONS IN ELECTRONIC-STRUCTURE CALCULATIONS, Physical review. B, Condensed matter, 48(23), 1993, pp. 17573-17575
We show that the Fermi distribution can be represented by an infinite
sum of contour integrals in the complex energy plane. The expansion co
nverges very rapidly and a few terms are sufficient to obtain high acc
uracy.