Valentin V. Karasiev ∗, Debajit Chakraborty, S.B. Trickey. Improved analytical representation of combinations of Fermi–Dirac integrals for finite-temperature density functional calculations
Computer Physics Communications 192 (2015) 114–123, 2015-03-09
Abstract: Smooth, highly accurate analytical representations of Fermi–Dirac (FD) integral combinations important
in free-energy density functional calculations are presented. Specific forms include those that occur in the
local density approximation (LDA), generalized gradient approximation (GGA), and fourth-order gradient
expansion of the non-interacting free energy as well as in the LDA and second-order gradient expansion
for exchange. By construction, all the representations and their derivatives of any order are continuous
on the full domains of their independent variables. The same type of technique provides an analytical
representation of the function inverse to the FD integral of order 1/2. It plays an important role in physical
problems related to the electron gas at finite temperature. From direct evaluation, the quality of these
improved representations is shown to be substantially superior to existing ones, many of which were
developed before the era of large-scale computation or early in the era.