Smearing scheme for finite-temperature electronic-structure calculations

The use of energy-dependent occupation numbers in density-functional theory has two purposes: simulating the canonical ensemble for the electrons at nonzero temperature (Fermi-Dirac occupation numbers), and improving the convergence with respect to the number of electronic wave vectors sampling the Brillouin zone. We present a scheme which combines both, providing finite-temperature eigenstate occupations with an additional smearing to improve sampling convergence. After developing the formalism and extracting a correction formula for the free energy, we test them on a small system of metallic aluminum for temperatures under 3000 K. In this regime, the Fermi-Dirac smearing alone gives only a modest reduction in the number of wave vectors needed for convergence. Our scheme reduces significantly the number of wave vectors, while preserving the correct physical temperature dependence.