Metals at finite temperature: a modified smearing scheme

The specification of electronic eigenstate occupation numbers, in density-functional theory, has two purposes: simulating the canonical ensemble for the electrons at non-zero temperature (Fermi–Dirac occupation numbers), and improving the convergence with respect to the number of electronic wavevectors sampling the Brillouin zone. We describe a scheme which combines both, providing finite-temperature eigenstate occupations with an additional smearing to improve sampling convergence. We present the correction formula obtained for the free energy, and test the method on a small system of metallic aluminium for temperatures under 3000 K. In this regime, the Fermi–Dirac smearing alone gives only a modest reduction in the number of wavevectors needed for convergence.