Fractional occupancies and temperature in electronic-structure calculations

Fractional occupancies are often used in electronic-structure calculations. We use a simple model that contains the essential elements of more elaborate first-principles techniques in order to evaluate the effects of four typical fractional occupancy schemes on a system's calculated physical properties. We find that when the broadenings used in such a scheme are not significantly larger than the characteristic energies of the system of interest, the results depend only marginally on the type of broadening function that is used, except for Lorentzian broadening. We have also studied differences between free-energy and total-energy formulations. Finally, we present closed formulas for those parts of the forces that originate from the fractional occupancies, both for our model and for electronic-structure calculations within the density-functional formalism. Based on our results, we recommend using a simple step-function broadening scheme, which, unlike some more common methods, does not require a highly nonlinear equation to be iteratively solved for the Fermi energy.