  Accurate rational approximations of the Fermi-Dirac distribution are a useful
component in many numerical algorithms for electronic structure calculations.
The best known approximations use $O( \log (\beta \Delta) \log
(\epsilon^{-1}))$ poles to achieve an error tolerance $\epsilon$ at temperature
$\beta^{-1}$ over an energy interval $\Delta$. We apply minimax approximation
to reduce the number of poles by a factor of four and replace $\Delta$ with
$\Delta_{\mathrm{occ}}$, the occupied energy interval. This is particularly
beneficial when $\Delta \gg \Delta_{\mathrm{occ}}$, such as in electronic
structure calculations that use a large basis set.
