Density-functional energies and forces with Gaussian-broadened fractional occupations

It is demonstrated that the Gaussian-broadening scheme for the explicit inclusion of fractional occupation numbers in density-functional calculations of crystals, as originally given by Fu and Ho [Phys. Rev. B 28, 5480 (1983)], contains an additional term to the total energy which makes the energy functional variational and exactly cancels a correction to the density-functional forces originating from changes in the occupation numbers.