Steepest-descent determination of occupation numbers and energy minimization in the local-density approximation

A method based on steepest-descent algorithms is described for calculating one-electron occupation numbers in finite-atomic-cluster calculations. Unlike zero-temperature Fermi-Dirac statistics, the technique can be used to determine fractional occupation numbers in those cases where they give the lowest self-consistent-field energy. Applications to the iron atom and an iron-aluminum cluster illustrate the principles of the method.