  In ab initio calculations of electronic structures, total energies, and
forces, it is convenient and often even necessary to employ a broadening of the
occupation numbers. If done carefully, this improves the accuracy of the
calculated electron densities and total energies and stabilizes the convergence
of the iterative approach towards self-consistency. However, such a boardening
may lead to an error in the calculation of the forces. Accurate forces are
needed for an efficient geometry optimization of polyatomic systems and for ab
initio molecular dynamics (MD) calculations. The relevance of this error and
possible ways to correct it will be discussed in this paper. The first approach
is computationally very simple and in fact exact for small MD time steps. This
is demonstrated for the example of the vibration of a carbon dimer and for the
relaxation of the top layer of the (111)-surfaces of aluminium and platinum.
The second, more general, scheme employs linear-response theory and is applied
to the calculation of the surface relaxation of Al(111). We will show that the
quadratic dependence of the forces on the broadening width enables an efficient
extrapolation to the correct result. Finally the results of these correction
methods will be compared to the forces obtained by using the smearing scheme,
which has been proposed by Methfessel and Paxton.
