  The development of variational density functional theory approaches to
excited electronic states is impeded by limitations of the commonly used
self-consistent field (SCF) procedure. A method based on a direct optimization
approach as well as the maximum overlap method is presented and the performance
compared with previously proposed SCF strategies. Excited-state solutions
correspond to saddle points of the energy as a function of the electronic
degrees of freedom. The approach presented here makes use of a preconditioner
determined with the help of the maximum overlap method to guide the convergence
on a target nth-order saddle point. The method is found to be more robust and
to converge faster than previously proposed SCF approaches for a set of 89
excited states of molecules. A limited-memory formulation of the symmetric
rank-one method for updating the inverse Hessian is found to give the best
performance. A conical intersection for the carbon monoxide molecule is
calculated without resorting to fractional occupation numbers. Calculations on
excited states of the hydrogen atom and a doubly excited state of the
dihydrogen molecule using a self-interaction corrected functional are
presented. For these systems, the self-interaction correction is found to
improve the accuracy of density functional calculations of excited states.
