Direct Minimization for Ensemble Electronic Structure Calculations

We consider a direct optimization approach for ensemble density func-tional theory electronic structure calculations. The update operator for the electronic orbitals takes the structure of the Stiefel manifold into ac-count and we present an optimization scheme for the occupation numbers that ensures that the constraints remain satisfied. We also compare se-quential and simultaneous quasi-Newton and nonlinear conjugate gradient optimization procedures, and demonstrate that simultaneous optimization of the electronic orbitals and occupation numbers improve performance compared to the sequential approach.