Ensemble Density-Functional Theory forAb InitioMolecular Dynamics of Metals and Finite-Temperature Insulators

A new method is presented for performing first-principles molecular-dynamics simulations of systems with variable occupancies. We adopt a matrix representation for the one-particle statistical operator $\hat{\gamma }$ to introduce a “projected” free energy functional $G$ that depends on the Kohn-Sham orbitals only and that is invariant under their unitary transformations. The Liouville equation $[\hat{\gamma },\hat{H}]=0\mathrm{}$ is always satisfied, guaranteeing a very efficient and robust variational minimization algorithm, that can also be extended to nonconventional entropic formulations.