Energy versus free-energy conservation in first-principles molecular dynamics

In applying first-principles molecular dynamics to metals, a fictitious temperature is usefully assigned to the electronic (Fermi-Dirac) occupation functions. This avoids instabilities associated with fluctuations in these occupations during the minimization of the energy density functional. Because these occupations vary with the ionic motion, they give rise to an extra contribution in addition to the usual Hellmann-Feynman forces. If this extra force is omitted, energy is not conserved. We point out, however, that ionic kinetic energy plus electronic free energy is conserved, and argue that this yields a sensible and realistic conservative dynamics.