  A rigorous two-thermostat formulation for ab-initio molecular dynamics using
the fictitious Lagrangian approach is presented. It integrates the concepts of
mass renormalization and temperature control for the wave functions. The new
thermostat adapts to the instantaneous kinetic energy of the nuclei and thus
minimizes its influence on the dynamics. Deviations from the canonical
ensemble, which are possible in the previous two-thermostat formulation, are
avoided. The method uses a model for the effective mass of the wave functions,
which is open to systematic improvement.
