Accuracy of time-dependent properties in electronic-structure calculations using a fictitious Lagrangian

We have used a self-consistent tight-binding Hamiltonian to investigate the accuracy of using a fictitious Lagrangian to determine time-dependent properties, and have compared the results with brute-force calculations in which self-consistent descent to the Born-Oppenheimer surface is ensured at each time step. We find that when frequency-dependent properties with a period of a few hundred time steps are required, then the fictitious Lagrangian method is perfectly satisfactory for most applications.