Classical combination frequencies in vibrational spectra

In theoretical vibrational spectroscopy, methods based on classical dynamics are widespread. In this paper, I examine the controversial presence of overtones and combination bands-features typically associated with quantum mechanics-in classical spectra. Using a perturbative approach both in time- and frequency-space, the presence of these features can be ascribed to the potential anharmonicity, rather than nuclear quantum effects. The analytical results are then confirmed by the autocorrelation spectra of some one- and two-dimensional potentials and the comparison with quantum calculations. The differences between classical combination frequencies and quantum combination bands are derived from both theory and numerical simulations, providing a sound method to discriminate between the two.