Anharmonicity and quantum nuclear effects in theoretical vibrational spectroscopy: a molecular tale of two cities

Anharmonic effects due to the shape of the molecular potential energy surface far from the equilibrium geometry are major responsible for the deviations of the actual frequencies of vibration from the harmonic estimates. However, anharmonic effects are not the solely responsible for this. Quantum nuclear effects also play a prominent role in theoretical vibrational spectroscopy as they contribute to drive away the molecular vibrational frequencies from their harmonic counterpart. The consequence of this is that anharmonicity and quantum effects may be difficult to separate spectroscopically and get often confused. In this work we show that anharmonicity can be detected by means of classical simulations, while quantum nuclear effects need to be identified by means of an approach originating from either the time independent or the time dependent Schroedinger equation of quantum mechanics. We show that classical methods are sensitive to the temperature or energy conditions under which they are undertaken. This leads to wrong frequency estimates, when dealing with few-Kelvin experiments, if one performs simulations simply matching the experimental temperature. Conversely, quantum approaches are not affected by this issue and they provide more and better information.