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.