Quantum correction factor, harmonic oscillators

A more interesting point was made by Bader and Berne, who noted that the vibrational relaxation rate of a classical oscillator in a classical harmonic bath is identical to that of a quantum oscillator in a quantum harmonic bath [71]. On the other hand, when the relaxation of the quantum system is calculated using the corrected correlation function of the classical bath [Eq. (31)], the predicted rate is slower by a factor of j/3h(i) coth(/3h(o/2), which can be quite substantial for high-frequency solutes. The conclusions of a number of recent studies were shown to be strongly affected by this inconsistency [42,43,72]. Quantizing the solvent by mapping the classical correlation functions onto a quantum harmonic bath corrects the discrepancy. 

---