One-dimensional anharmonic oscillator: Quantum versus classical vibrational partition functions

We analyze vibrational partition functions of low vibrational modes within the independent mode approximation to gain insight pertinent to the development of anharmonic corrections for transition state rate constants. As an example, we use a transition state for hydrogen abstraction on a lignin model compound. We found that for low frequencies, anharmonic effects are far more important than quantum effects. Our results suggest a hybrid model, where low-frequency modes are treated fully coupled using the classical or the Wigner–Kirkwood approximation, while high frequencies are described by the harmonic approximation. Mid-range frequencies could be expressed as independent anharmonic quantum modes.