Observing Intramolecular Vibrational Energy Redistribution via the Short-Time Fourier Transform

Intramolecular vibrational energy relaxation (IVR) is important in many problems in chemical physics. Here, we apply the short-time Fourier transform method for analyzing IVR with classical dynamics. Calculating time-dependent Fourier transforms to perform such an analysis requires extending the usual Fourier transform method, and we do that here. The guiding concept behind the generalization is that if there is a shift of vibrational energy from one frequency range to another, we see a difference between the spectrum before the shift and the spectrum after the shift. We use time-window functions to transform the power spectrum of a trajectory into a time-dependent density spectrum of the average kinetic energy. The time-dependent average kinetic energy for each interval of the spectrum becomes an indicator to monitor the extent and nature of the energy transfer into and out of the corresponding modes. We illustrate this method for the H₂O molecule. By analyzing cases with different initial conditions, we show that the short-time Fourier transform method can distinguish trends in IVR that depend on the initial distribution of energy and not just on the total energy.