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.