Computing the classical mechanical vibrational echo with the fluctuating frequency approximation

The vibrational photon echo is an infrared nonlinear spectroscopic measurement probing the time scales of dynamical processes that underlie a linear absorption spectrum. The challenges posed by the quantum mechanical treatment of large anharmonic systems motivate the consideration of this observable within classical mechanics. The rigorous calculation of the classical mechanical vibrational echo requires going beyond a conventional molecular dynamics simulation of trajectories to propagate stability matrix elements, which quantify the sensitivity of classical trajectories to small changes in initial conditions. As an alternative to this procedure, we present an approximate theory of the vibrational echo that avoids the numerical calculation of stability matrix elements. This approach, the fluctuating frequency approximation (FFA), generalizes a well established treatment of linear spectroscopy that models a driven anharmonic oscillator as a harmonic system with a fluctuating frequency. The FFA compares well with numerically exact calculations of the echo for a solvated anharmonic oscillator. (C) 2000 American Institute of Physics. [S0021-9606(00)51147-7].