THE SHORT-TIME DYNAMICS OF MOLECULAR LIQUIDS - INSTANTANEOUS-NORMAL-MODE THEORY

Since the sharply varying forces that control the arrangement of molecules in liquids are themselves intrinsically anharmonic, the natural assumption would be that any picture that regarded molecular motion as harmonic would be at best a rough phenomenological guide. This expectation is, in fact, not a correct one. While the packing forces that determine liquid structure are indeed strongly anharmonic, the short-time displacements and librations that molecules execute are actually quite harmonic. It is possible to show rigorously that, for short enough (subpicosecond) time intervals, the dynamics of liquids is governed by a set of independent, collective, harmonic modes-the instantaneous normal modes of the liquid. In this paper we illustrate this fact by predicting the translational and rotational dynamics of a model diatomic liquid using the instantaneous normal modes computed by simulation. When compared to the exact molecular-dynamics results for the same autocorrelation functions, we find that perfect agreement is maintained only for very short times, but that if one removes the artificial runaway dynamics caused by the imaginary-frequency modes, reasonable levels of agreement are maintained for much longer time intervals. We also investigate the nature of the coupled translational-rotational motion by looking at the relevant translational and rotational projections of the modes. We find that the negative (backscattering) regions of both the translational- and rotational-velocity autocorrelation functions can be understood in terms of these same instantaneous harmonic modes.