NON-CARTESIAN COORDINATES FOR INSTANTANEOUS NORMAL-MODE THEORY OF ATOMIC LIQUIDS

A hybrid coordinate system of spherical polar coordinates for the mutu al nearest-neighbor pairs and Cartesian coordinates for the unpaired a toms is introduced for instantaneous normal mode (INM) analysis of ato mic Liquids. Densities of states (dos) calculated with the hybrid coor dinates in a unit-density, supercooled Lennard-Jones liquid differ fro m those obtained with Cartesian coordinates, primarily at imaginary fr equency. A brief discussion of coordinate dependence is presented, wit h an analytic treatment of the frequency moments, and it is argued tha t the hybrid dos are more physically meaningful. INM theory strives to relate Im omega modes to diffusion and barrier crossing, but spurious nondiffusive contributions must be removed. Hybrid coordinates yield substantially fewer Im omega indicating that some nondiffusive modes a re simply Cartesian artifacts. Normalized hybrid and Cartesian Re omeg a dos are nearly identical, as are velocity correlation functions C(t) obtained by treating. the Re omega INM as a complete set of harmonic modes. These C(t) are in fair agreement with simulation, but, notably, reach an insufficiently deep negative minimum value at too short a ti me. A harmonic approximation using the hybrid-translational Re w dos, in which the hybrid modes are projected onto the center-of-mass transl ations of the mutual neighbor pairs plus the unpaired atoms, yields mu ch better agreement. (C) 1998 American Institute of Physics. [S0021-96 06(98)50444-8].