THE EVALUATION OF POWER SPECTRA IN MOLECULAR-DYNAMICS SIMULATIONS OF ANHARMONIC SOLIDS AND SURFACES

Histories of a molecular dynamics simulation of a chain of fifty anharmonically coupled atoms (taken as a prototype for a solid or a surface) are examined to obtain power spectra corresponding to a given k value. Two methods for obtaining the power spectra from the atom velocities are studied: (1) the method which involves computing the appropriate velocity-velocity autocorrelation function (ACF) and then taking its Fourier transform and (2) the direct method which involves finding the absolute value squared of the Fourier transform of the appropriate velocity. The long (in time) simulations necessary to obtain reasonably reproducible power spectrum parameters are rationalized in terms of a previous theoretical study of autocorrelation functions by Zwanzig and Ailawadi. The method of choice for obtaining power spectra is the use of long trajectories coupled with truncation of the ACF prior to its Fourier transform in such a way that the tail of the ACF is disregarded.