Analysis of eigenvalues and eigenvectors of polymer particles: random normal modes

We investigate the density of vibrational states g(omega) for 6000 atom pol ymer particles involving all 18,000 degrees of freedom. The particles are e fficiently generated using a molecular dynamics-based computational algorit hm and a molecular mechanics method. The density of states spectrum g(w) cl early shows two distinguishable frequency regions in the polymer system: hi gh (760 < <omega> < 1240 cm(-1)) and low (0 < omega < 350 cm(-1)) frequency modes. By calculating the level-spacing distributions, we find the distrib ution of the low eigenfrequency corresponds to that of a Wigner distributio n. In contrast, Poisson behavior is found for the high frequency region. Th e eigenvectors for the two regions are analyzed by using a random walk meth od and Stewart's perturbation theory, both indicate random character for th e eigenvectors of the low frequency modes. The random character of the eige nvectors should have ramifications to most types of spectroscopy since tran sformations of the transition operator to random normal coordinates will ca use a widespread mixing, i.e., no selection rules. (C) 2000 Elsevier Scienc e Ltd. All rights reserved.