Distribution of vibrational potential energy in molecular systems

It is shown that for a collection of n classical harmonic oscillators, the long-time distribution of potential energies P is approximated by sin(m)(pi P) for n greater than or equal to 4, where m=(8n/pi(2)-1/root 2) and P is scaled to lie between 0 and 1. As n-->infinity, the distribution tends to a delta-function centered about P=0.5. When coupling is present between the oscillators, the effective value of m is reduced, so that the breadth of th e potential energy distribution reflects the degree of randomization in the system. (C) 1999 American Institute of Physics. [S0021-9606(99)00617-0].