Journal of Physical Chemistry B, Vol.113, No.16, 5528-5536, 2009
Comparison of Two Simple Models for High Frequency Friction: Exponential versus Gaussian Wings
Liquid phase vibrational energy relaxation (VER) times T-1 typically depend critically on the relaxing mode's high frequency friction or wing function. The wing function may, in principle, be found from the mode's normalized force autocorrelation function (faf) C(t), since it is proportional to lim(omega ->infinity) integral(infinity)(0) cos omega t C(t) dt. However, the full form of C(t) is never available. Thus, the wing function is typically estimated from a model faf C-M(t) which duplicates the known part of C(t) and which (hopefully) approximates its unknown part with enough realism to yield meaningful omega -> infinity behavior. Unfortunately, apparently realistic C-M(t)'s can predict unphysical wing functions, and T-1's in error by tens of orders of magnitude. Thus, a condition is needed to discriminate between C-M(t)'s which yield meaningful and unphysical forms for the high frequency friction. This condition is shown to be that model faf's C-M(t) yield physical wing functions if and only if these functions derive from the short time "heads" of the faf's. This test is applied to the model faf's C-ga(t) equivalent to exp[-1/2(t/tau)(2)] and C-se(t) equivalent to sech(t/tau). These faf's cannot both be physical, since they yield incompatible Gaussian and exponential wing functions. The test accepts C-ga(t) as physical. It, however, rejects C-se(t), since its "tail" lim(t ->infinity) C-se(t) = 2 exp(-t/tau) (because of its long range) dominates the wing function.