HARMONIC INVERSION OF TIME CROSS-CORRELATION FUNCTIONS - THE OPTIMAL WAY TO PERFORM QUANTUM OR SEMICLASSICAL DYNAMICS CALCULATIONS

We explore two new applications of the filter-diagonalization method ( FDM) for harmonic inversion of time cross-correlation functions arisin g in various contexts in molecular dynamics calculations. We show that the Chebyshev cross-correlation functions c(i alpha)(n)=(Phi(alpha)\T -n((H) over cap)Phi(i)) obtained by propagation of a single initial wa ve packet Phi(i) correlated with a set of final states Phi(alpha), can be harmonically inverted to yield a complete description of the syste m dynamics in terms of the spectral parameters. In particular, all S-m atrix elements can be obtained in such a way. Compared to the conventi onal way of spectral analysis, when only a column of the S-matrix is e xtracted from a single wave packet propagation, this approach leads to a significant, numerical saving especially for resonance dominated mu ltichannel scattering. The second application of FDM is based on the;h armonic inversion of semiclassically computed time cross-correlation m atrices. The main assumption is that for a not-too-long time semiclass ical propagator can be approximated by an effective quantum one, exp[- i (H) over cap(eff)]. The adequate dynamical information can be extrac ted from an LxL short-time cross-correlation matrix whose informationa l content is by about a factor of L larger than that of a single time correlation function. (C) 1998 American Institute of Physics.