Harmonic inversion of time cross-correlation functions: The optimal way to perform quantum or semiclassical dynamics calculations

Abstract

We explore two new applications of the filter-diagonalization method (FDM) for harmonic inversion of time cross-correlation functions arising in various contexts in molecular dynamics calculations. We show that the Chebyshev cross-correlation functions ciα(n)=(Φα|Tn(Ĥ)Φi) obtained by propagation of a single initial wave packet Φi correlated with a set of final states Φα, can be harmonically inverted to yield a complete description of the system dynamics in terms of the spectral parameters. In particular, all S-matrix elements can be obtained in such a way. Compared to the conventional way of spectral analysis, when only a column of the S-matrix is extracted from a single wave packet propagation, this approach leads to a significant numerical saving especially for resonance dominated multichannel scattering. The second application of FDM is based on the harmonic inversion of semiclassically computed time cross-correlation matrices. The main assumption is that for a not-too-long time semiclassical propagator can be approximated by an effective quantum one, exp[−itĤeff]. The adequate dynamical information can be extracted from an L×L short-time cross-correlation matrix whose informational content is by about a factor of L larger than that of a single time correlation function.