Classical or quantum-classical Liouville equations of motion can be obtained as lowest order approximations from full quantum dynamics by means of a (partial) Wigner transform. In high di- mensionality these partial differential equations are preferentially solved by particle methods. In contrast to trajectory methods which are ubiquitous in molecular dynamics studies, smooth Gaussian particles offer the advantage of densely sampling phase space. Rothe methods can be used to control both temporal and spatial discretization errors on grounds of a global tolerance criterion. Time discretization is achieved by virtue of the implicit trapezoidal rule. The quality of the spatial approximation of phase-space distributions in terms of Gaussian packets is maximized while the numerical condition of the least-squares problem for the parameters of particles is minimized. The resulting dynamical scheme is fully adaptive both with respect to time and space.

I. Horenko, B. Schmidt, and Ch. Schütte

J. Chem. Phys. 117, 4643-4650 (2002)

I. Horenko, Ch. Salzmann, B. Schmidt, and Ch. Schütte

J. Chem. Phys. 117, 11075-11088 (2002)

I. Horenko and M.Weiser

J. Comp. Chem. 24, 1921-1929 (2003)

I. Horenko, M. Weiser, B. Schmidt, and Ch. Schütte

J. Chem. Phys. 120, 8913-8923 (2004)