19th GAMM-Seminar Leipzig on
High-dimensional problems - Numerical treatment and applications

Max-Planck-Institute for Mathematics in the Sciences
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  19th GAMM-Seminar
January, 23th-25th, 2003
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  Abstract Illia Horenko, Fri, 14.00-14.25 Previous Contents Next  
  An explicit particle method for molecular dynamics: Quantum-Classical Liouville Equation
Illia Horenko (FU Berlin)

In mixed quantum-classical molecular dynamics few but important degrees of freedom of a molecular system are modeled quantum-mechanically while the remaining degrees of freedom are treated within the classical approximation. Such models can be systematically derived as a first order approximation to the partial Wigner transform of the quantum Liouville-von Neumann equation. The resulting adiabatic quantum-classical Liouville equation (QCLE) can be decomposed into three individual propagators by means of a Trotter splitting:

Phase oscillations of the coherences resulting from the time evolution of the quantum-mechanical subsystem. Exchange of densities and coherences reflecting non-adiabatic effects in quantum-classical dynamics. Classical Liouvillian transport of densities and coherences along adiabatic potential energy surfaces or arithmetic means thereof.

A novel stochastic implementation of the QCLE is proposed in the present work. In order to substantially improve the traditional algorithm based on surface hopping trajectories [J. C. Tully, J. Chem. Phys. 93 (2), 1061 (1990)], we model the evolution of densities and coherences by a set of surface hopping Gaussian phase-space packets (GPPs) with adjustable real or complex amplitudes, respectively.

Numerical examples for the non-adiabatic dynamics are shown.

Finally, the need for fully adaptive propagation scheme based on optimisation strategy is motivated.

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Last updated:
30.11.2004 Impressum
Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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