Horenko, I. and Salzmann, Ch. and Schmidt, B. and Schütte, Ch. (2002) QuantumClassical Liouville Approach to Molecular Dynamics: Surface Hopping Gaussian PhaseSpace Packets. J. Chem. Phys., 117 (24). pp. 1107511088.

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Official URL: http://dx.doi.org/10.1063/1.1522712
Abstract
In mixed quantumclassical molecular dynamics few but important degrees of freedom of a molecular system are modeled quantummechanically 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 Liouvillevon Neumann equation. The resulting adiabatic quantumclassical 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 quantummechanical subsystem. Exchange of densities and coherences reflecting nonadiabatic effects in quantumclassical 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 phasespace packets (GPPs) with variable width and with adjustable real or complex amplitudes, respectively. The dense sampling of phasespace offers two main advantages over other numerical schemes to solve the QCLE. First, it allows to perform a quantumclassical simulation employing a constant number of particles, i. e. the generation of new trajectories at each surface hop is avoided. Second, the effect of nonlocal operators in the exchange of densities and coherences can be treated without having to invoke the momentum jump approximation. For the example of a single avoided crossing we demonstrate that convergence towards fully quantummechanical dynamics is much faster for surface hopping GPPs than for trajectorybased methods. For dual avoided crossings the Gaussianbased dynamics correctly reproduces the quantummechanical result even when trajectorybased methods not accounting for the transport of coherences fail qualitatively.
Item Type:  Article 

Subjects:  Mathematical and Computer Sciences > Mathematics 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group 
ID Code:  75 
Deposited By:  Admin Administrator 
Deposited On:  03 Jan 2009 20:20 
Last Modified:  03 Mar 2017 14:39 
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