Horenko, I. and Weiser, M. and Schmidt, B. and Schütte, Ch. (2004) Fully Adaptive Propagation of the QuantumClassical Liouville Equation. J. Chem. Phys., 120 (19). pp. 89138923.

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Official URL: http://dx.doi.org/10.1063/1.1691015
Abstract
In mixed quantumclassical molecular dynamics few but important degrees of freedom of a dynamical system are modeled quantummechanically while the remaining ones are treated within the classical approximation. Rothe methods established in the theory of partial differential equations are used to control both temporal and spatial discretization errors on grounds of a global tolerance criterion. The trapezoidal rule for adaptive integration of Liouville dynamics (TRAIL) [I. Horenko and M. Weiser, J. Comput. Chem. 24, 1921 (2003)] has been extended to account for nonadiabatic effects in molecular dynamics described by the quantumclassical Liouville equation. In the context of particle methods, the quality of the spatial approximation of the phasespace distributions is maximized while the numerical condition of the leastsquares problem for the parameters of particles is minimized. The resulting dynamical scheme is based on a simultaneous propagation of moving particles (Gaussian and Dirac deltalike trajectories) in phase space employing a fully adaptive strategy to upgrade Dirac to Gaussian particles and, vice versa, downgrading Gaussians to Diraclike trajectories. This allows for the combination of MonteCarlobased strategies for the sampling of densities and coherences in multidimensional problems with deterministic treatment of nonadiabatic effects. Numerical examples demonstrate the application of the method to spinboson systems in different dimensionality. Nonadiabatic effects occuring at conical intersections are treated in the diabatic representation. By decreasing the global tolerance, the numerical solution obtained from the TRAIL scheme are shown to converge towards exact results.
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:  65 
Deposited By:  Admin Administrator 
Deposited On:  03 Jan 2009 20:20 
Last Modified:  03 Mar 2017 14:39 
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