An explicit particle method for molecular dynamics: QuantumClassical Liouville Equation
Illia Horenko (FU Berlin)
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 adjustable real
or complex amplitudes, respectively.
Numerical examples for the nonadiabatic dynamics are shown.
Finally, the need for fully adaptive propagation scheme based on
optimisation strategy is motivated.
