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.