Quantum-Classical Liouville Approach to Molecular Dynamics

Sara Bonella, Giovanni Ciccotti, Raymond Kapral

Jörg Aichelin

Christof Schütte

In molecular dynamics applications there is a growing interest in mixed quantum-classical models. The quantum-classical Liouville equation (QCL) describes most atoms of the molecular system under consideration by means of a classical phase space density but an important, small portion of the system by means of quantum mechanics. The QCL is derived from the full quantum dynamical (QD) description by applying the Wigner transform to the \\classical part" of the system only. We discuss the conditions under which the QCL model approximates the full QD evolution of the system. First, analysis of the asymptotic properties of the Wigner transform shows that solving the QCL yields a rst order approximation of full quantum dynamics. Second, we discuss the adiabatic limit of the QCL. This discussion shows that the QCL solutions may be interpretated as classical phase space densities, at least near the adiabatic limit. Third, it is demonstrated that the QCL yields good approximations of non-adia...

Koji Ando

We implemented on GPU a mixed quantum-classical Liouville molecular dynamics simulation based on a momentum-jump-free theory. The trajectory spawning that was previously implemented on CPU for sampling enhancement was eliminated to avoid the overhead of thread divergence and dynamic memory allocation on the GPU. This achieved a speedup of an order of magnitude compared to the CPU computation with spawning, as well as a linear scaling with respect to the number of sampling trajectories.

Bradley P. Feuston

Arnaldo Donoso, Yujun Zheng, Craig C. Martens

In this paper, we describe a new method for simulating quantum processes using classical-like molecular dynamics. The approach is based on solving the quantum Liouville equation in the Wigner representation using ensembles of classical trajectories in phase space. The nonlocality of quantum mechanics is incorporated in the trajectory representation as nonclassical interactions between the members of the ensemble, leading to an entanglement of their evolution. The statistical independence of the individual trajectories making up an ensemble in the classical limit is lost when quantum effects are included, and the entire state of the system must be propagated as a unified whole. We develop the formalism and its numerical implementation, and illustrate its application on two model problems of quantum mechanical tunneling: escape from a metastable well and wave packet penetration of the Eckhart barrier.