Incorporation of quantum effects for selected degrees of freedom into the trajectory-based dynamics using spatial domains.

The approach of defining quantum corrections on nuclear dynamics of molecular systems incorporated approximately into selected degrees of freedom, is described. The approach is based on the Madelung-de-Broglie-Bohm formulation of time-dependent quantum mechanics which represents a wavefunction in terms of an ensemble of trajectories. The trajectories follow classical laws of motion except that the quantum potential, dependent on the wavefunction amplitude and its derivatives, is added to the external, classical potential. In this framework the quantum potential, determined approximately for practical reasons, is included only into the "quantum" degrees of freedom describing light particles such as protons, while neglecting with the quantum force for the heavy, nearly classical nuclei. The entire system comprised of light and heavy particles is described by a single wavefunction of full dimensionality. The coordinate space of heavy particles is divided into spatial domains or subspaces. The quantum force acting on the light particles is determined for each domain of similar configurations of the heavy nuclei. This approach effectively introduces parametric dependence of the reduced dimensionality quantum force, on classical degrees of freedom. This strategy improves accuracy of the quantum force and does not restrict interaction between the domains. The concept is illustrated for two-dimensional scattering systems, where the quantum force is required to reproduce vibrational energy of the quantum degree of freedom.