Multidimensional Quantum Trajectory Dynamics in Imaginary Time with Approximate Quantum Potential

The quantum trajectory dynamics in imaginary time with the momentum-dependent quantum potential [J. Chem. Phys. 2010, 132, 014112], which can be used for calculations of low-lying energy eigenstates or for Boltzmann evolution, is extended to many dimensions. Evolution of a nodeless initial wave function represented in exponential form is described in terms of a trajectory ensemble. In the Lagrangian frame of reference the trajectories evolve according to the classical equations of motion under the influence of the inverted classical potential and the quantum potential defined by the gradient of the trajectory momenta. The initial wave function is sampled by the trajectories randomly, which makes the approach scalable to high dimensions. Another practical feature is approximate computation of the quantum potential and force from the global least squares fit of the trajectory momenta in a small basis. The importance sampling and the Eulerian frame-of-reference formulation, compensating for divergent dynamics in bound potentials, are introduced to reduce the number of trajectories in multidimensional applications. The zero-point energies are computed for model and chemical (H(2)O and SO(2)) systems.