Quantum dynamics using pseudo-particle trajectories: A new approach based on the multiconfiguration time-dependent Hartree method

Abstract

Quantum molecular-dynamics simulations are an important way of gaining information on the molecular level about chemical systems. In this paper, a new method for the approximate solution of the time-dependent Schrödinger equation is presented. This is a reformulation of the multiconfiguration time-dependent Hartree (MCTDH) wave packet propagation method, which is transformed so that the evolution of the wave function can be represented by pseudo-particle trajectories. In this way, the poor scaling of computational resources with system size attending all exact solutions of the time-dependent Schrödinger equation are circumvented. The equations of motion for the trajectories and the wave function expansion coefficients (importance of each trajectory for the representation) are derived using a variational principle. Other than the MCTDH ansatz, no major approximations have been introduced, and the method converges on the numerically exact solution. Importantly, the trajectories are not classical trajectories, and are coupled by nonlocal effects. A strategy for the practical solution of the equations of motion is then detailed.