Basis expansion leaping: A new method to solve the time-dependent schrödinger equation for molecular quantum dynamics

A wide variety of molecular systems that have recently come into the reach of experimental and theoretical investigation is dominated by quantum phenomena. However, even state of the art quantum propagation techniques are either unsuitable for general application to molecular systems with strong interference and tunneling characteristics or are computationally prohibitive for systems with more than a few degrees of freedom. In this Letter, we introduce a novel quantum propagation technique with wide applicability, controllable accuracy, and efficient utilization of computational resources. Its performance is validated for tunneling and dissociating systems with 1, 2, and 3 degrees of freedom, and the scaling behavior with respect to system dimensionality and requested accuracy is discussed.