Variational Dynamics of Multicomponent Wave Functions Represented in a Basis Driven by a Time-Dependent Gaussian...

Large-amplitude motion of multidimensional molecular systems comprised of light quantum and heavy nearly classical particles is often described in terms of time-dependent Gaussian basis functions. To keep the basis size low, their dynamics should adapt 'on-the-fly' to the evolving wave function, which ideally is accomplished by solving the equations of motion on the basis parameters derived from the time-dependent variation principle, minimizing the local-in-time propagation error. However, the variational equations of motion are known for challenging implementation due to singularities in the complete basis limit and due to the sensitivity of their dynamics to low-amplitude features of a wave function. At the same time, a single multidimensional Gaussian wavepacket─its parameters defined by a local quadratic expansion of the potential around the Gaussian center or through variational equations─is well-known to capture the dominant quantum effects on dynamics of the nuclei close to the classical regime while being physically interpretable and computationally efficient. In this paper, we examine time-dependent product bases consisting of the Gaussian ansatz representing the heavy-particle degrees of freedom multiplied by a basis in the light-particle degrees of freedom, with the basis functions coupled through the variationally defined parameters. Dynamics following from the Dirac-Frenkel, Lagrange and McLachlan time-dependent variation principles are analyzed and compared to the results of the corresponding bases driven by the classical and quantum trajectories for model systems and for the H₂⁺ system represented in the minimal electronic basis.