Performance of fourth and sixth‐order commutator‐free Magnus expansion integrators for Ehrenfest dynamics

"Performance of fourth and sixth-order commutator-free Magnus expansion integrators for Ehrenfest Dynamics", Adrián Gómez Pueyo, Sergio Blanes, and Alberto Castro, Computational and Mathematical Methods, 2020

Hybrid quantum‐classical systems combine both classical and quantum degrees of freedom. Typically, in Chemistry, Molecular Physics, or Materials Science, the classical degrees of freedom describe atomic nuclei (or cations with frozen core electrons), whereas the quantum particles are the electrons. Although many possible hybrid dynamical models exist, the basic one is the so‐called Ehrenfest dynamics that results from the straightforward partial classical limit applied to the full quantum Schrödinger equation. Few numerical methods have been developed specifically for the integration of this type of systems. Here we present a preliminary study of the performance of a family of recently developed propagators: the (quasi) commutator‐free Magnus expansions. These methods, however, were initially designed for nonautonomous linear equations. We employ them for the nonlinear Ehrenfest system, by approximating the state value at each time step in the propagation, using an extrapolation from previous time steps.