Numerical Approach for Solving the Exact Factorization Equations of Motion

The Exact Factorization (EF) of the molecular wavefunction presents a compelling formalism to describe coupled electronic-nuclear motion in excited state molecules. However, efforts to numerically solve the EF equations of motion have been troubled by algorithmic instability due to the unique form the equations take. Here we present an effort toward a novel algorithm to numerically propagate the molecular wavefunction in the EF formalism. Focusing on a one-dimensional model of coupled harmonic oscillators we investigate the propagation of the nuclear and electronic wavefunctions using a Fourier expansion of the electronic population coefficients. We comment on the algorithmic implementation of this method and the computational scalability with a focus on expanding this work toward highly excited molecular dynamics.