“…Then, the time evolution of the basis is not variational anymore, and the solution to the SE is not optimal but is still variational. This decoupling is often employed for the time evolution of TDBFs associated with nuclear degrees of freedom, represented by Gaussians − or coherent states − whose centers follow classical trajectories: for example, using Erhenfest ,, or Born–Oppenheimer trajectories. ,, We can also mention that solving the electronic SE in mixed quantum-classical dynamics, such as Ehrenfest or surface hopping, requires propagating the electronic wavefunction expanded on a set of Gaussian TDBFs that follow nuclear motion…”