In the other approach, the required potential energy evaluations are carried out by calls to electronic structure calculations during the dynamics, thereby completely removing the need for a fitted PES. The big advantage of this direct dynamics approach, is that one is not limited by the availability of a fitted PES and the limitations in form of accuracy and domain it comes with. In classical molecular dynamics (MD) simulations, such an ab initio MD approach has long existed but is also known to be comparatively much more expensive than MD computations using fitted PESs or classical force fields. In the quantum dynamical context the problem is even more severe. In many quantum dynamical wave function computations integrals of the potential energy times the wave function or the basis set are needed. The numerical computation of such integrals would in a naive implementation lead to an extreme amount of SP evaluations and be intractable. This can be somewhat mitigated by using a wave function with basis sets consisting of evolving Gaussians that uses either classical-like equations of motion and/or approximations for integral evaluations, requiring only low-order derivative computations. This allows the individual Gaussians to be propagated forward in time using only local PES information obtained from single point calculations Variants of direct quantum dynamical methods has been developed and applied in different contexts. Still, the direct approach is inherently expensive.