Among the trajectory-based methods derived from the molecular time-dependent Schrödinger equation are, for instance, the direct-dynamics variational multiconfigurational Gaussian (DD-vMCG) , ab initio multiple spawning (AIMS) , and ab initio multiple cloning (AIMC) . There, nuclear trajectories are evolved according to variationally-determined (DD-vMCG), or adiabatic (AIMS), or mean-field (AIMC with multiconfigurational Ehrenfest) forces, and are used to guide the basis functions appearing in the expansion of the molecular wavefunction. Electron-nuclear coupling is obtained by solving, alongside the trajectories, the quantum evolution equation for the expansion coefficients. In addition, spawning or cloning procedures aim to improve over time the sampling of the nuclear configuration space. An approximate solution of the molecular time-dependent Schrödinger equation can be obtained via quantum-classical approaches as well, like Ehrenfest dynamics and trajectory surface hopping (TSH) . The former is a mean-field method, where the classical nuclear force and the electron-nuclear coupling are given by averaging either over the electronic or over the nuclear time-dependent states of the system. The latter evolves classical trajectories according to adiabatic forces, and the electronic state of the system according to a Schrödinger equation where the nuclear trajectory appears as a time-dependent parameter. To account for nonadiabatic effects TSH is supplemented with a hopping procedure allowing the trajectories to change electronic state over time.