The CTTSH algorithm was proposed with the aim to simultaneously tackle the issue of conservation of the classical energy in CTMQC and simplify the expression of the classical force (13) which requires the expensive calculation of the nonadiabatic coupling vectors. In CTTSH, while the electronic evolution equation is the same as the one used in CTMQC, namely Eq. ( ), the trajectories are evolved using adiabatic forces, i.e.