This work on the photodynamics of trans-azobenzene demonstrated that, in CTTSH, the accuracy of the approximation of the nuclear density is crucial for a proper description of the quantum momentum and, consequently, for a correct account of decoherence effects in the electronic dynamics. Indeed, reconstructing the nuclear density for a polyatomic molecule is much more challenging than for a fewdimensional system. Therefore, we proposed four variants of the CTTSH method depending on the set of nuclear coordinates considered to construct the quantum momentum and depending on the approaches used to determine the widths of the Gaussian functions. The implementations of CTTSH can be summarized as follows: