In a nutshell, the CT-TSH algorithm is a variation of the TSH method that includes an extra term, Ċα m,ct , in the electronic coefficients' propagations. This term depends on the accumulated adiabatic forces and quantum momentum. The latter is computed from the nuclear density, which is a fundamental quantum mechanical quantity that cannot be exactly calculated in CT-TSH. However, it can be reconstructed using a sum of Gaussians centered at the positions of the nuclear trajectories. The accuracy of the approximation of the nuclear density is crucial for a proper description of the quantum momentum and, consequently, for the propagation of electronic coefficients. It is worth noting that reconstructing the nuclear density for a polyatomic molecule is much more challenging than for a few-dimensional system (as the ones previously studied with CT-TSH). Hence, different flavours of CT-TSH are tested here to determine the most effective way to reconstruct this quantity and obtain reliable results.