First-principles [density-functional theory (DFT)] molecular-dynamic simulations of the Berry pseudorotation mechanism in SF4 were performed using the atom-centered density-matrix propagation method. The reaction was monitored by following the chemical shieldings of the fluorine atoms, computed on snapshots along the trajectories. In particular we compared the results obtained using a standard functional based on the generalized gradient approximation with those issuing from its hybrid Hartree-Fock-DFT counterpart using a number of basis sets. Our results show that both the basis set and the functional choice rule the quality of the molecular properties monitored as well as the trajectory over the potential-energy surface.