However the functions are not completely identical. The autocorrelation function differs on the order of 10 -7 and the difference very slowly increases during the dynamics. The normalized Fourier transform also shows small deviations on the order of 10 -6 this primarily arises from very slight displacements of the maximum frequency. The most intense peak is at around 2.8 E h . These difference are to be expected as the PESs are not exactly identical, but obviously the numerical difference should be small for PESs converged in the two different manners. A difference plot between the TD-ADGA and reference results can be found in Fig. in SI.