maximum and in terms of the band width (inhomogeneous broadening). There are small differences in fine structure, but, as we show below, these features become smoothed out when the sampling is increased. Thus, we conclude that for this system the core IE spectra are not sensitive to the differences between TIP3P and AIMD sampling of the equilibrium dynamics. The bottom panel of Fig. shows the convergence of the spectrum with respect to the number of snapshots. As one can see, while the band maximum and its width are captured by the simulation with 400 snapshots, the finer details continue to evolve and the spectrum converges only around 3,000 snapshots (although the remaining roughness remains visible). We note that the convergence can be accelerated when using more than one IEs, as we do in the simulations with larger QM sub-systems.