In comparison, the spectra in panels d), e) and f) show qualitatively similar peak profiles. Despite a significant percentage of the total hierarchy being terminated, the individual peaks have well resolved positions and have not been overbroadened. As demonstrated by 5 a) -c) regimes which are far into the overdamped limit tend to produce hugely overbroadened peaks with very minimal positional resolution -but this is not evident after secondary termination. In contrast, the peaks have clear Lorentzian character and additional peaks have become apparent, examples being at approximately (10 000, 11 750), (11 750, 10 000) and (11 750, 9 000) wavenumbers in fig. ). Therefore, the most significant virtual information is stored within the lowest tier ADOs. This gives clear indication that, in specific parameter regimes, it would be feasible and useful to truncate the hierarchy at different ADOs along different axes, thereby reducing its overall volume. Using the original termination criteria, equation 9, the hierarchy is a sealed volume which can only be reduced by decreasing Γ max resulting is a hierarchy of smaller volume, but similar shape. However, we propose that it may be possible to optimise the HEOM for specific cases by setting different lengths for each Matsubara axis. This could maximise the accuracy of the simulated spectra relative to the experimental spectra, while reducing the hierarchy volume and hence reducing the simulation time with minimal impact on the quality of the spectra The hierarchy reduction is demonstrated pictorially in fig. . FIG. : 2D electronic spectra for the IDR case before a) -c) and after d) -f) secondary termination at T = 0, 100, and 200 fs.