We also consider 2D electronic spectroscopy for the FDR and SDR regimes. and) present spectra for the FDR case for 0, 100 and 200 fs. The peak position is obscured by the very large inhomogeneous broadening introduced by the fast vibrational mode that is subsumed into the environment. This broadening results in what appears to be a single large peak, although the intensity differences at ∼ (10 300, 10 300) cm -1 for a) and ∼ (10 300, 9 750) cm -1 for b) and c) suggest that there is a large Stokes shift in which vibrational character and population is relaxing into the ground state. Clearly a large number of terminators, relative to the total ADO number, is associated with a significant increase in inhomogeneous broadening. In contrast, in the UDR case, d), e) and f) the spectra have very precise positions and many cross-peaks are Even at low times the peaks are Lorentzian in shape, with a mix- ture of inhomogeneous and homogeneous broadening as a consequence of the underdamping of the modes being subsumed into the spectral density. This results in high positional precision and low broadening accuracy due to a low number of terminators and a more uniform spread of relative virtual BLP over all of the ADOs. From these results it is clear that there is some redundancy with the behaviour of individual auxiliaries along a specific Matsubara axis. For example in figure , we observe that above. We consider the termination of ADOs that posses similar character to others but with the smallest amount of virtual information content. That is those with higher ADO numbers within a Matsubara axis. Continuing the example of n 1 for n = {1, 2, 3, 4}, the new termination scheme would reduce this to n 1 for n = {1, 2} where n = {3, 4} would now become terminators. By canonically subsuming a pure intramolecular vibrational mode as an underamped vibration, additional damping is added to the model. This is referred to as canonically derived damping or canonical damping. The additional termination scheme based on this damping is therefore termed canonically derived/canonical termination.