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ilar to the full TNL. Both theories predict population os- cillations during the life time of the electronic coherences. The full TNL equation, however, preserves positivity, at least for the parameters studied here, and can be there- fore used to calculate meaningful 2D spectra. For the same reason, both secular theories can also be success- fully used to calculate 2D spectrum. As the oscillation of the populations predicted by non-secular theories are too small to be reliably observed in 2D spectrum (only a small change of the crosspeak amplitude due to the pop- ulation transfer is observed after 140 fs of relaxation in 2D spectrum of Fig. 8 ) we expect only a small difference of the 2D spectrum to appear between the secular and full TNL theories. For the calculation of the representa- tive 2D spectrum we therefore choose the secular TL and the full TNL theories. These two differ from each other mainly in the prediction of the life time of the electronic coherences. The observable difference in the calculated 2D spectra should therefore predominantly result from the different life time of the electronic coherence. 

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Fig. 8 presents 2D spectra for λ = 30 cm − 1 and τ$_{c}$ = 100 fs. These parameters lead to a rather slow relaxation and consequently to narrow spectral peaks in both absorption (see Fig. 3) and 2D spectra. This allows us to clearly see characteristic T − dependent oscillations of the peaks in 2D spectrum. At T = 0 fs, both methods provide the same 2D spectrum, with four peaks. Two diagonal peaks arise when all three perturbations of the system by electric field occur on the same level, while two crosspeaks appear from interactions occurring on differ- 

