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TNL theory. The dependence of the coherence life time on λ in case of TNL equations is not monotonous. 

As discussed in the Introduction, the secular TL equa- tion of motion yields an exact result for the dephasing of an isolated optical coherence [35]. One can show, by comparison of the absorption spectra calculated by secu- lar TL and TNL methods (see Fig. 3), that the TNL theory leads to certain artifacts (second peak) and is 

## B. Two-dimensional spectrum 

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therefore not suitable for the description of the optical coherence evolution. Consequently, on can only hope to obtain valid results for the evolution superoperators at the first and the third time interval of the third order re- sponse functions by the TL theories. In Ref. [40] it was shown that non-secular terms in the TL equations for op- tical coherences lead to temperature dependence of the positions of excitonic bands in absorption spectra. This dependence was shown to be strong when the electronic states involved are characterized by significantly different reorganization energy [34, 40]. Indeed it can be shown for homodimer that the non-secular terms are exactly zero in second order TL theory if the monomers exhibit the same reorganization energy [34]. We can therefore ex- pect the non-secular effects in the optical coherences to be weak in our case, and we choose secular TL to cal- culate the evolution superoperators in the first and third time interval of the response function, Eq. (40). 

Concerning the population interval, the situation is somewhat different. As we have shown above, the non- secular TL theory leads to dynamics that breaks the pos- itivity condition for the population probabilities at long times. At the same time, short time dynamics is very sim- 

