Electronic and vibronic contributions to two-photon absorption in donor-acceptor-donor squaraine chromophores

Many squaraines have been observed to exhibit two-photon absorption at transition energies close to those of the lowest energy one-photon electronic transitions. Here, the electronic and vibronic contributions to these low-energy two-photon absorptions are elucidated by performing correlated quantum-chemical calculations on model chromophores that differ in their terminal donor groups (diarylaminothienyl, indolenylidenemethyl, dimethylaminopolyenyl, or 4-(dimethylamino)phenylpolyenyl). For squaraines with diarylaminothienyl and dimethylaminopolyenyl donors and for the longer examples of 4-(dimethylamino)phenylpolyenyl donors, the calculated energies of the lowest two-photon active states approach those of the lowest energy one-photon active (1B(u)) states. This is consistent with the existence of purely electronic channels for low-energy two-photon absorption (TPA) in these types of chromophores. On the other hand, for all squaraines containing indolinylidenemethyl donors, the calculations indicate that there are no low-lying electronic states of appropriate symmetry for TPA. Actually, we find that the lowest energy TPA transitions can be explained through coupling of the one-photon absorption (OPA) active 1B(u) state with b(u) vibrational modes. Through implementation of Herzberg-Teller theory, we are able to identify the vibrational modes responsible for the low-energy TPA peak and to reproduce, at least qualitatively, the experimental TPA spectra of several squaraines of this type.