Chemical asymmetry and α and β polarizabilities of D-A-D′ chromophores: a three-state-model and TDDFT-SOS analysis of a penta-heptamethine ketocyanine

Abstract

The essential-state model, here amounting to a three-state model, has been employed to account for the effects of chemical asymmetry on the electronic α and β polarizabilities of a penta-heptamethine ketocyanine (KC2,3), a prototypic D-A-D′ chromophore. A suitable model, based on the idea of a ‘chromophoric site’, has been set up in terms of the three-state model features previously derived for the parent symmetric pentamethine and heptamethine ketocyanines, KC2 and KC3. This approach has been found to reproduce very well the experimental transition energies and dipoles. From the resulting properties of the ground and two relevant lowest excited states, 〈α〉 and β_vec have been evaluated according to the SOS approach. The performances of the model have been tested by comparison with the results of TDDFT SOS (hyper) polarizability calculations considering up to twenty excited states. A detailed analysis of the results for the three ketocyanines has shown a rapid convergence of the SOS expansion that supports the reliability of descriptions based on a few low lying excited states (here corresponding to π → π* excitations). However, while only two excited states were necessary for the symmetric compounds, for KC2,3 a value of β_vec comparable with the converged value, as well as with that predicted by the experimentally-based three-state model, has been obtained including at least three excited states. Both the TDDFT SOS and the three-state model descriptions have emphasized the important role played by the three-level term contributions in the determination of β_vec. Moreover, both descriptions agree in predicting that KC2,3 features 〈α〉 and β_vec values in between those of KC2 and KC3.