Quantum-chemical characterization of ion-pairing effect on the linear and third-order nonlinear optical response in cyanine dyes

Abstract

The impact of counterion hardness, solvent polarity, and chain length on the geometry, electronic structure, and static third-order polarizability 〈γ〉 of cyanine–counterion pairs [(CH3)2N-(CH)n-N(CH3)2···X] (n = 5, 9; X = Cl¯, Br¯, I¯, BF4¯, ClO4¯, and PF6¯) were analysed. A number of density functional theory (DFT) methodologies were employed in order to assess their impact on the geometrical and optical properties of these compounds, while the SAC-CI method has been used for the evaluation of the 〈γ〉 values; benchmark calculations of the geometries were also performed at the CCSD(T) and MP2 levels. We find that the preferred ion-pair geometry corresponds to the positioning of the counterion in the plane of the cyanine system. The degrees of bond-length alternation (BLA) obtained with the MP2 method and different DFT functionals when taking into account polar solvents are very small and decrease with increasing solvent polarity; also, moderate reductions in S0→S1 transition energies and increases in their corresponding transition dipole moments are found with higher solvent polarity. As a result, the 〈γ〉 values calculated for the cyanines considered here are found to change by less than one order of magnitude when going from toluene to acetonitrile, irrespective of the nature of the counterions.