The excited state dipole moments of betaine pyridinium investigated by an innovative solvatochromic analysis and TDDFT calculations

This work reports on the solvatochromic properties of a simple heterocyclic betaine pyridinium, 2-(1-pyridinio)benzimidazolate (SBPa), having promising potentialities in non-linear optics. From advanced PCM-TDDFT calculations, the solvatochromism of SBPa was found to be unusual, involving two different electronic states for absorption (S0 → S2) and emission (S1→S′0). To account for this behavior, we developed an innovative physical treatment which consists in a non-linear fit of the solvatochromic data using the Bilot–Kawski theoretical model and visualizing the least-square coefficient χ2 on a 2D map as a function of the solute polarizability and gas phase absorption energy. In parallel, Kamlet–Taft correlations were undertaken to select a propitious set of electrostatic solvents usable in this treatment. Protic solvents that lead to specific interactions and nonpolar solvents that favor dimerization processes were excluded. From a choice of aprotic solvents with sufficiently high polarity, 4 dipole moments μg(S0) = +9.1 D, μe(S2) = −1.5 D, μe(S1) = 0 D and μg(S′0) = +3.31 D were determined, the 3 former values being in close agreement with TDDFT values, although the solute polarizability values seem underestimated. Anyhow, disregarding this discrepancy, we evaluated the static hyperpolarizability to β(0) = −64 × 10−30 esu from the solvatochromic data in close agreement with DFT calculations.