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 µ_g(S₀) = +9.1 D, µ_e(S₂) = -1.5 D, µ_e(S₁) = 0 D and µ_g(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.