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 (S(0)→ S(2)) and emission (S(1)→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 χ(2) 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)(S(0)) = +9.1 D, μ(e)(S(2)) = -1.5 D, μ(e)(S(1)) = 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.
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