Accurate determination and modeling of the dispersion of the first hyperpolarizability of an efficient zwitterionic nonlinear optical chromophore by tunable wavelength hyper-Rayleigh scattering

The wavelength-dependent molecular first hyperpolarizability beta of the zwitterionic nonlinear optical (NLO) chromophore picolinium quinodimethane (PQDM) is determined by hyper-Rayleigh scattering (HRS) and used to test and improve theoretical beta dispersion models. Experimental HRS data are obtained over a very wide fundamental wavelength range (780-1730 nm), spanning the entire range of two-photon resonance with the intramolecular charge-transfer (ICT) transition and reaching the onset of a higher energy resonance. Reliable calibration against the pure solvent (dimethylformamide, DMF, and DMF-d(7) at the longest wavelengths) was achieved over the full spectral range as a result of the high sensitivity of the HRS setup. Extremely high resonant beta values are obtained (up to 4560 x 10(-30) esu at 1360 nm) and also away from resonance beta remains very large (1210 x 10(-30) esu at 1730 nm). The two-photon resonance with the ICT band shows a pronounced red shift (similar to 33 nm in second-harmonic wavelength) relative to the absorption maximum. The various two-level beta dispersion models available in the literature are considered, and some important improvements are introduced. Furthermore, a vibronic model including a single vibrational mode and incorporating inhomogeneous broadening is developed and contrasted to the other extreme of a continuum of vibronic lines without inhomogeneous broadening. The red shift of the beta maximum can be largely explained by either an improved inhomogeneous broadening model or by vibronic coupling. However, the vibronic models are physically more realistic and lead to a better description of the observed beta dispersion. In general, models with more inhomogeneous broadening result in a narrower beta resonance, whereas incorporating more homogeneous broadening yields a broader resonance. Hence, the derived static electronic hyperpolarizability beta(0) depends very critically on the precise modeling of the broadening mechanisms. Upper and lower bounds to the true beta(0) are estimated from the two limiting vibronic models.