The solvatochromic dye betaine-30 is thermochromic as well, due to the temperature dependence of solvent polarity, which strongly influences the wavelength of the visible absorption band. We report an analysis of the temperature-dependent absorption spectrum of betaine-30 in CH 3 CN, incorporating the internal-mode displacements determined from the resonance Raman profiles at room temperature. The temperature-dependent solvent reorganization energy λ solv associated with the visible transition of betaine-30 influences the width and position of the absorption spectrum and is relevant to theories for the rate of return electron transfer. We have previously determined λ solv for betaine-30 in acetonitrile and deuterated acetonitrile from analysis of the room-temperature absorption and resonance Raman profiles using time-dependent spectroscopy theory. In this work, we present a revised set of normal-mode displacements, including the contribution from a torsional mode of betaine-30 at 133 cm -1 , obtained from an analysis of the room-temperature Raman profiles in CH 3 -CN and CD 3 CN. These displacements are then kept fixed, and the temperature-dependent absorption spectrum of betaine-30 in acetonitrile is modeled to obtain the solvent reorganization energy, 0-0 energy, and transition moment as a function of temperature. The solvent reorganization energy λ solv is found to decrease with increasing temperature, consistent with decreasing solvent polarity but opposite to the prediction of dielectric continuum theory. In contrast to our previous analysis, the nonlinear solvent response is included in the model, and the amplitude of the solvent response is found to be smaller in the excited than the ground electronic state, due to the decrease in solute dipole moment in the excited electronic state.

The solvatochromic properties of phenol blue [N-(4-dimethylaminophenyl)-1,4-benzoquinoneimine] have been investigated in polar and nonpolar solvents using variable-temperature 1 H NMR and electronic absorption spectroscopy. In acetonitrile, chloroform, and cyclohexane, protons on the quinoneimine ring are inequivalent at all temperatures, while in methanol an exchange process increasingly broadens the signals from these protons as the temperature is raised. The temperature-dependent absorption spectrum of phenol blue in methanol, acetonitrile, chloroform, and cyclohexane is reported, and the observed increase in peak frequency and bandwidth with temperature is found to exceed the predictions of continuum theory. The large increase in dipole moment on excitation results in a strong inductive contribution to the solvatochromism, and leads to large thermochromic shifts even in nonpolar solvents. The possible contributions of solvent-dependent electronic structure, low-frequency intramolecular vibrations, and conformational flexibility to the thermosolvatochromic properties of phenol blue are discussed. Evidence is presented for solvent dependence of the dipole difference µ eµ g between the ground and excited electronic states.

Resonance Raman profiles for 14 vibrational modes of betaine-30 in ethanol at room temperature were measured at wavelengths within the first charge-transfer absorption band. The absorption spectrum and resonance Raman profiles were analyzed using time-dependent theory and a Brownian oscillator model modified to account for nonlinear solvent response; i.e., dependence of the solvent reorganization energy on the electronic state of the solute. As in our previous study of betaine-30 in acetonitrile, the solvent reorganization energy for the excited electronic state, determined from resonance Raman spectroscopy, was found to be smaller than that for the ground electronic state, determined from the absorption spectrum. The mode-dependent internal reorganization energies of betaine-30 in ethanol were found to be slightly larger than those of betaine-30 in acetonitrile. Temperature-dependent solvent reorganization energies for the ground electronic state were determined from analysis of the absorption line shape from 279 to 332 K and were found to decrease with increasing temperature. The influence of hydrogen bonding on the solvent and internal reorganization energy of betaine-30 is considered, and the physical basis for nonlinear solvent response is discussed.

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The influence of solvent dynamics on optical spectra is often described by a stochastic model which assumes exponential relaxation of the time-correlation function for solvent-induced frequency fluctuations. In contrast, theory and experiment suggest that the initial (subpicosecond) phase of solvent relaxation, resulting from inertial motion of the solvent, is a Gaussian function of time. In this work, we employ numerical and analytical calculations to compare the predicted absorption line shapes and the derived solvent reorganization energies obtained from exponential (Brownian oscillator) versus Gaussian (inertial) solvent dynamics. Both models predict motional narrowing as the ratio kappa = Lambda/Delta is increased, where Lambda and Delta are the frequency and variance, respectively, of the solvent-induced frequency fluctuations. However, the motional narrowing limit is achieved at lower values of kappa for the Brownian oscillator model compared to the inertial model. For a given line shape, the derived value of the solvent reorganization energy lambdasolv is only weakly dependent on the solvent relaxation model employed, though different solvent parameters Lambda and Delta are obtained. The two models are applied to the analysis of the temperature-dependent absorption spectrum of beta-carotene in isopentane and CS2. The derived values of lambdasolv using the Gaussian model are found to be in better agreement with the high temperature limit of Delta2/2kBT than are the values obtained using the Brownian oscillator model. In either approach, the solvent reorganization energy is found to increase slightly with temperature as a result of an increase in the variance Delta of the solvent-induced frequency fluctuations.