Inertial solvent dynamics and the analysis of spectral line shapes: Temperature-dependent absorption spectrum of β-carotene in nonpolar solvent

Abstract

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.

Ultrafast Fluctuations in PM6 Domains of Binary and Ternary Organic Photovoltaic Thin Films Probed with Two-Dimensional White-Light Spectroscopy

“…The other observation of interest is that the time scales ( τ ) for the frequency fluctuations scale inversely with the expected efficiency of the devices that are made from films of this type. The sub-100-fs time scale for all of the films measured here is consistent with the inertial component often seen in ultrafast measurements that measure dynamics and reflect the strength of the system-environment coupling. − For example, it has been commonly observed that dye molecules exhibit different line shape dynamics in solvents of different polarity. , Because of the similarity in time scales, we attribute the spectral diffusion observed here to similar forces. Indeed, the structures of other semiconducting polymers fluctuate on similar time scales.…”

“…59−63 For example, it has been commonly observed that dye molecules exhibit different line shape dynamics in solvents of different polarity. 64,65 Because of the similarity in time scales, we attribute the spectral diffusion observed here to similar forces. Indeed, the structures of other semiconducting polymers fluctuate on similar time scales.…”

Theory of Transition–Dipole Coupling in Dye-Sensitized Semiconductor Nanoparticles

“…As in our study of RA on TiO 2 , this work employed TiO 2 and ACOA concentrations such that there was an average of about 1 dye molecule per nanoparticle. The unshifted molecular energies E φ n and Franck–Condon factors used to simulate the spectrum of the free molecule were initially taken to be the same as those for β-carotene, for which the absorption spectrum has been simulated using three Franck–Condon active normal modes with frequencies 1525, 1155, and 1005 cm –1 and dimensionless displacements Δ k of 1.12, 0.95, and 0.65, respectively. The displacements were then optimized to better match the experimental free ACOA absorption spectrum, resulting in the final fitted values shown in Table .…”

Effect of solvent on absorption spectra of all-trans-β-carotene under high pressure

“…14 The linear dependence of 0-0 wavenumber on BP was obtained, but the slope ͑19 000 cm −1 ͒ is much smaller than the value ͑27 000 cm −1 ͒ obtained at room temperature under high pressure. 16 Although the molecular amount in the first solvation layer increases at low temperature, the inactive solvent motion weakens this effect and leads to a gentler BP dependence of 0-0 wavenumbers than that under high pressure at ambient temperature. 7 In fact, the dispersive force depends not only on the amount of solvent molecules in the first solvation layer but also on the extent of the solvent motion.…”

“…As light-harvesting molecules and photoprotective pigments, carotenoids play an important role in photosynthetic systems. 16 A general knowledge about the properties of carotenoids in solution is the prerequisite for understanding their functions in more complex natural and artificial systems. Andersson et al measured the absorption spectral shifts in various solvents and concluded that the major factor which determines the energy of the S 2 state relative to that of the ground state is the dispersive interactions of the carotenoids with the surrounding molecules.…”