Calculated solvent reorganization entropies, free energies, and fluctuations of the energy gaps for intramolecular electron transfer and excitation of the solvatochromic dye B30

60 Years of Betaine 30─From Solvatochromic Discovery to Future Frontiers

Betaine-30 (B30) was reported by Karl Dimroth and Christian Reichardt et al. in 1963 as a solvatochromic probe that can be easily synthesized, shows good solubility, and remains stable in various organic solvents and solutions. Its strongly negatively solvatochromic behavior arises from differential solvation between its electronic ground and excited states, making it a valuable tool for assessing solvent polarity using the ET(30) polarity scale, also devised by Dimroth and Reichardt. In addition, advancements in femtosecond laser spectroscopy in the 1990s greatly improved the understanding of B30's relaxation dynamics following photoexcitation. In solvents capable of hydrogen bonding, such as alcohols, intermolecular hydrogen-bond rearrangement contributes to the multiple relaxation components observed. Since the 1990s, the applications of B30 have expanded beyond simple organic solvents to include complex solvent mixtures, such as electrolyte solutions for battery technologies and eutectic solvent mixtures. Given the growing importance of these complex solvent mixtures, B30 is becoming an increasingly valuable tool for studying previously unexplored solvation properties.

Entropy-Enthalpy Compensation in Electron-Transfer Processes

Solvent reorganization energies, free energies, and entropies are obtained for photoexcitation of three molecules that exhibit strong solvatochromism [Nile red, 5-(dimethylamino)-5'-nitro-2,2-bisthiophene, and Reichardt's dye B30] by measuring their optical absorption spectra at temperatures between 150 and 300 K in solvents with a range of polarities. Energies, free energies, and entropies of solvent reorganization are also obtained from computer simulations of three intramolecular electron-transfer reactions (charge separation and recombination in Zn-porphyrin-quinone cyclophane and charge transfer in a bis-biphenylandrostane radical anion). Entropy-enthalpy compensation in the solvent reorganization free energy for photoexcitation or electron transfer is found to be essentially complete (having nearly equal and opposite contributions from entropic and enthalpic effects) for all of the processes with solvent reorganization energies less than about 0.1 eV. Compensation becomes less complete as the reorganization energy becomes larger. A semiclassical treatment of the solvent reorganization entropy can rationalize these results.

Electron transfer in a crystalline cytochrome with four hemes

Diffusion of electrons over distances on the order of 100 μm has been observed in crystals of a small tetraheme cytochrome (STC) from Shewanella oneidensis [J. Huang et al. J. Am. Chem. Soc. 142, 10459-10467 (2020)]. Electron transfer between hemes in adjacent subunits of the crystal is slower and more strongly dependent on temperature than had been expected based on semiclassical electron-transfer theory. We here explore explanations for these findings by molecular-dynamics simulations of crystalline and monomeric STC. New procedures are developed for including time-dependent quantum mechanical energy differences in the gap between the energies of the reactant and product states and for evaluating fluctuations of the electronic-interaction matrix element that couples the two hemes. Rate constants for electron transfer are calculated from the time- and temperature-dependent energy gaps, coupling factors, and Franck-Condon-weighted densities of states using an expression with no freely adjustable parameters. Back reactions are considered, as are the effects of various protonation states of the carboxyl groups on the heme side chains. Interactions with water are found to dominate the fluctuations of the energy gap between the reactant and product states. The calculated rate constant for electron transfer from heme IV to heme Ib in a neighboring subunit at 300 K agrees well with the measured value. However, the calculated activation energy of the reaction in the crystal is considerably smaller than observed. We suggest two possible explanations for this discrepancy. The calculated rate constant for transfer from heme I to II within the same subunit of the crystal is about one-third that for monomeric STC in solution.

Temperature-dependent solvent reorganization entropies, free energies, and transition dipole strengths for the photoexcitation of Reichardt's dye B30

Absorption spectra of the solvatochromic dye 2,6-diphenyl-4-2,4,6-triphenyl-1-pyridinophenolate (B30) were measured in seven solvents of varying polarity over temperature ranging from each solvent's freezing point to 300 K. The excitation energies and their variances allowed calculations of the solvent reorganization energies, reorganization free energies and reorganization entropies as functions of temperature. The entropies of solvent packing around the chromophore are found to make major contributions to the reorganization free energies. The variances of the excitation energies depend only weakly on temperature, in disagreement with an expression that is often used for solvent reorganization free energies. Polar solvents reduce the transition dipole strength of B30's long-wavelength absorption band, probably because interactions with the solvent enhance the charge-transfer character of the transition. The dipole strength drops further at low temperatures.