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Reassessment of the Four-Point Approach to the Electron-Transfer Marcus-Hush Theory.

ABSTRACT: The Marcus-Hush theory has been successfully applied to describe and predict the activation barriers and hence the electron-transfer (ET) rates in several physicochemical and biological systems. This theory assumes that in the ET reaction, the geometry of the free Gibbs energy landscape is parabolic, with equal curvature near the local minimum for both reactants and products. In spite of its achievements, more realistic models have included the assumption of the two parabolas having not the same curvature. This situation is analyzed by the Nelsen's four-point method. As a benchmark to compare the Marcus-Hush approximation to a precise calculation of the excitation energy, we studied the non-ET process of the electronic excitation of the aluminum dimer that has two local minima (³?_g ^- and ³?_u electronic states) and allows to obtain analytically the Marcus-Hush nonsymmetric parameters. We appraise the ability of the Marcus-Hush formula to approximate the analytical results by using several averages of the two reorganization energies associated with the forward and backward transitions and analyze the error. It is observed that the geometric average minimizes the relative error and that the analytical case is recovered. The main results of this paper are obtained by the application of the Nelsen's four-point method to compute the reorganization energies of a large set of potential ?-conjugated molecules proposed for organic photovoltaic devices using the above-mentioned averages for the Marcus-Hush formula. The activation energies obtained with the geometric average are significantly larger for some donor-acceptor pairs in comparison with the previously employed arithmetic average, their differences being suitable for experimental testing.

SUBMITTER: Lopez-Estrada O

PROVIDER: S-EPMC6641260 | biostudies-literature | 2018 Feb

REPOSITORIES: biostudies-literature

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Reassessment of the Four-Point Approach to the Electron-Transfer Marcus-Hush Theory.

López-Estrada Omar O Laguna Humberto G HG Barrueta-Flores Cihuapilli C Amador-Bedolla Carlos C

ACS omega 20180221 2

The Marcus-Hush theory has been successfully applied to describe and predict the activation barriers and hence the electron-transfer (ET) rates in several physicochemical and biological systems. This theory assumes that in the ET reaction, the geometry of the free Gibbs energy landscape is parabolic, with equal curvature near the local minimum for both reactants and products. In spite of its achievements, more realistic models have included the assumption of the two parabolas having not the same ...[more]

PMID: 31458519

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Project description:Photo-oxidations of hydrogen-bonded phenols using excited-state polyarenes are described to derive fundamental understanding of multiple-site concerted proton-electron transfer reactions (MS-CPET). Experiments have examined phenol bases having -CPh(2)NH(2), -Py, and -CH(2)Py groups ortho to the phenol hydroxyl group and tert-butyl groups in the 4,6-positions for stability (HOAr-NH(2), HOAr-Py, and HOAr-CH(2)Py, respectively; Py = pyridyl; Ph = phenyl). The photo-oxidations proceed by intramolecular proton transfer from the phenol to the pendent base concerted with electron transfer to the excited polyarene. For comparison, 2,4,6-(t)Bu(3)C(6)H(2)OH, a phenol without a pendent base and tert-butyl groups in the 2,4,6-positions, has also been examined. Many of these bimolecular reactions are fast, with rate constants near the diffusion limit. Combining the photochemical k(CPET) values with those from prior thermal stopped-flow kinetic studies gives data sets for the oxidations of HOAr-NH(2) and HOAr-CH(2)Py that span over 10(7) in k(CPET) and nearly 0.9 eV in driving force (?G(o)'). Plots of log(k(CPET)) vs ?G(o)', including both excited-state anthracenes and ground state aminium radical cations, define a single Marcus parabola in each case. These two data sets are thus well described by semiclassical Marcus theory, providing a strong validation of the use of this theory for MS-CPET. The parabolas give ?(CPET) ? 1.15-1.2 eV and H(ab) ? 20-30 cm(-1). These experiments represent the most direct measurements of H(ab) for MS-CPET reactions to date. Although rate constants are available only up to the diffusion limit, the parabolas clearly peak well below the adiabatic limit of ca. 6 × 10(12) s(-1). Thus, this is a very clear demonstration that the reactions are nonadiabatic. The nonadiabatic character slows the reactions by a factor of ~45. Results for the oxidation of HOAr-Py, in which the phenol and base are conjugated, and for oxidation of 2,4,6-(t)Bu(3)C(6)H(2)OH, which lacks a base, show that both have substantially lower ? and larger pre-exponential terms. The implications of these results for MS-CPET reactions are discussed.

Project description:Concerted proton-coupled electron transfer (PCET) in the Marcus inverted region was recently demonstrated (Science 2019, 364, 471-475). Understanding the requirements for such reactivity is fundamentally important and holds promise as a design principle for solar energy conversion systems. Herein, we investigate the solvent polarity and temperature dependence of photoinduced proton-coupled charge separation (CS) and charge recombination (CR) in anthracene-phenol-pyridine triads: 1 (10-(4-hydroxy-3-(4-methylpyridin-2-yl)benzyl)anthracene-9-carbonitrile) and 2 (10-(4-hydroxy-3-(4-methoxypyridin-2-yl)benzyl)anthracene-9-carbonitrile). Both the CS and CR rate constants increased with increasing polarity in acetonitrile:n-butyronitrile mixtures. The kinetics were semi-quantitatively analyzed where changes in dielectric and refractive index, and thus consequently changes in driving force (-ΔG°) and reorganization energy (λ), were accounted for. The results were further validated by fitting the temperature dependence, from 180 to 298 K, in n-butyronitrile. The analyses support previous computational work where transitions to proton vibrational excited states dominate the CR reaction with a distinct activation free energy (ΔG*CR ∼ 140 meV). However, the solvent continuum model fails to accurately describe the changes in ΔG° and λ with temperature via changes in dielectric constant and refractive index. Satisfactory modeling was obtained using the results of a molecular solvent model [J. Phys. Chem. B 1999, 103, 9130-9140], which predicts that λ decreases with temperature, opposite to that of the continuum model. To further assess the solvent polarity control in the inverted region, the reactions were studied in toluene. Nonpolar solvents decrease both ΔG°CR and λ, slowing CR into the nanosecond time regime for 2 in toluene at 298 K. This demonstrates how PCET in the inverted region may be controlled to potentially use proton-coupled CS states for efficient solar fuel production and photoredox catalysis.

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Reassessment of the Four-Point Approach to the Electron-Transfer Marcus-Hush Theory.

Publications

Reassessment of the Four-Point Approach to the Electron-Transfer Marcus-Hush Theory.

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