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Marcus treatment of endergonic reactions: a commentary.

ABSTRACT: Two forms of the equation for expression of the rate constant for electron transfer through a Marcus-type treatment are discussed. In the first (exergonic) form, the Arrhenius exponential term was replaced by its classical Marcus term; in the second (endergonic) form, the forward rate constant was replaced by the reverse rate constant (the forward rate constant in the exergonic direction), which was expanded to an equivalent Marcus term and multiplied by the equilibrium constant. When the classical Marcus treatment was used, these two forms of the rate equation give identical curves relating the logarithm of the rate constant to the driving force. The Marcus term for the relation between activation free-energy, DeltaG#, reorganization energy, lambda, and driving force, DeltaG(o), derived from parabolas for the reactant and product states, was identical when starting from exergonic or endergonic parabolas. Moser and colleagues introduced a quantum mechanical correction factor to the Marcus term in order to fit experimental data. When the same correction factor was applied in the treatment for the endergonic direction by Page and colleagues, a different curve was obtained from that found with the exergonic form. We show that the difference resulted from an algebraic error in development of the endergonic equation.

SUBMITTER: Crofts AR

PROVIDER: S-EPMC2238675 | biostudies-literature | 2007 Oct

REPOSITORIES: biostudies-literature

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Marcus treatment of endergonic reactions: a commentary.

Crofts Antony R AR Rose Stuart S

Biochimica et biophysica acta 20070706 10

Two forms of the equation for expression of the rate constant for electron transfer through a Marcus-type treatment are discussed. In the first (exergonic) form, the Arrhenius exponential term was replaced by its classical Marcus term; in the second (endergonic) form, the forward rate constant was replaced by the reverse rate constant (the forward rate constant in the exergonic direction), which was expanded to an equivalent Marcus term and multiplied by the equilibrium constant. When the classi ...[more]

PMID: 17720135

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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 (ΔG(o)'). Plots of log(k(CPET)) vs ΔG(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 λ(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 λ and larger pre-exponential terms. The implications of these results for MS-CPET reactions are discussed.

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Marcus treatment of endergonic reactions: a commentary.

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Marcus treatment of endergonic reactions: a commentary.

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