Enthalpy and electrostriction in the electron-transfer reaction between triplet zinc uroporphyrin and ferricyanide

The electron-transfer reaction of triplet-state zinc uroporphyrin (ZnU) with ferricyanide ion, using pulsed, time-resolved photoacoustics, has a very large volume contraction of -35 +/- 2 Angstrom(3)/molecule and an enthalpy change of -1.5 +/- 0.15 eV/molecule. Via the known free energy of this reaction, -1.31 eV/molecule, the TDeltaS is -0.2 +/- 0.2 eV/molecule (T = 25 degreesC). The volume change is somewhat larger than that observed in bacterial reaction centers: the high charge of the ferri/ferrocyanides compensates for the much larger dielectric coefficient of water causing the electrostriction to be about the same. The classical Drude-Nernst equation predicts a volume change of about half the observed value. This failure for small or highly charged ions has been often noted in the literature. We partially account for this failure with a simple saturation function for the orientation polarization of the water dipoles in the electric field of the ions using the integral form of the Drude-Nernst equation. X-ray structural data show that the ions themselves do not change volume with change of charge. Electrochemical measurements show that the ferri- (+electron) to ferrocyanide reaction has a molar enthalpy of -1.15 +/- 0.1 eV and entropy (TDeltaS, T = 25 degreesC) of -0.65 +/- 0.15 eV at standard conditions versus the normal hydrogen electrode. Allowing for errors, we may assign the differences between the photoacoustic and electrochemical data to the ZnU --> ZnU+ (+electron) partial reaction. Its enthalpy is -0.35 +/- 0.2 eV and TDeltaS is +0.45 +/- 0.35 eV under the same condtions. Continuing in this manner, we can use the previously measured thermodynamic values for the triplet ZnU+ naphthoquinone-2-sulfonate (NQS) to obtain those for the partial reaction NQS (+electron) --> NQS(-). Its molar enthalpy is -0.75 +/- 0.3 eV and the TDeltaS is -0.7 +/- 0.4 eV. The entropy changes are clearly important contributions to the free energy. It is the unique ability of pulsed, time-resolved photoacoustics to easily obtain such thermodynamic data that renders it a most useful tool.