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 Å 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 T Δ S is −0.2 ± 0.2 eV/molecule ( T = 25 °C). 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 ( T Δ S, T = 25 °C) 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 T Δ S 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 T Δ S 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.