Directly relating reduction energies of gaseous Eu(H2O)n(3+), n = 55-140, to aqueous solution: the absolute SHE potential and real proton solvation energy

An improved cluster pair correlation method for obtaining the absolute proton hydration energy and enthalpy evaluated with an expanded data set

An improved cluster pair correlation method that is based on the method originally introduced by Tuttle et al. ( Tuttle et al. J. Phys. Chem. A 2002 , 106 , 925 - 932 ) was developed and evaluated using a significantly larger data set than used previously. With this larger data set, values for the absolute proton hydration free energy of -259.3 and -265.0 kcal/mol were obtained using the original and improved method, respectively. The former value is ∼4.5 kcal/mol less negative than previously reported values obtained with the same method but with smaller data sets. The dependence of this value on data set size indicates that the uncertainty in the original method may be greater than previously realized. The improved method has the advantages of higher precision, and the effects of cluster size on the proton hydration free energy and enthalpy values can be more readily evaluated. Data for ions with extreme pK(a)s, many of which were included in previous estimates of the proton hydration free energy, were found to be unreliable and were eliminated from the extended data set. There is only a subtle effect of cluster size on the Gibbs free energy values, and within the limits of the approximation inherent in the cluster pair correlation method, the "best" value for the standard absolute proton hydration free energy obtained with this new method and larger data set is -263.4 kcal/mol (average for clusters with 4-6 water molecules). The absolute proton hydration enthalpy values decrease from -273.1 to -275.3 kcal/mol with increasing cluster size (one to six water molecules, respectively). This trend, along with an anomalously high value for the absolute proton hydration entropy, indicates that the enthalpy obtained with this method may not have converged for these relatively small clusters.

Average sequential water molecule binding enthalpies of M(H2O)(19-124)2+ (M = Co, Fe, Mn, and Cu) measured with ultraviolet photodissociation at 193 and 248 nm

The average sequential water molecule binding enthalpies to large water clusters (between 19 and 124 water molecules) containing divalent ions were obtained by measuring the average number of water molecules lost upon absorption of an UV photon (193 or 248 nm) and using a statistical model to account for the energy released into translations, rotations, and vibrations of the products. These values agree well with the trend established by more conventional methods for obtaining sequential binding enthalpies to much smaller hydrated divalent ions. The average binding enthalpies decrease to a value of ~10.4 kcal/mol for n > ~40 and are insensitive to the ion identity at large cluster size. This value is close to that of the bulk heat of vaporization of water (10.6 kcal/mol) and indicates that the structure of water in these clusters may more closely resemble that of bulk liquid water than ice, owing either to a freezing point depression or rapid evaporative cooling and kinetic trapping of the initial liquid droplet. A discrete implementation of the Thomson equation using parameters for liquid water at 0 °C generally fits the trend in these data but provides values that are ~0.5 kcal/mol too low.

Absolute potential of the standard hydrogen electrode and the problem of interconversion of potentials in different solvents

The absolute potential of the standard hydrogen electrode, SHE, was calculated on the basis of a thermodynamic cycle involving H(2(g)) atomization, ionization of H((g))* to H((g))(+), and hydration of H(+). The most up-to-date literature values on the free energies of these reactions have been selected and, when necessary, adjusted to the electron convention Fermi-Dirac statistics since both e(-) and H(+) are fermions. As a reference state for the electron, we have chosen the electron at 0 K, which is the one used in computational chemistry. Unlike almost all previous estimations of SHE, DeltaG(aq)(theta)(H(+)) was used instead of the real potential, alpha(aq)(H(+)). This choice was made to obtain a SHE value based on the chemical potential, which is the appropriate reference to be used in theoretical computations of standard reduction potentials. The result of this new estimation is a value of 4.281 V for the absolute potential of SHE. The problem of conversion of standard reduction potentials (SRPs) measured or estimated in water to the corresponding values in nonaqueous solvents has also been addressed. In fact, thermochemical cycles are often used to calculate SRPs in water versus SHE, and it is extremely important to have conversion factors enabling estimation of SRPs in nonaqueous solvents. A general equation relating E(theta) of a generic redox couple in water versus the SHE to the value of E(theta) in an organic solvent versus the aqueous saturated calomel electrode is reported.

"Weighing" photon energies with mass spectrometry: effects of water on ion fluorescence

We report a new, highly sensitive method for indirectly measuring fluorescence from ions with a discrete number of water molecules attached. Absorption of a 248 nm photon by hydrated protonated proflavine, PH(+)(H(2)O)(n) (n = 13-50), results in two resolved product ion distributions that correspond to full internal conversion of the photon energy (loss of approximately 11 water molecules) and to partial internal conversion of the photon energy and emission of a lower energy photon (loss of approximately 6 water molecules). In addition to fluorescence, a long-lived triplet state with a half-life of approximately 0.5 s (for n = 50) is formed. The energy of the emitted photon can be obtained from the number of water molecules lost from the precursor to form each distribution. The photon energies generally red shift from approximately 450 to 580 nm with increasing cluster size (the onset of the PH(+)(aq) fluorescence spectrum is 600 nm and the maximum is 518 nm) consistent with preferential stabilization of the first excited singlet state versus the ground state. The fluorescence quantum yield of PH(+)(H(2)O)(n) for n > or = 30 is 0.36 +/- 0.02, the same as that in bulk solution, and increases dramatically with decreasing cluster sizes, due to less efficient conversion of electronic-to-vibrational energy. The high sensitivity of this method should make it possible to perform Forster resonance energy transfer experiments with gas-phase biomolecules in a microsolvated environment to investigate how a controlled number of water molecules facilitates dynamical motions in proteins or other molecules of interest.

Measuring internal energy deposition in collisional activation using hydrated ion nanocalorimetry to obtain peptide dissociation energies and entropies

The internal energy deposited in both on- and off-resonance collisional activation in Fourier transform ion cyclotron resonance mass spectrometry is measured with ion nanocalorimetry and is used to obtain information about the dissociation energy and entropy of a protonated peptide. Activation of Na(+)(H(2)O)(30) results in sequential loss of water molecules, and the internal energy of the activated ion can be obtained from the abundances of the product ions. Information about internal energy deposition in on-resonance collisional activation of protonated peptides is inferred from dissociation data obtained under identical conditions for hydrated ions that have similar m/z and degrees-of-freedom. From experimental internal energy deposition curves and Rice-Ramsperger-Kassel-Marcus (RRKM) theory, dissociation data as a function of collision energy for protonated leucine enkephalin, which has a comparable m/z and degrees-of-freedom as Na(+)(H(2)O)(30), are modeled. The threshold dissociation energies and entropies are correlated for data acquired at a single time point, resulting in a relatively wide range of threshold dissociation energies (1.1 to 1.7 eV) that can fit these data. However, this range of values could be significantly reduced by fitting data acquired at different dissociation times. By measuring the internal energy of an activated ion, the number of fitting parameters necessary to obtain information about the dissociation parameters by modeling these data is reduced and could result in improved accuracy for such methods.

Measuring the extent and width of internal energy deposition in ion activation using nanocalorimetry

The recombination energies resulting from electron capture by a positive ion can be accurately measured using hydrated ion nanocalorimetry in which the internal energy deposition is obtained from the number of water molecules lost from the reduced cluster. The width of the product ion distribution in these experiments is predominantly attributable to the distribution of energy that partitions into the translational and rotational modes of the water molecules that are lost. These results are consistent with a singular value for the recombination energy. For large clusters, the width of the energy distribution is consistent with rapid energy partitioning into internal vibrational modes. For some smaller clusters with high recombination energies, the measured product ion distribution is narrower than that calculated with a statistical model. These results indicate that initial water molecule loss occurs on the time scale of, or faster than energy randomization. This could be due to inherently slow internal conversion or it could be due to a multi-step process, such as initial ion-electron pair formation followed by reduction of the ion in the cluster. These results provide additional evidence for the accuracy with which condensed phase thermochemical values can be deduced from gaseous nanocalorimetry experiments.