PMC

Calculated effective temperatures (T*) for the sequential cluster ions as a function of water molecules lost (y) from the reduced clusters ([Cu(H₂O)_32−y]¹⁺ and [Os(NH₃)₆(H₂O)_55−y]²⁺).

Sequential binding enthalpies (ΔH_n,n−1) calculated as a function of cluster size for hydrated Cu⁺ and M²⁺ using the Thomson liquid drop model and parameters for bulk water at 298 K. Dashed line indicates the bulk heat of vaporization of liquid water (ΔH_bulk). Cluster sizes relevant to this study are indicated.

Energy level diagram of the ionization and reduction of a hydrated metal cluster cation, with a hydration number of n, in the gas phase. The adiabatic ionization energy (AIE), vertical ionization energy (VIE), vertical reduction energy (VRE), recombination energy (RE), and the solvent reorganization energies of the z+ and (z − 1)+ clusters (λ_z+ and λ_(z−1)+, respectively) are shown.

Absolute solution-phase ΔG values for the [M(NH₃)₆]^3+/2+, M = Ru, Co, Os, Cr, and Ir, and Cu^2+/1+, couples obtained from gas-phase nanodrop measurements versus the corresponding relative solution-phase values. The solid line is a linear regression fit with a slope of 1.4 and y-intercept of −4.2 eV or +4.2 V. The y-axis (dashed line) intercept corresponds to the absolute SHE versus a free electron. Error bars reflect a select range of reported solution-phase values and estimates of the uncertainty in the gas-phase measurements.

Product ion mass spectra resulting from EC by [M(NH₃)₆(H₂O)₅₅]³⁺, M = Ru, Co, Os, Cr, and Ir, to form [M(NH₃)₆(H₂O)_n−y]²⁺ + yH₂O. Spectra are aligned by the number of water molecules lost from the reduced precursor ions. Insets are theoretical isotope distributions calculated for the most abundant product ion. Fragment ions corresponding to the loss of one or two ammonia molecules in addition to water molecule loss overlap in m/z with the isotopic contribution from the all water loss dissociation channel.

The reduction energies of these gas-phase nanodrops can be related to bulk solution-phase reduction energies by the thermodynamic cycle shown in , where ΔH_solv is the Born enthalpy associated with solvating a droplet with n water molecules and nominal charge z into bulk solution. A modified Born equation () is used to obtain the free energy of solvation, ΔG_solv, of the product and reactant charged nanodrops (5) where ze is the charge, n is the number of water molecules, R_s is the size-exclusion radius of a water molecule, ∊_o is the vacuum permittivity, and ∊ is the dielectric constant of the solvent, a_am and a_i are factors that relate the size of an ammonia molecule and a metal ion, respectively, to that of a water molecule. The differential of the negative of with respect to temperature is used to estimate the entropy of solvation () (6) and is combined with the free energy of solvation at 298 K to obtain the enthalpy of solvation at this temperature. The enthalpic AEA is omitted in our subsequent analysis and the solution-phase reduction potentials are referenced to a gas-phase electron. Values of the enthalpic AEA have been reported;,, the absolute half-cell potential could be referenced to a solvated electron by including this term.

Ion-electron recombination, depicted in , results in an activated reduced species (Pathway III) from which water molecule loss occurs (Pathway V). If this process occurs without heat exchange with the surroundings, that is, the process is adiabatic, ΔU(III) and ΔU(V) = 0. In these experiments, the pressure is ∼1 × 10⁻⁸ Torr so that effects of collisions on the sub 40.4 ms time frame should be negligible. In addition, effects of radiative cooling should also be minimal both because of the short time frame and because of the fast evaporative cooling by weakly bound water molecules. The energy corresponding to Pathway IV is equivalent to the combined sum of the E₀ values for each water molecule lost and the energy partitioned into the translational, rotational, and vibrational modes of each water molecule via Pathway II. This quantity is the RE and ΔU(I) = −RE and ΔU(II) = RE. Thus, if the energetics for water molecule loss from the activated reduced precursor are known, the adiabatic ionization energy of the reduced cluster may be obtained (Pathway I) as well as the ionization enthalpy at 298 K from (1) in which the change in constant pressure heat capacities is integrated over the temperature range 0–298 K.