Mass spectrometric and quantum chemical determination of proton water clustering equilibria

We report on the thermochemistry of proton hydration by water in the gas phase both experimentally using high-pressure mass spectrometry (HPMS) and theoretically using multilevel G3, G3B3, CBS-Q, CBS-QB3, CBS/QCI-APNO as well as density functional theory (DFT) calculations. Gas phase hydration enthalpies and entropies for protonated water cluster equilibria with up to 7 waters (i.e., n ⩽ 7H3O+·(H2O)n) were observed and exhibited non-monotonic behavior for successive hydration steps as well as enthalpy and entropy anomalies at higher cluster rank numbers. In particular, there is a significant jump in the stepwise enthalpies and entropies of cluster formation for n varying from 6 to 8. This behavior can be successfully interpreted using cluster geometries obtained from quantum chemical calculations by considering the number of additional hydrogen bonds formed at each hydration step and simultaneous weakening of ion–solvent interaction with increasing cluster size. The measured total hydration energy for the attachment of the first six water molecules around the hydronium ion was found to account for more than 60% of total bulk hydration free energy.