Microsolvation of Hot Ions: Spectroscopy and Statistical Mechanics of Phenide-Water Interactions

Thermal excitation alters the spectroscopic signatures of solvated ions and affects their interactions with neighboring molecules. By analyzing the photoelectron spectra of microhydrated phenide (Ph^-), the temperatures of the Ph^-·H₂O and Ph^-·(H₂O)₂ clusters from a hot ion source were determined to be 560 and 520 K, respectively, vs 700 K for unsolvated Ph^-. Compared to theory predictions for cold clusters, the high temperature of the environment significantly reduces the average hydration stabilization of the ions and the corresponding band shifts in their spectra. The results are discussed in terms of a statistical model that describes the energy content of the intermolecular (IM) degrees of freedom of the cluster, ⟨E_IM⟩. We show that over the entire solvation energy range, the density of states associated with the IM modes of Ph^-·H₂O, of which there are only 6, is more than an order of magnitude greater than that associated with the 27 internal vibrations of the core anion. The results suggest that the observed cluster temperatures are not determined by the ion source but represent the intrinsic properties of the clusters. The energetics and statistical mechanics of microsolvation limit the excitation that the IM degrees of freedom can sustain without significant solvent evaporation on the timescale of the experiment. The limit is expressed as a characteristic solvation temperature (CST), which is the maximum canonical temperature of a stable cluster ensemble. Driven by evaporative cooling, the terminal cluster temperature from a hot ion source will always be close to the cluster's CST. Only if the source temperature is lower than CST will the observed cluster temperature be determined by the source conditions. An approximate rule is proposed for estimating the characteristic temperature of any cluster using the inflection point on the ⟨E_IM⟩ vs T curve.