We explore the kinetic processes that sustain equilibrium in a microscopic, finite system. This is accomplished by monitoring the spontaneous, time-dependent frequency evolution (the frequency autocorrelation) of a single OH oscillator, embedded in a water cluster held in a temperature-controlled ion trap. The measurements are carried out by applying two-color, infrared-infrared photodissociation mass spectrometry to the D3O+·(HDO)(D2O)19 isotopologue of the "magic number" protonated water cluster, H+·(H2O)21 The OH group can occupy any one of the five spectroscopically distinct sites in the distorted pentagonal dodecahedron cage structure. The OH frequency is observed to evolve over tens of milliseconds in the temperature range (90 to 120 K). Starting at 100 K, large "jumps" are observed between two OH frequencies separated by ∼300 cm-1, indicating migration of the OH group from the bound OH site at 3,350 cm-1 to the free position at 3,686 cm-1 Increasing the temperature to 110 K leads to partial interconversion among many sites. All sites are observed to interconvert at 120 K such that the distribution of the unique OH group among them adopts the form one would expect for a canonical ensemble. The spectral dynamics displayed by the clusters thus offer an unprecedented view into the molecular-level processes that drive spectral diffusion in an extended network of water molecules.
