A quantum statistical mechanical study of the enthalpy of formation of the water dimer

Monte Carlo simulations of quantum statistical mechanical properties using the Feynman path integral method were carried out over a temperature range from 50 to 400 K to study the energetics of the water dimer $(H2O)2.$ These results were then used to understand the relation between estimates of the enthalpy of formation obtained from recent ab initio electronic structure calculations and estimates of the enthalpy of formation deduced from experimental measurements of thermal conductivity, second virial coefficients and submillimeter spectroscopy. The full quantum mechanical and anharmonic theoretical results were compared to results obtained from classical mechanical simulation and those obtained from a quantum mechanical harmonic analysis. In performing the analysis for temperatures above 200 K, the definition of a water dimer becomes poorly defined as thermal activation leading to dissociation becomes more probable. The calculated enthalpy of the dimer is strongly dependent on the manner in which trapped and independent monomer species are defined. To address these issues we employ an energy threshold as a dividing surface to separate trapped dimers from those that eventually dissociate on the time scale of an experiment. Approximate quantum mechanical expressions that are consistent with an energy definition of the water dimer were introduced and used in the simulation. It is found that experimental observations are consistent with theoretical calculations once a characteristic time scale for the experimental technique is identified.