Equilibrium Constant for Water Dimerization: Analysis of the Partition Function for a Weakly Bound System

Abstract

The treatment of dissociative states in the calculation of the partition function of a weakly bound system, such as the water dimer, is discussed. For a dissociative system, the number of phase-space configurations that contribute to the total partition function from energies above the dissociation energy depends on the system volume. For a sufficiently large system volume, entropy from these configurations will dominate over the energy contribution of the local minimum and contributions from dissociative states will dominate the total partition function. The calculation of the dimer partition function requires limiting the phase space of the cluster or providing a definition of those phase-space points that correspond to a dimer. Because there is no unique procedure to constrain the phase space of a dimer, we provide an analysis of the dimer partition function using a series of constraints. For the water dimer at temperatures in the range 200−500 K, the values of the dimer partition function change by over 2 orders of magnitude depending on the choice of the constraint.