Variational transition state theory of vapor phase nucleation

An expression for the rate of vapor phase nucleation is developed that is based on variational transition state theory. The method depends on a definition of a dividing surface in phase space that separates reactants from products. For this surface we choose a spherical shell in coordinate space that is centered about the center of mass of a cluster of i molecules having an interior volume v. In a manner that is consistent with variational transition state theory, we vary v to minimize the reactive flux through our chosen dividing surface. The resulting expression for the rate constant involves a definition of a physical cluster that is consistent with previous developments in nucleation theory. In formulating the rate in this manner we obtain a new expression for the evaporation rate constant that is proportional to the derivative with respect to v of the Helmholtz free energy for cluster formation. In addition, we have a fundamentally justified procedure for selecting a unique volume v for each i cluster. Application of the method to the nucleation of water clusters will be presented.