Gregory K. Schenter

Understanding the sensitivity of nucleation kinetics: A case study on water

Small atomic or molecular clusters provide the bridge between vapor and liquid phases. Nucleation is a rare event process by which clusters of a new phase are produced. This process is inherently dynamic and as such the new phase cannot exist until an activation barrier is surmounted. Dynamical nucleation theory (DNT) utilizes variational transition state theory to provide a framework in which cluster evaporation and condensation rate constants can be determined directly. To date, the fundamental nature regarding the intrinsic instability of the kinetics of the nucleation process has eluded theoretical efforts. In this paper we present a sensitivity analysis of the homogeneous nucleation rate on kinetic parameters used in DNT. Moreover, several classical interaction potentials for water exist, most of which have been parametrized to reproduce some bulk properties of water at ambient conditions. Thus, an analysis was undertaken to explore what effects different water potentials have on the dynamical quanti...

Dynamical benchmarks of the nucleation kinetics of water

Recently a theory of vapor-to-liquid phase nucleation was developed based on the kinetics of cluster formation and decomposition. The new method used variational transition state theory (VTST) to obtain the evaporation and condensation rate constants needed in the kinetic model of nucleation. VTST provides a means to systematically improve estimates of rate constants involved in the nucleation process. In the current work, we perform dynamical simulations of the condensation process, estimating the effective reactive cross section using a definition of a cluster that is determined from VTST. These calculations allow us to characterize dynamical corrections to the VTST rate constants. We find that for water cluster sizes ranging from 10–40 waters, VTST estimates of the condensation and evaporation rate constants using a spherical dividing surface require dynamical corrections that are approximately a factor of two.

Dynamical nucleation theory: Calculation of condensation rate constants for small water clusters

In previous work we began the description of a molecular theory of homogeneous vapor-to-liquid nucleation based on the kinetics of cluster formation and decomposition. In this work we focused on a new theoretical approach to calculating rate constants for evaporation of molecules from clusters. In the present work, we present a molecular theory for calculating condensation rate constants that are consistent with the evaporation rate constants. The new method, which uses variational transition state theory (VTST), provides an expression for the evaporation rate constant that is proportional to the derivative of the Helmholtz free energy for cluster formation with respect to the radius of the spherical volume constraining the cluster. Furthermore, the theory provides a physically justified procedure for selecting a unique value of the radius of the spherical volume for each i-molecule cluster. Since VTST obeys detailed balance, condensation rate constants can be obtained from the evaporation rate constants ...

Quantum statistical mechanical simulation of the ion–water cluster I−(H2O)n: The importance of nuclear quantum effects and anharmonicity

Monte Carlo simulations of quantum statistical mechanical properties using the Feynman path integral method were carried out at temperatures of 70, 100, 200, and 300 K to study the structure and energetics of the ion–water cluster I−(H2O)n, with n=1–6. Simulation results at low temperatures (i.e., 70 K) can be directly compared with data from photoelectron spectroscopy (PES). The temperature dependence of binding enthalpies and stabilization energies indicate that at low temperatures the classical description of nuclear motion is qualitatively incorrect. The binding enthalpies are also computed within the harmonic approximation using the energy and frequencies at the minimum energy geometry, a method widely used in conjunction with electronic structure calculations to extend zero temperature information to finite temperatures. It is found that the harmonic approximation works well for the cluster with a single water molecule, but not for clusters with more than one water molecule, where the temperature de...

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 cluste...

The development of effective classical potentials and the quantum statistical mechanical second virial coefficient of water

The second virial coefficient of water is calculated at low temperature by considering full quantum statistical mechanical effects. At low enough temperatures experimental results are limited and molecular models can be used for accurate extrapolation. In doing so, one must separate deficiencies of the intermolecular potential from limitations of the simulation methodology such as the neglect of higher-order quantum corrections. Effective classical potentials may be used to understand the limitations of classical simulation. In this work we calculate the exact quantum statistical mechanical second virial coefficient and find that using a semiclassical form for the effective classical potential we are able to nearly reproduce the exact quantum statistical results. This approach provides a significant improvement to conventional first order expansions of the second virial coefficient.

A variational centroid density procedure for the calculation of transmission coefficients for asymmetric barriers at low temperature

The low temperature behavior of the centroid density method of Voth, Chandler, and Miller (VCM) [J. Chem. Phys. 91, 7749 (1989)] is investigated for tunneling through a one‐dimensional barrier. We find that the bottleneck for a quantum activated process as defined by VCM does not correspond to the classical bottleneck for the case of an asymmetric barrier. If the centroid density is constrained to be at the classical bottleneck for an asymmetric barrier, the centroid density method can give transmission coefficients that are too large by as much as five orders of magnitude. We follow a variational procedure, as suggested by VCM, whereby the best transmission coefficient is found by varying the position of the centroid until the minimum value for this transmission coefficient is obtained. This is a procedure that is readily generalizable to multidimensional systems. We present calculations on several test systems which show that this variational procedure greatly enhances the accuracy of the centroid densi...

The quantum vibrational dynamics of Cl−(H2O)n clusters

The centroid molecular dynamics technique is applied to the case of chloride–water clusters to estimate their finite temperature quantum vibrational structure. We employ the flexible RWK2 water potential [J. R. Reimers, R. O. Watts, and M. L. Klein, Chem. Phys. 64, 95 (1982)] and the parametrization of a chloride–water interaction potential of Dorsett, Watts and Xantheas [J. Phys. Chem. A 103, 3351 (1999)]. We then investigate the temperature-dependent vibrational structure (infrared spectra). We find that the centroid molecular dynamics technique is capable of recovering a majority of the red shift associated with hydrogen bonding.

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...

Classical and quantum mechanical studies of ice Ih near the melting temperature

Classical and path integral Monte Carlo methods have been used to study the structure and energetics of ice Ih. The water–water interaction is described by the SPC water model. We compute the change in average intermolecular potential energy, radial distribution function, and structural factor as a function of temperature. It is found that near 280 K, the structural and energetic properties from quantum and classical simulations are quite different.