^{1,a)}, J. Douady

^{2,b)}and F. Spiegelman

^{2}

### Abstract

Unimolecular evaporation of selected pure and heterogeneous water clusters containing a single hydronium or ammonium impurity is investigated in the framework of phase space theory (PST) in its orbiting transition state version. Using the many-body polarizable Kozack–Jordan potential and its extensions for and , the thermal evaporation of clusters containing 21 and 50 molecules is simulated at several total energies. Numerous molecular dynamics (MD) trajectories at high internal energies provide estimates of the decay rate constant, as well as the kinetic energy and angular momentum released upon dissociation. Additional Monte Carlo simulations are carried out to determine the anharmonic densities of vibrational states, which combined with suitable forms for the rotational densities of states provide expressions for the energy-resolved differential rates. Successful comparison between the MD results and the independent predictions of PST for the distributions of kinetic energy and angular momentum released shows that the latter statistical approach is quantitative. Using MD data as a reference, the absolute evaporation rates are calculated from PST over broad energy and temperature ranges. Based on these results, the presence of an ionic impurity is generally found to decrease the rate, however the effect is much more significant in the 21-molecule clusters. Our calculations also suggest that due to backbendings in the microcanonical densities of states the variations of the evaporation rates may not be strictly increasing with energy or temperature.

We thank GDR 2758 for financial support. Some calculations have been performed at the Pôle Scientifique de Modélisation Numérique, which we gratefully acknowledge.

I. INTRODUCTION

II. METHODS

A. Potentials

B. Evaporative trajectories

C. Phase space theory

D. Vibrational densities of states

III. ASSESSMENT OF THE STATISTICAL APPROACH FOR THERMAL EVAPORATION

IV. EVAPORATION RATES AND FINITE-TEMPERATURE PROPERTIES

A. Evaporation rates at fixed energy

B. Finite-temperature evaporation

C. Discussion

V. CONCLUDING REMARKS

### Key Topics

- Dissociation
- 29.0
- Dissociation energies
- 23.0
- Electron densities of states
- 21.0
- Monte Carlo methods
- 18.0
- Nucleation
- 16.0

## Figures

Lowest-energy structures obtained for selected water clusters with the polarizable KJ potential. Left: neutral 20-molecule cluster. Middle: protonated 21-molecule cluster. Right: 48-molecule cluster doped with one ammonium.

Lowest-energy structures obtained for selected water clusters with the polarizable KJ potential. Left: neutral 20-molecule cluster. Middle: protonated 21-molecule cluster. Right: 48-molecule cluster doped with one ammonium.

Relative number of MD trajectories having not yet evaporated one water molecule as a function of time. The symbols are the results of the simulations, while the solid lines are the exponential fits . Left panel: 21-molecule clusters at a same excess energy of . Right panel: the cluster at different excess energies.

Relative number of MD trajectories having not yet evaporated one water molecule as a function of time. The symbols are the results of the simulations, while the solid lines are the exponential fits . Left panel: 21-molecule clusters at a same excess energy of . Right panel: the cluster at different excess energies.

Total kinetic energy released distributions in the unimolecular evaporation of a water molecule from the (left) and (right) clusters at fixed excess energy. The symbols are the results from MD simulations, while the solid lines are predictions of PST.

Total kinetic energy released distributions in the unimolecular evaporation of a water molecule from the (left) and (right) clusters at fixed excess energy. The symbols are the results from MD simulations, while the solid lines are predictions of PST.

Distributions of the products angular momentum in the unimolecular evaporation of a water molecule from the (left) and (right) clusters at fixed excess energy. The symbols are the results from MD simulations, while the solid lines are predictions of PST.

Distributions of the products angular momentum in the unimolecular evaporation of a water molecule from the (left) and (right) clusters at fixed excess energy. The symbols are the results from MD simulations, while the solid lines are predictions of PST.

Average (total) kinetic energy released vs excess energy in the 21-molecule (upper panel) and 50-molecule (lower panel) clusters, as obtained from MD simulations (symbols) and from the predictions of PST (solid lines). The straight lines are the harmonic predictions for the pure water clusters (see text for details).

Average (total) kinetic energy released vs excess energy in the 21-molecule (upper panel) and 50-molecule (lower panel) clusters, as obtained from MD simulations (symbols) and from the predictions of PST (solid lines). The straight lines are the harmonic predictions for the pure water clusters (see text for details).

Average products angular momentum vs excess energy, as obtained from MD simulations (symbols) and from the predictions of PST (solid lines) for the 21-molecule (left panel) and 50-molecule (right panel) clusters, respectively.

Average products angular momentum vs excess energy, as obtained from MD simulations (symbols) and from the predictions of PST (solid lines) for the 21-molecule (left panel) and 50-molecule (right panel) clusters, respectively.

Absolute evaporation rate of 21-molecule water clusters as a function of excess energy, as obtained from MD simulations (symbols) and from the predictions of PST (solid lines) after calibration at internal energy. The inset highlights the energy range where trajectories have been performed.

Absolute evaporation rate of 21-molecule water clusters as a function of excess energy, as obtained from MD simulations (symbols) and from the predictions of PST (solid lines) after calibration at internal energy. The inset highlights the energy range where trajectories have been performed.

Absolute evaporation rate of 50-molecule water clusters as a function of excess energy, as obtained from MD simulations (symbols) and from the predictions of PST (solid lines) after calibration at internal energy. The inset highlights the energy range where trajectories have been performed.

Absolute evaporation rate of 50-molecule water clusters as a function of excess energy, as obtained from MD simulations (symbols) and from the predictions of PST (solid lines) after calibration at internal energy. The inset highlights the energy range where trajectories have been performed.

Average kinetic energy released in the unimolecular evaporation from 21-molecule (left) and 50-molecule (right) clusters, as a function of canonical temperature.

Average kinetic energy released in the unimolecular evaporation from 21-molecule (left) and 50-molecule (right) clusters, as a function of canonical temperature.

Absolute evaporation rate of 21-molecule water clusters as a function of canonical temperature, as predicted from PST.

Absolute evaporation rate of 21-molecule water clusters as a function of canonical temperature, as predicted from PST.

Absolute evaporation rate of 50-molecule water clusters as a function of canonical temperature, as predicted from PST.

Absolute evaporation rate of 50-molecule water clusters as a function of canonical temperature, as predicted from PST.

## Tables

Static ingredients used for the PST calculations: dissociation energies , product rotational constants , long-range interaction parameters ( for ion/neutral, for neutral/neutral dissociations), and mean square radius of the product cluster.

Static ingredients used for the PST calculations: dissociation energies , product rotational constants , long-range interaction parameters ( for ion/neutral, for neutral/neutral dissociations), and mean square radius of the product cluster.

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