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Exploring the importance of quantum effects in nucleation: The archetypical Ne_{ n } case

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10.1063/1.4730033

### Abstract

The effect of quantum mechanics (QM) on the details of the nucleation process is explored employing Ne clusters as test cases due to their semi-quantal nature. In particular, we investigate the impact of quantum mechanics on both condensation and dissociation rates in the framework of the microcanonical ensemble. Using both classical trajectories and two semi-quantal approaches (zero point averaged dynamics, ZPAD, and Gaussian-based time dependent Hartree, G-TDH) to model cluster and collision dynamics, we simulate the dissociation and monomer capture for Ne_{8} as a function of the cluster internal energy, impact parameter and collision speed. The results for the capture probability *P* _{ s }(*b*) as a function of the impact parameter suggest that classical trajectories always underestimate capture probabilities with respect to ZPAD, albeit at most by 15%–20% in the cases we studied. They also do so in some important situations when using G-TDH. More interestingly, dissociation rates *k* _{ diss } are grossly overestimated by classical mechanics, at least by one order of magnitude. We interpret both behaviours as mainly due to the reduced amount of kinetic energy available to a quantum cluster for a chosen total internal energy. We also find that the decrease in monomerdissociation energy due to zero point energyeffects plays a key role in defining dissociation rates. In fact, semi-quantal and classical results for *k* _{ diss } seem to follow a common “corresponding states” behaviour when the proper definition of internal and dissociation energies are used in a transition state model estimation of the evaporation rate constants.

© 2012 American Institute of Physics

Received 28 March 2012
Accepted 06 June 2012
Published online 02 July 2012

Acknowledgments: M.M. acknowledges the financial support provided by the “Rientro dei Cervelli” scheme funded by the Italian Ministry for the University and Reserach (MIUR), a Visiting Research grant awarded by the Université Paul Sabatier, as well as the hospitality at the Laboratoire Collisions Agrégats Réactivité-CNRS. We also acknowledge the calculation facilities provided by CALMIP. N.H. acknowledges support from the French National Research Agency under Programme Blanc (ANR-08-BAN-0146-02, DYNHELIUM).

Article outline:

I. INTRODUCTION

II. THEORY

A. Diffusion Monte Carlo

B. Classical trajectory simulations

C. Zero point averaged dynamics

D. Gaussian-based time dependent Hartree (G-TDH) dynamics

III. RESULTS

A. DMC results

B. Dissociation rates

1. ZPAD effective potentials

2. Ne_{8}dissociation rates

3. Rice–Ramsberger-Kassel (RRK) analysis of Ne_{8}dissociation rates

C. Capture probabilities

1. Classical and ZPAD results

2. G-TDH results, frozen width projectile

3. G-TDH, variable projectile width

4. Capture cross sections

IV. DISCUSSION AND CONCLUSIONS

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2012-07-02

2014-04-19

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