Absolute classical densities of states for very anharmonic systems and applications to the evaporation of rare gas clusters

Abstract

We have simulated the cluster dissociation reaction Arn→Arn−1+Ar (12≤n≤14) using molecular dynamics (MD) with well defined internal energy and total angular momentum. Reaction rates and kinetic energy release distributions are compared to the predictions of several statistical theories: Rice, Ramsperger, and Kassel (RRK), Engelking, and phase space theory (PST). We employ the Nosé prescription for constant temperature dynamics coupled with the multiple histogram method of Labastie and Whetten to obtain highly accurate vibrational densities of states for the clusters. The absolute densities are determined by the adiabatic switching method of Reinhardt. Incorporation of these accurate anharmonic vibrational densities of states into classical PST allows us to make a direct comparison with the simulation results and eliminates any parameters from the theory. Then PST predictions for the kinetics of evaporation are given for the low energy (long time scale) regime where MD simulations are prohibitively expensive. A critical evaluation of the approximate statistical theories is presented.

On possible simplifications in the theoretical description of gas phase atomic cluster dissociation

“…Overall, the results shown in Fig. 2 support the previous observation on LJ [12][13][14] ͑Ref. 13͒ and Al 6 ͑Ref.…”

“…The MD rate constants were estimated assuming a first order kinetic law and fitting the long time behavior of ln͓͑N 0 − N t ͒ / N 0 ͔ with a straight line. Here, N 0 is the total number of trajectories and N t is the number of trajectories dissociated at time t. This approach differs somewhat from the procedure used by Weerasinghe and Amar, 13 who used the last negative minimum of the radial momentum for the dissociating atom to define the dissociation time. It also introduces some arbitrariness in the results, which are independent of the separatrix location only when the latter is placed in a region where the interaction potential has completely died off.…”

“…I, the task of modeling vapor nucleation using a set of MEs would be substantially simplified if one was allowed to neglect the dependence on the system angular momentum J. It therefore appears important to explore whether the weak sensitivity of k n d ͑E , J͒ on J, the angular momentum of the parent cluster, suggested for LJ [12][13][14] ͑Ref. 13͒ and Al 6 ͑Ref.…”

“…In considering the usage of Eq. ͑3͒ to describe the system time evolution, it is easy to realize that both k n d and k n−1 c could, in principle, be exactly computed using molecular dynamics 12,13 ͑MD͒ without employing statistical theories. The latter, however, provides a computational advantage with respect to MD, which becomes inefficient in computing k n d for low temperature ͑T͒ or energy ͑E͒ clusters.…”

“…For instance, phase space theory 16,17 ͑PST͒ has been previously used to estimate k n d for relatively small rare gas 13 and aluminum 18 clusters and found to perform well. Similarly, Schenter et al 19 provided evidence that their version of canonical vTST, developed to tackle the calculation of k n d ͑T͒ for molecular clusters, is in agreement with MD results to within a factor of 2.…”