Discretization error-free estimate of low temperature statistical dissociation rates in gas phase: Applications to Lennard-Jones clusters $X13−nYn$ $(n=–3)$

In this work, an improved approach for computing cluster dissociation rates using Monte Carlo (MC) simulations is proposed and a discussion is provided on its applicability as a function of environmental variables (e.g., temperature). With an analytical transformation of the integrals required to compute variational transition state theory (vTST) dissociation rates, MC estimates of the expectation value for the Dirac delta $δ(qrc−qc)$ have been made free of the discretization error that is present when a prelimit form for $δ$ is used. As a by-product of this transformation, the statistical error associated with $⟨δ(qrc−qc)⟩$ is reduced making this step in the calculation of vTST rates substantially more efficient (by a factor of 4–2500, roughly). The improved MC procedure is subsequently employed to compute the dissociation rate for Lennard-Jones clusters $X13−nYn$ $(n=0–3)$ as a function of temperature $(T)$⁠, composition, and $X-Y$ interaction strength. The $X13−nYn$ family has been previously studied as prototypical set of systems for which it may be possible to select and stabilize structures different from the icosahedral global minimum of $X13$⁠. It was found that both the dissociation rate and the dissociation mechanism, as suggested by the statistical simulations, present a marked dependence on $n$⁠, $T$⁠, and the nature of $Y$⁠. In particular, it was found that a vacancy is preferentially formed close to a surface impurity when the $X-Y$ interaction is weaker than the $X-X$ one whatever the temperature. Differently, the mechanism was found to depend on $T$ for stronger $X-Y$ interactions, with vacancies being formed opposite to surface impurities at higher temperature. These behaviors are a reflex of the important role played by the surface fluctuations in defining the properties of clusters.