Identification of molecular cluster evaporation rates, cluster formation enthalpies and entropies by Monte Carlo method

Abstract. We address the problem of identifying the evaporation rates for neutral molecular clusters from synthetic (computer-simulated) cluster concentrations. We applied Bayesian parameter estimation using a Markov chain Monte Carlo (MCMC)algorithm to determine cluster evaporation/fragmentation rates from known cluster distributions, assuming that the clustercollision rates are known. We used the Atmospheric Cluster Dynamic Code (ACDC) with evaporation rates based on quantumchemical calculations to generate cluster distributions for a set of electrically neutral sulphuric acid and ammonia clusters. We then treated these concentrations as synthetic experimental data, and tested two approaches for estimating the evaporation rates. First we have studied a scenario where at one single temperature time-dependent cluster distributions are measured before thesystem reaches a time-independent steady-state. In the second scenario only steady-state cluster distributions are measured, butat several temperatures. This allowed us to use multiple sets of concentrations at different temperatures. Additionally, in thelatter case the evaporation rates were represented in terms of cluster formation enthalpies and entropies which were considered to be free parameters. This reparametrization reduced the number of unknown parameters, since several evaporation ratesdepend on the same cluster formation enthalpy and entropy values. We show that in the second setting, even if only two temperatures were used, the temperature-dependent steady-state dataoutperforms the first setting for parameter identification. We can thus conclude that for experimentally determining evaporationrates, cluster distribution measurements at several temperatures are recommended over time-dependent measurements at one temperature.