A multiscale approach is proposed to address short-time nonadiabatic dynamics and long-time decay. We show the role of both radiative and non-radiative processes in cluster decay mechanisms on examples of rare-gas cluster fragmentation after electron impact ionization. Nonadiabatic molecular dynamics is used as an efficient tool for theoretical study on femto- and picosecond scales and a multiscale approach based on kinetic rates of radiative as well as non-radiative transitions, both considered as parallel reaction channels, is used for the analysis of the long-time system relaxation spanning times over microseconds to infinity. While the radiative processes are typically slow, the system relaxation through non-radiative electronic transitions connected with electron-nuclear interchange of energy may, on the other hand, significantly vary in kinetic rates according to kinetic couplings between relevant adiabatic states. While the predictions of picosecond molecular dynamics themselves fail, the results of the multiscale model for the electron-impact post-ionization fragmentation of krypton and xenon tetramers are in agreement with experiment, namely, in leading to the conclusion that charged monomers prevail. More specifically, on microsecond and longer scales, mainly slow radiative processes are substantial for krypton cluster decay, while for xenon the radiative and slow non-radiative processes compete. In general, the role of slow decay processes through non-radiative transitions is comparable with the role of radiative decay mechanism. The novel multiscale model substantially improves theoretical predictions for the xenon tetramer decay and also further improves the good agreement between theory and experiment we reached previously for krypton.

Post-ionization fragmentation of small ionic krypton clusters, Kr (N = 3-13), has been investigated using a semiclassical non-adiabatic dynamics approach consisting of classical treatment of atomic nuclei and full quantum treatment of electrons, and an extended diatomics-in-molecules model including the spin-orbit coupling as well as leading three-body interaction corrections. Electronic quantum decoherence has also been considered via a simplified scheme proposed previously. The positive charge has been initially localized on a randomly selected atom in the form of a localized P positive hole. It follows from the calculations that the data are not converged at timescales usually considered in dynamical calculations (t = 200 ps in this work) and that an extension to t ≈ 1 μs is needed. An approximate multi-scale treatment developed recently has been used to provide such an extension of the output of dynamical calculations. A qualitative agreement with available experimental data has been achieved, in particular, the experimental observation that the monomer fragment, Kr, completely dominates has been reproduced. Interestingly, stabilized neutral dimer and trimer fragments have been observed in our calculations at non-negligible abundances despite extremely weak bonding in these species.

In this supplementary material, we recollect, for reader's convenience, the general scheme of suggested multiscale model (Sec. 1), and basic informations about approaches used for pilot study: a detailed description of the interaction model (Sec. 2) and dynamical methods used for the dark dynamics step (Sec. 3) reported previously in two preceding studies [1,2]. In addition, a detailed description of the treatment of radiative processes is also given (Sec. 4).