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Calculations of the electron-impact ionization cross-section of pyrene, anthracene, benzoyl chloride, benzophenone, and phthalonitrile are reported over a wide energy range. A comparison of theoretical models, viz. spherical complex optical potential (SCOP), pixel counting method (PCM), and the binary encounter Bethe (BEB) model is carried out. SCOP calculations provide the inelastic cross-section, and the ionization cross-section is extracted from it. This result is modified with PCM, a model previously applied to ion collisions which takes geometric screening corrections into account. The BEB model is used as an independent approach to calculate the ionization cross-section. It is demonstrated that all model results are in reasonable agreement with each other. Comparison is also made with other theoretical data where available.
Melting Transitions in Small Aluminum Clusters Simulated with Energies Approaching DFT Accuracy.
(2025)
We describe a computational framework for modelling melting-like transitions in atomic clusters that combines first-principles energy calculations, global optimization, and machine-learned interatomic potentials. A diverse set of configurations is generated by global optimization, and energies are calculated by Density Functional Theory. The energies are fitted to an accuracy of 10 meV/atom or better with an Allegro E(3)-equivariant neural network potential. The model allows efficient parallel tempering Monte Carlo simulations with near DFT-level accuracy. This methodology was validated by simulating Na_20 and comparing it to earlier experimental and computational results. We used it to study melting-like transitions in Al_n+ clusters (n=9 to 16), and Al_n and Al_n^- (n=12, 13,14). The simulated heat capacity of these clusters, in particular Al_16+, are in qualitative agreement with experiments.
The melting point of Al_n+ clusters with n=11-16 are well above the bulk melting point (934 K). The closed-shell Al_13- species has an exceptionally high melting point, close to 2100 K.
Melting-like transitions in clusters are normally identified by a peak in the heat capacity curve C(T ) at T = Tc. Computing C(T ) requires costly simulations with millions of steps. We discuss four easily calculated functions of temperature that help detect and characterize melting-like transitions. The first, f1 (or WU ), is the width of the potential energy distribution which shows an abrupt increase near Tc. The other three are statistics of the ordered set of N(N − 1)/2
interatomic distances rij: (i) f2 is a measure of dissimilarity to the lowest energy configuration, or global minimum; (ii) f3 is the effective number of rij’s found in a small interval centered around (r1 + r2)/2 where r1, r2 are the positions of the first two peaks in the pair distribution function; and (iii) f4 is a measure of non-uniformity in the distribution of the
ri j’s. Numerical tests with empirical potentials that model three types of bonding (van der Waals, covalent, and metallic) show that f1, f2, f3, and f4 produce estimates for the middle of the melting region in general agreement with Tc. An Artificial Neural Network (ANN) classifier that takes, as inputs, f2, f3, and many variants of f4, is used to calculate the solid fraction FS(T) and find the solid-liquid coexistence region between freezing and melting temperatures, [Tf , Tm]. Inflection points in f3(T ) and FS(T ) are very sensitive indicators of phase transitions. Estimates of Tc obtained from them converge one to three orders of magnitude faster, in simulation time, than those obtained with C(T ).