Geometric features and a neural network classifier for detecting melting-like transitions in clusters

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 is WU, 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) a measure of dissimilarity to the lowest energy configuration, or global minimum; (ii) the 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) a measure of non-uniformity in the distribution of the rij's. Numerical tests with empirical potentials that model three types of bonding (van der Waals, covalent, and metallic) show that these four functions produce estimates for the middle of the melting region in general agreement with Tc. An artificial neural network classifier 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 the third function 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).