A novel statistical mechanical methodology is applied to clusters of N ≤ 7 atoms. Exact statistical analogs for any energy derivative of entropy ∂mS/∂Em are used in rigorous microcanonical Monte Carlo simulations to vastly enlarge the pool of measurable thermodynamic properties relative to previous work. All analogs are given for two alternative partition functions of the microcanonical ensemble. Coarse grained energy distributions are used to establish the existence of melting transitions. LJ7, LJ5, and LJ4 are found to exhibit trimodal distributions, a feature not being reported before. Varieties of combinations of entropy derivatives are tested for a direct detection of the melting region. It is shown that for such a purpose, derivatives of at least fourth order are necessary.
REFERENCES
The value of a random variable X at a maximum is called a mode of the distribution p(X). In this work, distributions are measured along random walks as histograms with sufficiently small bin widths. The identifiable peaks then provide accurate measures of modes.
Reference 29, Sec. 8.2, Appendix B.