Informational thermodynamic model for nanostructures

Nanostructures may be fabricated from metal nanoclusters such as gold or platinum, which are of interest for catalytic and structural characteristics, or from nano forms of carbon allotropes. Here, informational thermodynamic properties such as free energy, enthalpy, and entropy are calculated using a graph network model at T = 298.15 K. We calculate the partition function using Euclidean adjacency matrices from the Hamiltonian and estimated bond energies. The summed atomic displacement from the Kirchhoff index has power law behavior, while the thermodynamic properties exhibit large $N$ logarithmic behavior: however, the data shows structurally related anomalies.