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Evaluation of internal energy and the inter-atomic or ionic interactions in a crystal lattice usually requires precise calculation of lattice sums. This in the case of small nano-particles (as space-limited domains) presents several challenges, as conventional methods are usually valid only for infinite lattices, tailored for a specific potential. In this work, a new method has been developed for calculation of atomic interactions based on the radial density function with the geometric probability approach, extended to arbitrary fixed lattices and potentials in a nano-particle.

On Calculation of Lattice Energy in Spatially Confined Domains