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We analyze the possible expansions of the interatomic potential$U(|\textbf{r}_{1}-\textbf{r}_{2}|)$ in a Fourier series for a cyclic systemand a system with boundaries. We also study the transition from exactexpansions for a finite system to the expansion that is commonly used in thethermodynamic limit. The analysis shows that such a transition distorts thepotential of a bounded system by making it cyclic.

Expansions of the interatomic potential for different boundary conditions and the transition to the thermodynamic limit