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

Abstract

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