Geometrical considerations in model systems with periodic boundaries

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Abstract
Model systems with periodic boundaries in the shape of an arbitrary parallelepiped are discussed. The locus of minimum images with respect to a given atom is determined, and algorithms for computing minimum image distances, as well as locating significantly interacting atom pairs are presented. It is also shown that, by exhausting the structural information provided by the model system, pair distribution functions can be computed for distances up to the semidiagonal of the minimum image locus. Comparison of the algorithms proposed with existing ones on a typical model system clearly shows that the new algorithms are correct and superior in computational efficiency, for cubic as well as noncubic systems.