Overcoming the minimum image constraint using the closest point search

• We present a robust and efficient means of enumerating all periodic images of a region that come within a cutoff distance of the origin.
• This calculation simplifies computation of distance-dependent properties, even when the cutoff exceeds the minimum image constraint.
• The algorithm applies in arbitrary dimensions, and is also useful for visualization of the minimal cell.

Finding the set of nearest images of a point in a simulation cell with periodic (torus) boundary conditions is of central importance for molecular dynamics algorithms. To compute all pairwise distances closer than a given cutoff in linear time requires region-based neighbor-listing algorithms. Available algorithms encounter increasing difficulties when the cutoff distance exceeds half the shortest cell length. This work provides details on two ways to directly and efficiently generate region–region interaction lists in n-dimensional space, free from the minimum image restriction. The solution is based on a refined version of existing algorithms solving the closest vector problem. A self-contained discussion of lattice reduction methods for efficient higher-dimensional searches is also provided. In the MD setting, these reduction criteria provide useful guidelines for lattice compaction.

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