Neighborlist

Neighborlist, also spelled neighbour list, is a data structure used in computational simulations, particularly molecular dynamics and Monte Monte Carlo methods, to keep track of particles that lie within a specified cutoff distance of each other. By maintaining a list of nearby particles for each atom, the neighborlist allows the algorithm to avoid evaluating pairwise interactions over the entire system, reducing the computational cost from O(N²) to O(N) for systems with short‑range forces.

The construction of a neighborlist typically involves dividing the simulation domain into cells whose dimensions are at least as large as the cutoff radius. Particles are assigned to cells, and the list for a given particle is built by examining only particles in the same or adjacent cells. To reduce the frequency of rebuilding, a skin distance is added to the cutoff; the list is updated only when any particle moves more than half the skin width, ensuring that all true neighbors remain included.

Neighborlists are employed in a variety of software packages for materials modeling, biomolecular simulations, and coarse‑grained dynamics. Variants include the Verlet list, where each particle stores a simple array of neighbor indices, and the linked‑cell list, which combines cell indexing with dynamic updates. Advanced implementations may incorporate hierarchical spatial trees (e.g., k‑d trees or octrees) to handle heterogeneous particle distributions or long‑range interactions.

While neighborlists greatly improve efficiency for short‑range potentials, they must be carefully managed to maintain accuracy. The choice of cutoff, skin thickness, and update frequency influences both performance and the physical fidelity of the simulation, and best practices are often established through benchmarking for specific systems.