Verlet list explained

A Verlet list (named after Loup Verlet) is a data structure in molecular dynamics simulations to efficiently maintain a list of all particles within a given cut-off distance of each other.^[1]

This method may easily be applied to Monte Carlo simulations. For short-range interactions, a cut-off radius is typically used, beyond which particle interactions are considered "close enough" to zero to be safely ignored. For each particle, a Verlet list is constructed that lists all other particles within the potential cut-off distance, plus some extra distance so that the list may be used for several consecutive Monte Carlo "sweeps" (set of Monte Carlo steps or moves) before being updated. If we wish to use the same Verlet list

times before updating, then the cut-off distance for inclusion in the Verlet list should be , where is the cut-off distance of the potential, and is the maximum Monte Carlo step (move) of a single particle. Thus, we will spend of order time to compute the Verlet lists ( is the total number of particles), but are rewarded with Monte Carlo "sweeps" of order instead of . By optimizing our choice of it can be shown that Verlet lists allow converting the problem of Monte Carlo sweeps to an problem.

Using cell lists to identify the nearest neighbors in

further reduces the computational cost.

See also

• Verlet integration
• Fast multipole method
• Molecular mechanics
• Software for molecular mechanics modeling

External links

• Constructing a Neighbour List - from Introduction to Atomistic Simulations course at the University of Helsinki.

Notes and References

1. Verlet, L. . Loup Verlet . Computer 'experiments' on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules . Phys. Rev. . 159 . 98–103 . 1967 . 1 . 10.1103/physrev.159.98. 1967PhRv..159...98V . free .