Verlet list
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" before being updated. If we wish to use the same Verlet list n 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 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 
). Optimizing our choice of , it can be shown that the 
problem of Monte Carlo sweeps has been converted to an 
problem by using Verlet lists.
Using cell lists to identify the nearest neighbors in 
further reduces the computational cost.
See also
References
- ^ Verlet, L. (1967). "Computer 'experiments' on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules". Phys. Rev. 159: 98–103.
External links
- Constructing a Neighbour List — from Introduction to Atomistic Simulations course at the University of Helsinki.