Verlet list
Encyclopedia
A Verlet list 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.
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.
Molecular dynamics
Molecular dynamics is a computer simulation of physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a period of time, giving a view of the motion of the atoms...
simulations to efficiently maintain a list of all particles within a given cut-off distance of each other.
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
Monte Carlo method
Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in computer simulations of physical and mathematical systems...
"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
Cell lists
Cell lists are a tool for finding all atom pairs within a given cut-off distance of each other in Molecular dynamics simulations...
to identify the nearest neighbors in
further reduces the computational cost.External links
- Constructing a Neighbour List — from Introduction to Atomistic Simulations course at the University of HelsinkiUniversity of HelsinkiThe University of Helsinki is a university located in Helsinki, Finland since 1829, but was founded in the city of Turku in 1640 as The Royal Academy of Turku, at that time part of the Swedish Empire. It is the oldest and largest university in Finland with the widest range of disciplines available...
.