A Verlet list (named after
Loup Verlet
Loup Verlet (; 24 May 1931 – 13 June 2019) was a French physicist who pioneered the computer simulation of molecular dynamics models. In a famous 1967 paper he used what is now known as Verlet integration (a method for the numerical integration ...
) is a data structure in
molecular dynamics
Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of th ...
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 simulation
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be determi ...
s. 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
Verlet integration () is a numerical method used to integrate Newton's equations of motion. It is frequently used to calculate trajectories of particles in molecular dynamics simulations and computer graphics. The algorithm was first used in 1791 ...
*
Fast multipole method __NOTOC__
The fast multipole method (FMM) is a numerical technique that was developed to speed up the calculation of long-ranged forces in the ''n''-body problem. It does this by expanding the system Green's function using a multipole expansion, w ...
*
Molecular mechanics
Molecular mechanics uses classical mechanics to model molecular systems. The Born–Oppenheimer approximation is assumed valid and the potential energy of all systems is calculated as a function of the nuclear coordinates using Force field (chemi ...
*
Software for molecular mechanics modeling
References
External links
Constructing a Neighbour List— from ''Introduction to Atomistic Simulations'' course at the
University of Helsinki
The University of Helsinki ( fi, Helsingin yliopisto, sv, Helsingfors universitet, abbreviated UH) is a public research university located in Helsinki, Finland since 1829, but founded in the city of Turku (in Swedish ''Åbo'') in 1640 as the R ...
.
Molecular dynamics
Computational chemistry
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