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| 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.<ref name="Verlet1967">{{cite journal |author=Verlet, L. |title=Computer 'experiments' on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules |journal=Phys. Rev. |volume=159 |page=98–103 |year=1967}}</ref>
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| 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 method|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 <math>R_c + 2nd</math>, where <math>R_c</math> is the cut-off distance of the potential, and <math>d</math> is the maximum Monte Carlo step of a single particle. Thus, we will spend of order <math>N^2</math> time to compute the Verlet lists (<math>N</math> is the total number of particles), but are rewarded with <math>n</math> Monte Carlo "sweeps" of order <math>Nn^2</math> (instead of <math>NN</math>). Optimizing our choice of <math>n</math>, it can be shown that the <math>O(N^2)</math> problem of Monte Carlo sweeps has been converted to an <math>O(N^{5/3})</math> problem by using Verlet lists.
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| Using [[cell lists]] to identify the nearest neighbors in <math>O(N)</math> further reduces the computational cost.
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| ==See also==
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| *[[Cell lists]]
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| *[[Verlet integration]]
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| *[[Fast multipole method]]
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| ==References==
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| {{reflist}}
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| ==External links==
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| *[http://www.physics.helsinki.fi/courses/s/atomistiset/lecturenotes/2004/landscape3a.pdf Constructing a Neighbour List] — from ''Introduction to Atomistic Simulations'' course at the [[University of Helsinki]].
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| [[Category:Molecular dynamics]]
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| [[Category:Computational chemistry]]
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| {{Comp-sci-stub}}
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Latest revision as of 18:20, 19 October 2014
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