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The '''Verlet leap-frog algorithm''' <ref>R. W. Hockney "The potential calculation and some applications", Methods in Computational Physics vol. '''9''' pp. 135-211 Academic Press, New York  (1970)</ref> is a variant of the original Verlet scheme <ref>[http://dx.doi.org/10.1103/PhysRev.159.98 Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review '''159''' pp. 98-103 (1967)]</ref> for use in [[molecular dynamics]] simulations. The algorithm is given by:
The '''Verlet leap-frog algorithm''' is a variant of the original Verlet scheme (Ref. 1)


:<math>r(t + \delta t) = r (t) + \delta t v\left(t+ \frac{1}{2} \delta t\right)</math>
:<math>r(t + \delta t) = r (t) + \delta t v\left(t+ \frac{1}{2} \delta t\right)</math>


:<math>v \left(t+ \frac{1}{2} \delta t\right) = v\left(t - \frac{1}{2} \delta t\right) + \delta t a (t)</math>
:<math>v \left(t+ \frac{1}{2} \delta t\right) = v\left(t - \frac{1}{2} \delta t\right) + \delta t a (t)</math>
where ''r'' is the position, ''v'' is the velocity, ''a'' is the acceleration and ''t'' is the time. <math>\delta t</math> is known as the [[time step]].
==See also==
*[[Velocity Verlet algorithm]]
==References==
==References==
<references/>
#[http://dx.doi.org/10.1103/PhysRev.159.98 Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review '''159''' pp. 98 - 103 (1967)]
'''Related reading'''
#R. W. Hockney, Methods in Computational Physics vol. '''9''', Academic Press, New York  pp. 135–211 (1970)
*[http://dx.doi.org/10.1063/1.2779878 Michel A. Cuendet and Wilfred F. van Gunsteren "On the calculation of velocity-dependent properties in molecular dynamics simulations using the leapfrog integration algorithm", Journal of Chemical Physics '''127''' 184102 (2007)]
[[category: Molecular dynamics]]
[[category: Molecular dynamics]]
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