Velocity Verlet algorithm

The Velocity Verlet algorithm for use in molecular dynamics is given by

$r(t+\delta t)=r(t)+\delta tv(t)+{\frac {1}{2}}\delta t^{2}a(t)$

$v\left(t+\delta t\right)=v(t)+{\frac {1}{2}}\delta t[a(t)+a(t+\delta t)]$

where $r$ is the position, $v$ is the velocity, $a$ is the acceleration and $t$ is the time.

See also

• Verlet leap-frog algorithm

References

1. Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review 159 pp. 98-103 (1967)
2. William C. Swope, Hans C. Andersen, Peter H. Berens and Kent R. Wilson "A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters", Journal of Chemical Physics 76 pp. 637-649 (1982)

External resources

• Velocity version of Verlet algorithm sample FORTRAN computer code from the book M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989).