Velocity Verlet algorithm

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

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r(t + \delta t) = r (t) + \delta t v(t) + \frac{1}{2} \delta t^2 a(t)}

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle v \left(t+ \delta t\right) = v(t) + \frac{1}{2} \delta t [ a(t) + a(t+\delta t)]}

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r} is the position, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle v} is the velocity, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} is the acceleration and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t} is the time. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \delta t} is known as the time step.

See also

• Verlet leap-frog algorithm

References

Related reading

• 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)
• Jaewoon Jung, Chigusa Kobayashi, and Yuji Sugita "Kinetic energy definition in velocity Verlet integration for accurate pressure evaluation", Journal of Chemical Physics 148 164109 (2018)

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).