Velocity Verlet

Velocity Verlet is the current standard for integration in MD. It is a symplectic, explicit method with a single force evaluation per time step. Equation 2 shows how the positions, velocities and accelerations are updated at every time step.

$\displaystyle v_{n+\frac{1}{2}}$ $\textstyle =$ $\displaystyle v_{n}+\frac{1}{2}\Delta ta_{n}$ (2)
$\displaystyle r_{n+1}$ $\textstyle =$ $\displaystyle r_{n}+\Delta tv_{n+\frac{1}{2}}$  
$\displaystyle Ma_{n+1}$ $\textstyle =$ $\displaystyle F_{n+1}$  
$\displaystyle v_{n+1}$ $\textstyle =$ $\displaystyle v_{n+\frac{1}{2}}+\frac{1}{2}\Delta ta_{n+1}$  

The notable aspects of this algorithm are that the velocity is updated in two stages and that the position is updated using the intermediate velocity.

root 2008-04-23