# Verlet Propagation

We are now ready to perform the time propagation of the system. The following input file

input file

The input file specifies the propagator as:


TDSystemPropagator = verlet


According to Wikipedia, the Verlet algorithm is defined as:

• Calculate $\vec{x}(t + \Delta t) = \vec{x}(t) + \vec{v}(t) \Delta t + \tfrac12 \vec{a}(t) \Delta t^2$.
• Calculate interaction potential using $\vec{x}(t + \Delta t)$.
• Derive $\vec{a}(t + \Delta t)$ from the interaction potential using $\vec{x}(t + \Delta t)$.
• Calculate $\vec{v}(t + \Delta t) = \vec{v}(t) + \tfrac12 \big(\vec{a}(t) + \vec{a}(t + \Delta t)\big)\Delta t$.

These 4 steps have to be performed for each time step.

Detailled description of the algorithmic steps