Verlet Propagation
We are now ready to perform the time propagation of the system. The following 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.