The velocity Verlet method algorithm is as follows:
Calculate: $$\vec{x}(t + \Delta t) = \vec{x}(t) + \vec{v}(t)\, \Delta t+\tfrac12 \,\vec{a}(t)\,\Delta t^2$$
Derive: $\vec{a}(t + \Delta t)$ from the interaction potential using $\vec{x}(t + \Delta t)$
Calculate: $$\vec{v}(t + \Delta t) = \vec{v}(t) + \tfrac12\,\left(\vec{a}(t)+\vec{a}(t + \Delta t)\right)\Delta t\,$$
How do you derive the acceleration $\vec{a}(t + \Delta t)$ from the interaction potential using $\vec{x}(t + \Delta t)$? Also, could someone please explain the term "interaction potential"?
Velocity Verlet is an algorithm used to integrate Newton's equations of motion. I typically use it in order to compute trajectories of particles in molecular dynamics. These particles can interact due to Coulomb force for example. Depending on the model you use and the situation you're in, you can have different kinds of potential (a common one is Lennard-Jones potential).
So interacting potential is a potential which couples particles. Since $\overrightarrow{F}= - \nabla V$, a potential different from zero will generate a force and so an acceleration. I think in order to compute $\overrightarrow{a}(t+\Delta t)$ you need to know the potential in which the particles move, this will let you derive a formula for the force and then you could implement something like:
I'm studying it right now, so I could have made mistakes. Please comment if something is not clear