Which order do the steps in the Verlet algorithm come?
The short answer is “it doesn’t matter”. One of the attractions of the Verlet algorithm for molecular dynamics is that you only have to store three values for each particle (position velocity and acceleration). At each step (or half step) one of these is updated using the current values of the others. If you write a Verlet method, it is best to start with the new force calculation: then the acceleration can be passed into the method, and the method can be used for all force models (no need to call LennardJonesPotential from inside VerletAlgorithm).