The Demonstration aims to simulate a classical molecular model for bond vibrations  in which the force fields  are approximated as harmonic oscillators . Usually simulations are carried out in isolated conservative systems so it is important to have both energy and the total number of particles  conserved by the approximate solution. This is achieved by conservtion of the product
. In the above example you can see the best that can be achieved for the former product is a strongly oscillating value with a constant mean and not a single point constant value. This result is reached by the VV algorithm but not by the RK algorithm. Algorithms able to conserve
are referred to as symplectic integrators . Typical molecular calculations are carried out with .
A typical real vibration has
used in molecular dynamics to approximate the equations is roughly consistent with the width of a single vibration (or at least, the shortest vibration in the system).
The harmonic oscillator in the simulation has
so the following values of
(in seconds) have been chosen: 0.01; 0.06; 0.1; 0.3.
increases the difference in behavior of the two algorithms up to the
(at this value, molecular world and real world proportions are the same). It is clear that RK, not being a symplectic integrator, cannot be used as an algorithm to integrate the equation of motion in a molecular dynamics simulation.