Consider two particles that are interacting via a Lennard–Jones potential,

The dynamic equation for the distance r between these particles is given by the force balance (in dimensionless form),

where we used the relationship between potential energy and force, f = −dV/dr. Write a MATLAB program that uses implicit Euler to find the position r as a function of time t for an initial separation of r = 1.3 and no initial velocity. The program should produce a plot of the position versus time. Include the residual and Jacobian you used to solve this problem. There is something bizarre about the result, explain. Think about the minimum value of the potential energy and the dynamics of a particle in a potential field.

V = r-12_r-6