## About the Lennard-Jones potential graph

The Lennard-Jones potential is a relatively-simple mathematical model describing the potential
energy \(V_{LJ}\) between a pair of neutral atoms as a function of both the distance in units
of radii where the potential is zero \(\sigma\) (sigma) and the maximum depth of the potential
well \(\varepsilon\) (epsilon).

$$V_{LJ}=4\varepsilon \left[ \left( \dfrac {\sigma } {r}\right) ^{12}-\left( \dfrac {\sigma } {r}\right) ^{6}\right]$$

The force between two neutral atoms is the derivative of the Lennard-Jones potential.

The slope of the potential function at the point where the potential is zero \(\sigma\) (sigma)
is negative so when two neutral atoms have a separation of \(\sigma\) radii there is a repulsive force.

The slope of the potential function at \(\varepsilon\) (epsilon) is zero -- this is the
maximum depth of the potential well. At this distance apart two neutral atoms experience zero
net-force, they neither attract or repel.

As the distance between two neutral atoms becomes greater than \(\varepsilon\) the slope of the
potential function becomes strongly positve and two atoms experience a attractive force that
diminishes as the distance becomes greater.

In the graph above you can change effective the force as a function of distance by either
changing the depth of the potential well by dragging \(\varepsilon\) (epsilon) up and down
or changing the zero point for the potential by dragging \(\sigma\) (sigma) left and right.

## References:

Wikipedia: Lennard-Jones Potential