## 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.