Buckingham potential

The Buckingham potential is given by

$\Phi _{12}(r)=A\exp \left(-Br\right)-{\frac {C}{r^{6}}}$

where $\Phi _{12}(r)$ is the intermolecular pair potential, $r:=|\mathbf {r} _{1}-\mathbf {r} _{2}|$, and $A$, $B$ and $C$ are constants.

It is named for R. A. Buckingham, and not as is often thought for David Buckingham.

The Buckingham potential describes the repulsive exchange repulsion that originates from the Pauli exclusion principle by a more realistic exponential function of distance, in contrast to the inverse twelfth power used by the Lennard-Jones potential. However, since the Buckingham potential is finite even at very small distances, it runs the risk of an unphysical "Buckingham catastrophe" at short range when used in simulations of charged systems; this occurs when the electrostatic attraction artifactually overcomes the repulsive barrier. The Lennard-Jones potential is also quicker to compute, and is more frequently used in molecular dynamics and other simulations.

References

1. R. A. Buckingham "The Classical Equation of State of Gaseous Helium, Neon and Argon", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 168 pp. 264-283 (1938)