Buckingham potential

In theoretical chemistry, the Buckingham potential is a formula proposed by Richard Buckingham which describes the Pauli exclusion principle and van der Waals energy formula_1 for the interaction of two atoms that are not directly bonded as a function of the interatomic distance formula_2. It is a variety of interatomic potentials.
Here, formula_4, formula_5 and formula_6 are constants. The two terms on the right-hand side constitute a repulsion and an attraction, because their first derivatives with respect to formula_2 are negative and positive, respectively.
Buckingham proposed this as a simplification of the Lennard-Jones potential, in a theoretical study of the equation of state for gaseous helium, neon and argon.
As explained in Buckingham's original paper and, e.g., in section 2.2.5 of Jensen's text, the repulsion is due to the interpenetration of the closed electron shells. "There is therefore some justification for choosing the repulsive part (of the potential) as an exponential function". The Buckingham potential has been used extensively in simulations of molecular dynamics.
Because the exponential term converges to a constant as formula_2→formula_9, while the formula_10 term diverges, the Buckingham potential becomes attractive as formula_2 becomes small. This may be problematic when dealing with a structure with very short interatomic distances, as any nuclei that cross a certain threshold will become strongly (and unphysically) bound to one another at a distance of zero.
Coulomb–Buckingham potential.
The Coulomb–Buckingham potential is an extension of the Buckingham potential for application to ionic systems (e.g. ceramic materials). The formula for the interaction is
where "A", "B", and "C" are suitable constants and the additional term is the electrostatic potential energy.
The above equation may be written in its alternate form as
where formula_14 is the minimum energy distance, formula_15 is a free dimensionless parameter and formula_16 is the depth of the minimum energy.