Exact Non-Linear Relationship Between Exponential-6 and Lennard-Jones (12-6) Potential Functions

The relationship between two of the most frequently adopted van der Waals potential functions – Exponential-6 and Lennard-Jones (12-6) – is shown to be faulty upon comparison of the repulsive terms. By using the Maclaurin's series expansions, an exact relationship between both the potential functions is obtained by means of a non-linear correction factor. A purely Exponential-6 form is recovered when the correction factor is taken at zeroth order, while a purely Lennard-Jones (12-6) form is attained as the order of the correction factor tends to infinity. For real van der Waals systems that are bounded by the Exponential-6 and Lennard-Jones (12-6) potential functions, a positive integer order of the correction factor may possibly provide good curve-fitting to experimental data.