Molecular Simulation/Example Problem 5: The Lennard-Jones potential

The Lennard-Jones potential describes the interaction between two non-polar, neutral atoms or molecules. It encompasses two different forces at a molecular level: the Pauli repulsion at short range due to steric overlap, and the attractive London dispersion forces at long range. The potential energy of the interaction between 2 particles is given by: Lennard-Jones potential In this formula, r is the distance between the two particles in question. The parameter ε is the depth of the potential energy well, which represents the strength of the interaction. The parameter σ is the distance at which potential energy is zero. The r-12 term represents the Pauli repulsion and the r-6 term represents the London dispersion attraction. Example: What is the Lennard-Jones potential energy between two argon atoms seperated by 4.00 Å? Given: εAr=1.07799 kJ/mol and σAr=3.39449 Å Solution: The final result of -1.020 kJ/mol indicates that the interaction is attractive. At a separation of 4.00 Å, the atoms are near the potential energy minimum. Å At this distance, the attractive and repulsive forces are nearly balanced. The Lennard-Jones potential is especially useful for modeling intermolecular interaction in molecular simulations where the potential energy is minimized.