Buckingham potential

Buckingham potential. The Buckingham potential is an intermolecular potential function used to model the repulsive and attractive interactions between non-bonded atoms or molecules. It is particularly noted for its more realistic exponential treatment of the repulsive term compared to the simpler power-law form used in the widely adopted Lennard-Jones potential. This potential finds significant application in molecular dynamics simulations and studies of condensed matter physics, especially for systems where short-range repulsion is critical.

Definition and mathematical form

The standard form of the Buckingham potential, also known as the **Buckingham–Corner potential**, describes the potential energy \( V(r) \) between two interacting particles as a function of their separation \( r \). Its mathematical expression is given by: \[ V(r) = A e^{-Br} - \frac{C}{r^6} \] Here, the first term represents the short-range Pauli repulsion, modeled with an exponential decay, which arises from the overlap of electron clouds. The second term represents the attractive London dispersion force, which is a long-range interaction proportional to \( r^{-6} \). The parameters \( A \), \( B \), and \( C \) are positive constants specific to the interacting pair, such as argon atoms or water molecules, and are typically determined from quantum chemistry calculations or fitted to experimental data like virial coefficients or crystal lattice energies.

Physical interpretation and parameters

The parameter \( A \) governs the strength of the repulsive interaction, while \( B \) controls its range; a larger \( B \) indicates a harder, more steeply rising repulsive wall. The parameter \( C \) determines the strength of the attractive van der Waals force. These parameters are not universal and must be derived for each specific atomic or molecular interaction, often through ab initio methods or by fitting to properties of materials like solid argon or liquid nitrogen. The exponential repulsion is considered more physically accurate than a power-law repulsion at very short interatomic distances, as it better reflects the results of quantum mechanical calculations for the overlap of molecular orbitals.

Comparison with other intermolecular potentials

The primary alternative to the Buckingham potential is the ubiquitous Lennard-Jones potential, which uses a \( r^{-12} \) term for repulsion. While the Lennard-Jones 12-6 potential is computationally simpler and adequate for many fluids like liquid methane, the Buckingham form's exponential repulsion is often more accurate for modeling noble gas solids and dense phases. However, it is computationally more expensive to evaluate. Other related potentials include the Morse potential, often used for chemical bonds, and the Born–Mayer potential, used in ionic crystal simulations like sodium chloride. The Stockmayer potential extends these models to include permanent dipole moment effects.

Applications in molecular simulation

The Buckingham potential has been extensively used in classical mechanics-based molecular dynamics and Monte Carlo method simulations. It is a key component in many empirical force fields, such as those developed for clay minerals, zeolite frameworks, and ceramic materials like magnesium oxide. Early simulations of liquid water and aqueous solutions sometimes employed this potential to model oxygen-oxygen interactions. Its application is crucial in materials science for predicting properties of condensed phase systems, including thermal conductivity, diffusion coefficients, and phase diagrams, particularly under high-pressure conditions relevant to geophysics.

Limitations and modifications

A significant limitation of the standard Buckingham potential is its behavior at very small interatomic distances, where the attractive \( r^{-6} \) term diverges to negative infinity faster than the exponential repulsion can rise, leading to an unphysical "Buckingham catastrophe" or pole. To remedy this, a repulsive \( r^{-12} \) or other hard-core term is often added, resulting in the **Buckingham–Exp–6 potential**. Further modifications include the Tang–Toennies potential, which dampens the dispersion term at short range. Hybrid potentials that switch functions at certain cutoffs are also used in modern software packages like LAMMPS and GROMACS to maintain computational stability while preserving accuracy for systems such as carbon dioxide or ionic liquids.

Category:Interatomic potentials Category:Computational chemistry Category:Physical chemistry