Buckingham potential: Difference between revisions
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where <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math>, and <math>A</math>, <math>B</math> and <math>C</math> are constants. | where <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math>, and <math>A</math>, <math>B</math> and <math>C</math> 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 exponsential function of distance, in contrast to the inverse twelfth power used by the Lennard-Jones potential. However, since they Buckingham potential is finite even at very small distance, 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== | ==References== | ||
#[http://dx.doi.org/10.1098/rspa.1938.0173 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)] | #[http://dx.doi.org/10.1098/rspa.1938.0173 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)] | ||
[[category: models]] | [[category: models]] | ||
Revision as of 18:11, 1 February 2010
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The Buckingham potential is given by
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi_{12}(r) = A \exp \left(-Br\right) - \frac{C}{r^6}}
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi_{12}(r)} is the intermolecular pair potential, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r := |\mathbf{r}_1 - \mathbf{r}_2|} , and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 exponsential function of distance, in contrast to the inverse twelfth power used by the Lennard-Jones potential. However, since they Buckingham potential is finite even at very small distance, 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.