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The '''Buckingham potential''' is a [[mathematical formula|formula]] proposed by [[Richard Buckingham]] which describes the [[Wolfgang Pauli|Pauli]] [[Exchange interaction|repulsion energy]] and [[van der Waals force|van der Waals energy]] <math>\Phi_{12}(r)</math> for the interaction of two atoms that are not directly bonded as a function of the [[Atomic spacing|interatomic distance]] <math>r</math>. | |||
:<math>\Phi_{12}(r) = A \exp \left(-Br\right) - \frac{C}{r^6}</math> | |||
Here, <math>A</math>, <math>B</math> and <math>C</math> are constants. The two terms on the right-hand side constitute a repulsion and an attraction, because their first [[derivative]]s with respect to <math>r</math> 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 [[gas]]eous [[helium]], [[neon]] and [[argon]].<ref>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)]</ref> | |||
As explained in Buckingham's original paper and, e.g., in section 2.2.5 of Jensen's text,<ref name=jensen>F. Jensen, ''Introduction to Computational Chemistry'', 2nd ed., Wiley, 2007,</ref> the repulsion is due to the interpenetration of the closed [[electron shell]]s. "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 <math>r</math>→<math>0</math>, while the <math>r^{-6}</math> term diverges, the Buckingham potential "turns over" as <math>r</math> becomes small. This may be problematic when dealing with a structure with very short interatomic distances, as the nuclei that cross the turn-over will become strongly (and unphysically) bound to one another at a distance of zero.<ref name=jensen/> | |||
==References== | |||
{{Reflist}} | |||
==External links== | |||
*[http://www.sklogwiki.org/SklogWiki/index.php/Buckingham_potential Buckingham potential] on [http://www.sklogwiki.org/SklogWiki/index.php/Main_Page SklogWiki] | |||
{{DEFAULTSORT:Buckingham potential}} | |||
[[Category:Theoretical chemistry]] | |||
[[Category:Computational chemistry]] | |||
[[Category:Thermodynamics]] | |||
[[Category:Chemical bonding]] | |||
[[Category:Intermolecular forces]] | |||
[[Category:Potentials]] | |||
Latest revision as of 14:20, 9 May 2013
The Buckingham potential is a formula proposed by Richard Buckingham which describes the Pauli repulsion energy and van der Waals energy for the interaction of two atoms that are not directly bonded as a function of the interatomic distance .
Here, , and are constants. The two terms on the right-hand side constitute a repulsion and an attraction, because their first derivatives with respect to 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.[1]
As explained in Buckingham's original paper and, e.g., in section 2.2.5 of Jensen's text,[2] 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 →, while the term diverges, the Buckingham potential "turns over" as becomes small. This may be problematic when dealing with a structure with very short interatomic distances, as the nuclei that cross the turn-over will become strongly (and unphysically) bound to one another at a distance of zero.[2]
References
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