Recursively inseparable sets

2013-05-09T12:20:43Z

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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]]

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Recursively inseparable sets