9-6 Lennard-Jones potential: Difference between revisions
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Carl McBride (talk | contribs) (New page: The '''9-6 Lennard-Jones potential''' (also known as the 6-9 potential) is a variant the more well known Lennard-Jones model. It is used for computing non-bonded interactions. The pote...) |
Carl McBride (talk | contribs) (Corrected equation (r_m not sigma)) |
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The '''9-6 Lennard-Jones potential''' (also known as the 6-9 potential) is a variant the more well known [[Lennard-Jones model]]. It is used for computing non-bonded interactions. The potential is given by <ref>[http://dx.doi.org/10.1063/1.1674031 Arieh Warshel and Shneior Lifson "Consistent Force Field Calculations. II. Crystal Structures, Sublimation Energies, Molecular and Lattice Vibrations, Molecular Conformations, and Enthalpies of Alkanes", Journal of Chemical Physics '''53''' pp. 582-594 (1970)]</ref> : | The '''9-6 Lennard-Jones potential''' (also known as the 6-9 potential) is a variant the more well known [[Lennard-Jones model]]. It is used for computing non-bonded interactions. The potential is given by <ref>[http://dx.doi.org/10.1063/1.1674031 Arieh Warshel and Shneior Lifson "Consistent Force Field Calculations. II. Crystal Structures, Sublimation Energies, Molecular and Lattice Vibrations, Molecular Conformations, and Enthalpies of Alkanes", Journal of Chemical Physics '''53''' pp. 582-594 (1970)]</ref> : | ||
:<math> \Phi_{12}(r) = \epsilon \left[ 2\left(\frac{ | :<math> \Phi_{12}(r) = \epsilon \left[ 2\left(\frac{r_m}{r} \right)^{9} - 3\left( \frac{r_m}{r}\right)^6 \right] </math> | ||
where | where | ||
* <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math> | * <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math> | ||
* <math> \Phi_{12}(r) </math> is the [[intermolecular pair potential]] between two particles or ''sites'' | * <math> \Phi_{12}(r) </math> is the [[intermolecular pair potential]] between two particles or ''sites'' | ||
* <math> | * <math> r_m </math> is the distance, <math>r</math>, at which <math> \Phi_{12}(r)</math> is a minimum. | ||
* <math> \epsilon </math> is the well depth (energy) | * <math> \epsilon </math> is the well depth (energy) | ||
Revision as of 12:38, 2 June 2011
The 9-6 Lennard-Jones potential (also known as the 6-9 potential) is a variant the more well known Lennard-Jones model. It is used for computing non-bonded interactions. The potential is given by [1] :
![{\displaystyle \Phi _{12}(r)=\epsilon \left[2\left({\frac {r_{m}}{r}}\right)^{9}-3\left({\frac {r_{m}}{r}}\right)^{6}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f4586c45272c1fe20c892c60666876adafd20a56)
where
- is the intermolecular pair potential between two particles or sites
- is the distance, , at which is a minimum.
- is the well depth (energy)
It is worth noting that the inclusion of an odd power (here the 9) adds an additional computational overhead, and the 8-6 Lennard-Jones potential has been suggested as a viable alternative.