9-6 Lennard-Jones potential: Difference between revisions

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(Corrected equation (r_m not sigma))
(Added Eq in terms of sigma)
 
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:<math> \Phi_{12}(r) = \epsilon  \left[ 2\left(\frac{r_m}{r} \right)^{9} -  3\left( \frac{r_m}{r}\right)^6 \right] </math>
:<math> \Phi_{12}(r) = \epsilon  \left[ 2\left(\frac{r_m}{r} \right)^{9} -  3\left( \frac{r_m}{r}\right)^6 \right] </math>
or in terms of <math> \sigma </math> (the value of <math>r</math> at which <math> \Phi_{12}(r)=0</math>) one has:
:<math> \Phi_{12}(r) = 6.75 \epsilon  \left[ \left(\frac{\sigma}{r} \right)^{9} -  \left( \frac{\sigma}{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> r_m </math> is the  distance, <math>r</math>, at which <math> \Phi_{12}(r)</math> is a minimum.
* <math> r_m </math> is the  distance, <math>r</math>, at which <math> \Phi_{12}(r)</math> is a minimum, which corresponds to <math> r_m =    1.5^{1/3} \sigma</math>.
* <math> \epsilon </math> is the well depth (energy)
* <math> \epsilon </math> is the well depth (energy)



Latest revision as of 13:41, 4 February 2014

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] :

or in terms of (the value of at which ) one has:

where

  • is the intermolecular pair potential between two particles or sites
  • is the distance, , at which is a minimum, which corresponds to .
  • 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.

References[edit]