Fermi-Jagla model: Difference between revisions
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Carl McBride (talk | contribs) (Created page with "The '''Fermi-Jagla model''' is a smooth variant of the Jagla model. It is given by (Eq. 1 in <ref>[http://dx.doi.org/10.1021/jp205098a Joel Y. Abraham, Sergey...") |
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:<math>\Phi_{12}(r) = \epsilon_0 \left[ \left( \frac{a}{r} \right)^n + \frac{A_0}{1+\exp \left[ \frac{A_1}{A_0} \frac{r}{a-A_2} \right]} - \frac{B_0}{1+\exp \left[ \frac{B_1}{B_0} \frac{r}{a-B_2} \right]} \right]</math> | :<math>\Phi_{12}(r) = \epsilon_0 \left[ \left( \frac{a}{r} \right)^n + \frac{A_0}{1+\exp \left[ \frac{A_1}{A_0} \frac{r}{a-A_2} \right]} - \frac{B_0}{1+\exp \left[ \frac{B_1}{B_0} \frac{r}{a-B_2} \right]} \right]</math> | ||
There is a relation between Fermi function and hyperbolic tangent: | |||
:<math>\frac{1}{1+e^x}=\frac{1}{2}-\frac{1}{2}tanh(x/2)</math> | |||
Using this relation one can deduce Fermi-Jagla model to Fomin potential introduced earlier and described in another section of this site. | |||
==References== | ==References== | ||
Revision as of 19:42, 22 January 2014
The Fermi-Jagla model is a smooth variant of the Jagla model. It is given by (Eq. 1 in [1]):
![{\displaystyle \Phi _{12}(r)=\epsilon _{0}\left[\left({\frac {a}{r}}\right)^{n}+{\frac {A_{0}}{1+\exp \left[{\frac {A_{1}}{A_{0}}}{\frac {r}{a-A_{2}}}\right]}}-{\frac {B_{0}}{1+\exp \left[{\frac {B_{1}}{B_{0}}}{\frac {r}{a-B_{2}}}\right]}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e44449caa9a8f37cb2ead06142358c54adcf6a79)
There is a relation between Fermi function and hyperbolic tangent:
Using this relation one can deduce Fermi-Jagla model to Fomin potential introduced earlier and described in another section of this site.
References
- Related reading