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====== Analytic potentials ======
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Analytic potentials use the parameters $\alpha_i$ as arguments to analytic function templates.
A well-known example for this would be the Lennard-Jones potential, which uses two parameters $\epsilon$ and $\sigma$ to define a potential:

$$V(r)=4\varepsilon\left[\left(\frac{\sigma}{r}\right)^{12}-\left(\frac{\sigma}{r}\right)^{6}\right]$$ 

{{ :analytic.png?300 }}

Using an analytic form for $V(r)$ allows to define the atomic interaction for all possible distances between atoms with very few parameters compared to tabulated potentials. The problem of local parameters (see [[tabulated|Tabulated potentials]]) is also not present, parameters are usually global parameters. In certain cases it is even possible to attribute some physical meaning to individual parameters.

The analytic potential implementation in //potfit// has additional features which are only useful with this kind of interactions. They are described on the [[potfiles::format0|analytic format]] page.