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--- models:analytic [2018/09/16 10:49] – ↷ Links adapted because of a move operation daniel
+++ models:analytic [2019/02/23 09:52] (current) – daniel
@@ Line 3: / Line 3: @@
 ----
-Analytic potentials can be enabled in //potfit// by compiling it with the ''apot'' switch.
+Analytic potentials use the parameters $\alpha_i$ as arguments to analytic function templates.
-There are some additional options for analytic potentials like the chemical potentials or the smooth cutoff.
+A well-known example for this would be the Lennard-Jones potential, which uses two parameters $\epsilon$ and $\sigma$ to define a potential:
-====  Global parameters  ====
+$$V(r)=4\varepsilon\left[\left(\frac{\sigma}{r}\right)^{12}-\left(\frac{\sigma}{r}\right)^{6}\right]$$
-//potfit// supports global parameters, which can occur in different potentials. With this feature it is possible for any potential to "share" parameters with each other.
+{{ :analytic.png?300 }}
-To use them, you need a section called ''global n'' after the header in your potential file, where ''n'' is the number of global parameters.
-The format for the parameters is the same as for normal parameters: ''name value min max''.
-If you want to use a global parameter in a potential, use the name of the global parameter and add an exclamation mark.
-<code potfit>
+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.
-#F 0 3
-#C Mg Zn
-#I 0 0 0
-#E
-global 2
-glob1 1 0 2
-glob2 2 0 5
-type lj
-cutoff 8
-glob1!
-glob2!
-type lj
-cutoff 8
-glob2!
-glob1!
-</code>
-====  Smooth Cutoff  ====
-The smooth cutoff function is very important for analytic potentials since it ensures that the
-potential and its gradient vanish at the desired cutoff radius.
-Therefore the potential is multiplied with a cutoff function $\Psi$.
-$$V_{SC}(r)=\Psi\left(\frac{r-r_c}{h}\right)V(r)\qquad\text{where}\qquad\Psi(x)=\frac{x^4}{1+x^4}$$
-To enable the smooth cutoff for a potential, ''_sc'' has to be added to the potential identifier.
-<code potfit>
-type lj_sc
-cutoff 7
-epsilon 0.1 0 1
-sigma 2.5 1 4
-h 1 0 2
-</code>
-Potentials fitted with the ''_sc'' option will have an additional parameter ''h'' at the end.
-If you omit it, it will be kept fixed at a value of 1.
-====  Implemented Potential Functions  ====
-The currently implemented analytic potential functions can be found [[:analytic_functions|here]].
-====  Adding New Potential Functions  ====
-If you want to add other analytic potentials see [[:add_new_functions|this guide]].
+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.