~~NOTOC~~
====== Pair Potentials ======
----

The most simple interaction that can be used are pair potentials.
They are assumed to be isotropic, i.e. they only depend on the pair distance
$r_{ij}=|\boldsymbol{r}_j-\boldsymbol{r}_i|$ of the two atoms $i$ and $j$. The potential energy for a system
described by pair interactions is given as
$$  E_\text{total} = \frac{1}{2} \sum_{i\neq j}V_2(\boldsymbol{r}_i,\boldsymbol{r}_j) = \sum_{i<j}V_2(r_{ij}) $$
and the force $\boldsymbol{F}_i$, acting on atom $i$, as
$$  \boldsymbol{F}_i = - \sum_{j}\nabla_iV_2(r_{ij}).$$
  
=====  Tabulated Pair Potentials  =====

For use in //potfit//, the potential function $V_2$ needs to be specified at a limited number of 
sampling points. Position and value of these sampling points are given in the file 
specified with the parameter ''potfile''. The format used in this file is described 
[[potfiles:main|here]]. It is essential that the potential is tabulated equidistant 
in the the atom distance, not in the square (as it is done in 
[[http://imd.itap.physik.uni-stuttgart.de/|IMD]]). Note that if the potential does not 
extend to radii small enough to cover all pair distances appearing in the configurations, 
the program will exit with a short distance error.

=====  Analytic Pair Potentials  =====

In order to use analytic potentials in //potfit//, the potential function $V_2$ has to be
specified by a functional name and the values of its parameters in the potential file. 
The format used in this file is described [[potfiles:main|here]]. With analytic potentials 
there is also the option to add an additional energy term to the fit, the so called chemical potential.

====  Chemical Potentials  ====

For fitting simple pair potentials the use of the chemical potentials will always be disabled unless the ''enable_cp'' switch in the parameter file is set to 1.
This option effectively adds a second energy term into the calculations, the energy will be calculated as

$$E_{tot}=\sum_{\text{species}}\mu_iN_i,+\sum_{\text{pairs}}V(r)$$

With this feature enabled, the potential file has to be altered, an additional block with the chemical potentials $\mu_i$ has to be added right after the header.

<code potfit>
#F 0 3
#C Mg Zn
#I 0 0 0
#E

cp_Mg -1 -10 0
cp_Zn -1 -10 0
</code>

There has to be one line per element, starting with ''cp_'', the rest of the name will be replaced by the element name (if the ''#C'' line is available) or the element number.
The following three values are the starting value, the minimum and maximum for that parameter.

**This feature is only available for analytic pair potentials.**

=====  Number of potential functions  =====

To describe a system with $N$ atom types you need $N(N+1)/2$ potentials.

^ $N$ ^ $N(N+1)/2$ ^
| 1 | 1 |
| 2 | 3 |
| 3 | 6 |

=====  Order of potential functions  =====

The potential table is assumed to be symmetric, i.e. the potential for the atom types 1-0 is the same as the potential 0-1.

The order of the pair potentials in the potential file for $N$ atom types is:

$\Phi_{00}, \ldots, \Phi_{0N}, \Phi_{11}, \ldots, \Phi_{1N}, \ldots, \Phi_{NN}$