~~NOTOC~~
====== Potential File Format 4 ======

-----

===== Format specification =====

The potential formats 3 and 4 are used for tabulated potentials. Format 4 allows arbitrary sampling points for the potential function tables and supports all header lines. 

As with potential files in format 3 each data column has its own spacing. But with potential format 
4 the requirement that the sampling points be equidistant is dropped. Arbitrarily spaced sampling 
points are possible, but the sampling points have to be given in ascending order.

== Header ==

All potential files need a header block at the beginning, which is described in detail here: [[potfiles:main|Potential files]].

== Sampling points block ==

Preceding the data columns is a block with one line per potential, containing the number of sampling 
points in the corresponding potential. 

Here is an example for a pair potential for two atom types, which requires three potential functions:
<code>
## last header line
#E

15
15
15
</code>

== Function tables ==

Seperated by blank lines then the data columns follow. Each of the tables has the form
<code>
r_0     f(r_0)
r_1     f(r_1)
...
r_steps f(r_steps)
</code>

Please note that $r_0 < r_1 < \ldots < r_{steps}$ is required. The order of the columns is the same 
as with format 3.

Similarly as for format 3, for potential functions that are a function of distance (e.g. pair potentials, EAM transfer functions), a smooth cutoff at the final sampling value is assumed and the value is not varied.

If the ''#G'' header line is specified, each function table must be preceded by two values specifying the 
gradient of the function at the lower and upper boundaries. A value of $10^{30}$ or greater triggers the 
usage of natural splines (curvature 0 at boundaries). You should not make the gradient variable at 
boundaries where natural splines are specified. This will lead to undesired results.

-----

===== Examples =====

A sample format 4 potential file for a binary system (EAM potential) is available 
{{:format_4g.pot.txt|here}} (with the ''#G'' header line).

And here is a very simple pair potential for a monoatomic system. All lines starting with ''##'' are comments and can be removed.
<code>
## This is the header
## F -- this is the Format line
## 4 -- this is the Format number
## 1 -- this is the number of potentials in this file
#F 4 1
## E -- this is the End of the header
#E

## Sampling points block
## There needs to be one line with the number of sampling points for each potential (1 in this example)
14

## Function tables
## One function table for each potential (1 in this example)
## The number of lines must be equal to the number provided in the respective line in the distance block (14 in this example)
## Each line has two values, the distance and the potential value
## The first and the last line define the range of the potential
2.7785714285714285e+00 8.4255614529302880e-01
3.2571428571428571e+00 2.0271471509245159e-01
3.7357142857142858e+00 2.2155522312087100e-02
4.2142857142857144e+00 -6.8303638148139376e-02
4.6928571428571431e+00 -4.9043278969706922e-02
5.1714285714285717e+00 -1.0946697911942214e-02
5.6500000000000004e+00 -1.0298525723152156e-02
6.1285714285714290e+00 -6.5685589306463460e-03
6.6071428571428577e+00 -2.0283626156443295e-03
7.0857142857142854e+00 1.2197714420628298e-02
7.5642857142857141e+00 2.2148801387662245e-02
8.0428571428571427e+00 1.4461939319528331e-02
8.5214285714285722e+00 9.9020972820913523e-03
9.0000000000000000e+00 0.0000000000000000e+00
</code>