# fix numdiff command

## Syntax

    fix ID group-ID numdiff Nevery delta

-   ID, group-ID are documented in [fix](fix) command
-   numdiff = style name of this fix command
-   Nevery = calculate force by finite difference every this many
    timesteps
-   delta = size of atom displacements (distance units)

## Examples

``` LAMMPS
fix 1 all numdiff 10 1e-6
fix 1 movegroup numdiff 100 0.01
```

## Description

Calculate forces through finite difference calculations of energy versus
position. These forces can be compared to analytic forces computed by
pair styles, bond styles, etc. This can be useful for debugging or other
purposes.

The group specified with the command means only atoms within the group
have their averages computed. Results are set to 0.0 for atoms not in
the group.

This fix performs a loop over all atoms in the group. For each atom and
each component of force it adds *delta* to the position, and computes
the new energy of the entire system. It then subtracts *delta* from the
original position and again computes the new energy of the system. It
then restores the original position. That component of force is
calculated as the difference in energy divided by two times *delta*.

:::: note
::: title
Note
:::

It is important to choose a suitable value for delta, the magnitude of
atom displacements that are used to generate finite difference
approximations to the exact forces. For typical systems, a value in the
range of 1 part in 1e4 to 1e5 of the typical separation distance between
atoms in the liquid or solid state will be sufficient. However, the best
value will depend on a multitude of factors including the stiffness of
the interatomic potential, the thermodynamic state of the material being
probed, and so on. The only way to be sure that you have made a good
choice is to do a sensitivity study on a representative atomic
configuration, sweeping over a wide range of values of delta. If delta
is too small, the output forces will vary erratically due to truncation
effects. If delta is increased beyond a certain point, the output forces
will start to vary smoothly with delta, due to growing contributions
from higher order derivatives. In between these two limits, the
numerical force values should be largely independent of delta.
::::

:::: note
::: title
Note
:::

The cost of each energy evaluation is essentially the cost of an MD
timestep. Thus invoking this fix once for a 3d system has a cost of 6N
timesteps, where N is the total number of atoms in the system. So this
fix can be very expensive to use for large systems. One expedient
alternative is to define the fix for a group containing only a few
atoms.
::::

------------------------------------------------------------------------

The *Nevery* argument specifies on what timesteps the force will be used
calculated by finite difference.

The *delta* argument specifies the size of the displacement each atom
will undergo.

------------------------------------------------------------------------

## Restart, fix_modify, output, run start/stop, minimize info

No information about this fix is written to [binary restart
files](restart). None of the [fix_modify](fix_modify) options are
relevant to this fix.

This fix produces a per-atom array which can be accessed by various
[output commands](Howto_output), which stores the components of the
force on each atom as calculated by finite difference. The per-atom
values can only be accessed on timesteps that are multiples of *Nevery*
since that is when the finite difference forces are calculated. See the
examples in *examples/numdiff* directory to see how this fix can be used
to directly compare with the analytic forces computed by LAMMPS.

The array values calculated by this compute will be in force
[units](units).

No parameter of this fix can be used with the *start/stop* keywords of
the [run](run) command. This fix is invoked during [energy
minimization](minimize).

## Restrictions

This fix is part of the EXTRA-FIX package. It is only enabled if LAMMPS
was built with that package. See the [Build package](Build_package) page
for more info.

## Related commands

[dynamical_matrix](dynamical_matrix), [fix
numdiff/virial](fix_numdiff_virial),

## Default

none