# fix numdiff/virial command

## Syntax

    fix ID group-ID numdiff/virial Nevery delta

-   ID, group-ID are documented in [fix](fix) command
-   numdiff/virial = style name of this fix command
-   Nevery = calculate virial by finite difference every this many
    timesteps
-   delta = magnitude of strain fields (dimensionless)

## Examples

``` LAMMPS
fix 1 all numdiff/stress 10 1e-6
```

## Description

::: versionadded
17Feb2022
:::

Calculate the virial stress tensor through a finite difference
calculation of energy versus strain. These values can be compared to the
analytic virial tensor computed by pair styles, bond styles, etc. This
can be useful for debugging or other purposes. The specified group must
be \"all\".

This fix applies linear strain fields of magnitude *delta* to all the
atoms relative to a point at the center of the box. The strain fields
are in six different directions, corresponding to the six Cartesian
components of the stress tensor defined by LAMMPS. For each direction it
applies the strain field in both the positive and negative senses, and
the new energy of the entire system is calculated after each. The
difference in these two energies divided by two times *delta*,
approximates the corresponding component of the virial stress tensor,
after applying a suitable unit conversion.

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

It is important to choose a suitable value for delta, the magnitude of
strains that are used to generate finite difference approximations to
the exact virial stress. For typical systems, a value in the range of 1
part in 1e5 to 1e6 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 values will vary erratically due to truncation
effects. If delta is increased beyond a certain point, the output values
will start to vary smoothly with delta, due to growing contributions
from higher order derivatives. In between these two limits, the
numerical virial values should be largely independent of delta.
::::

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

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 global vector which can be accessed by various
[output commands](Howto_output), which stores the components of the
virial stress tensor as calculated by finite difference. The global
vector can only be accessed on timesteps that are multiples of *Nevery*
since that is when the finite difference virial is calculated. See the
examples in *examples/numdiff* directory to see how this fix can be used
to directly compare with the analytic virial stress tensor computed by
LAMMPS.

The order of the virial stress tensor components is *xx*, *yy*, *zz*,
*yz*, *xz*, and *xy*, consistent with Voigt notation. Note that the
vector produced by [compute pressure](compute_pressure) uses a different
ordering, with *yz* and *xy* swapped.

The vector values calculated by this compute are \"intensive\". The
vector values will be in pressure [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

[fix numdiff](fix_numdiff), [compute pressure](compute_pressure)

## Default

none