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# fix numdiff/virial command

## Syntax

    fix ID group-ID numdiff/virial Nevery delta

- ID, group-ID are documented in 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

    fix 1 all numdiff/stress 10 1e-6

## Description

Added in version 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

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. None of the fix_modify options are relevant to this fix.

This fix produces a global vector which can be accessed by various output commands, 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 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.

No parameter of this fix can be used with the start/stop keywords of the run command. This fix is invoked during energy minimization.

## 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 page for more info.

## Related commands

fix numdiff, compute pressure

## Default

none