\(\renewcommand{\AA}{\text{Å}}\)

# fix numdiff command

## Syntax

    fix ID group-ID numdiff Nevery delta

- ID, group-ID are documented in 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

    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

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

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

This fix produces a per-atom array which can be accessed by various output commands, 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.

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

dynamical_matrix, fix numdiff/virial,

## Default

none