\(\renewcommand{\AA}{\text{Å}}\)

# third_order command

Accelerator Variant: third_order/kk

## Syntax

    third_order group-ID style delta args keyword value ...

- group-ID = ID of group of atoms to displace

- style = regular or eskm

- delta = finite different displacement length (distance units)

- one or more keyword/arg pairs may be appended

      keyword = file or binary
        file name = name of output file for the third order tensor
        binary arg = yes or no or gzip

## Examples

    third_order 1 regular 0.000001
    third_order 1 eskm 0.000001
    third_order 3 regular 0.00004 file third_order.dat
    third_order 5 eskm 0.00000001 file third_order.dat binary yes

## Description

Calculate the third order force constant tensor by finite difference of the selected group,

\[\Phi^{\alpha\beta\gamma}_{ijk} = \frac{\partial^3 U}{\partial x_{i,\alpha} \partial x_{j,\beta} \partial x_{k, \gamma}}\]

where Phi is the third order force constant tensor.

The output of the command is the tensor, three elements at a time. The three elements correspond to the three gamma elements for a specific i/alpha/j/beta/k. The initial five numbers are i, alpha, j, beta, and k respectively.

If the style eskm is selected, the tensor will be using energy units of 10 J/mol. These units conform to eskm style from the dynamical_matrix command, which will simplify operations using dynamical matrices with third order tensors.

Styles with a gpu, intel, kk, omp, or opt suffix are functionally the same as the corresponding style without the suffix. They have been optimized to run faster, depending on your available hardware, as discussed on the Accelerator packages page. The accelerated styles take the same arguments and should produce the same results, except for round-off and precision issues.

These accelerated styles are part of the GPU, INTEL, KOKKOS, OPENMP, and OPT packages, respectively. They are only enabled if LAMMPS was built with those packages. See the Build package page for more info.

You can specify the accelerated styles explicitly in your input script by including their suffix, or you can use the -suffix command-line switch when you invoke LAMMPS, or you can use the suffix command in your input script.

See the Accelerator packages page for more instructions on how to use the accelerated styles effectively.

## Restrictions

The command collects a 9 times the number of atoms in the group on every single MPI rank, so the memory requirements can be very significant for large systems.

This command is part of the PHONON package. It is only enabled if LAMMPS was built with that package. See the Build package page for more info.

## Related commands

fix phonon dynamical_matrix

## Default

The default settings are file = “third_order.dat”, binary = no