# angle_style dipole command

Accelerator Variants: *dipole/omp*

## Syntax

``` LAMMPS
angle_style dipole
```

## Examples

``` LAMMPS
angle_style dipole
angle_coeff 6 2.1 180.0
```

## Description

The *dipole* angle style is used to control the orientation of a dipolar
atom within a molecule [(Orsi)](Orsi). Specifically, the *dipole* angle
style restrains the orientation of a point dipole $\mu_j$ (embedded in
atom $j$) with respect to a reference (bond) vector
$\vec{r}_{ij} = \vec{r}_i - \vec{r}_j$, where $i$ is another atom of the
same molecule (typically, $i$ and $j$ are also covalently bonded).

It is convenient to define an angle gamma between the \'free\' vector
$\vec{\mu}_j$ and the reference (bond) vector $\vec{r}_{ij}$:

$$\cos\gamma = \frac{\vec{\mu}_j\cdot\vec{r}_{ij}}{\mu_j\,r_{ij}}$$

The *dipole* angle style uses the potential:

$$E = K (\cos\gamma - \cos\gamma_0)^2$$

where $K$ is a rigidity constant and gamma0 is an equilibrium
(reference) angle.

The torque on the dipole can be obtained by differentiating the
potential using the \'chain rule\' as in appendix C.3 of
[(Allen)](Allen1):

$$\vec{T}_j = \frac{2K(\cos\gamma - \cos\gamma_0)}{\mu_j\,r_{ij}}\, \vec{r}_{ij} \times \vec{\mu}_j$$

Example: if $\gamma_0$ is set to 0 degrees, the torque generated by the
potential will tend to align the dipole along the reference direction
defined by the (bond) vector $\vec{r}_{ij}$ (in other words,
$\vec{\mu}_j$ is restrained to point towards atom $i$).

The dipolar torque $\vec{T}_j$ must be counterbalanced in order to
conserve the local angular momentum. This is achieved via an additional
force couple generating a torque equivalent to the opposite of
$\vec{T}_j$:

$$\begin{aligned}
-\vec{T}_j & = \vec{r}_{ij} \times \vec{F}_i \\
\vec{F}_j  & = -\vec{F}_i
\end{aligned}$$

where $\vec{F}_i$ and $\vec{F}_j$ are applied on atoms $i$ and $j$,
respectively.

The following coefficients must be defined for each angle type via the
[angle_coeff](angle_coeff) command as in the example above, or in the
data file or restart files read by the [read_data](read_data) or
[read_restart](read_restart) commands:

-   $K$ (energy)
-   $\gamma_0$ (degrees)

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

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](Speed_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](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](Run_options) when you invoke LAMMPS, or you can use the
[suffix](suffix) command in your input script.

See the [Accelerator packages](Speed_packages) page for more
instructions on how to use the accelerated styles effectively.

## Restrictions

This angle style can only be used if LAMMPS was built with the DIPOLE
package. See the [Build package](Build_package) doc page for more info.

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

In the \"Angles\" section of the data file, the atom ID $j$ defining the
direction of the dipole vector to restrain must come before the atom ID
of the reference atom $i$. A third atom ID $k$ must also be provided to
comply with the requirement of a valid angle definition. This atom ID
$k$ should be chosen to be that of an atom bonded to atom $i$ to avoid
errors with \"lost angle atoms\" when running in parallel. Since the
LAMMPS code checks for valid angle definitions, cannot use the same atom
ID of either $i$ or $j$ (this was allowed and recommended with older
LAMMPS versions).
::::

The [newton](newton) command for intramolecular interactions must be
\"on\" (which is the default except when using some accelerator
packages).

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

This angle style should **NOT** be used with fix shake.
::::

## Related commands

[angle_coeff](angle_coeff), [angle_hybrid](angle_hybrid)

## Default

none

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

::: {#Orsi}
**(Orsi)** Orsi & Essex, The ELBA force field for coarse-grain modeling
of lipid membranes, PloS ONE 6(12): e28637, 2011.
:::

::: {#Allen1}
**(Allen)** Allen & Tildesley, Computer Simulation of Liquids, Clarendon
Press, Oxford, 1987.
:::