# fix polarize/functional command¶

## Syntax¶

fix ID group-ID style nevery tolerance ...

• ID, group-ID are documented in fix command

• style = polarize/bem/gmres or polarize/bem/icc or polarize/functional

• Nevery = this fixed is invoked every this many timesteps

• tolerance = the tolerance for the iterative solver to stop

## Examples¶

fix 2 interface polarize/bem/gmres 5 0.0001
fix 1 interface polarize/bem/icc 1 0.0001
fix 3 interface polarize/functional 1 0.001


Used in input scripts:

examples/PACKAGES/dielectric/in.confined
examples/PACKAGES/dielectric/in.nopbc


## Description¶

These fixes compute induced charges at the interface between two impermeable media with different dielectric constants.

There are some example scripts for using this fix with LAMMPS in the examples/PACKAGES/dielectric directory.

For fix polarize/bem/gmres and fix polarize/bem/icc the induced charges of the atoms in the specified group, which are the vertices on the interface, are computed using the equation:

..math:

\sigma_b(\mathbf{s}) = \dfrac{1 - \bar{\epsilon}}{\bar{\epsilon}}
\sigma_f(\mathbf{s}) - \epsilon_0 \dfrac{\Delta \epsilon}{\bar{\epsilon}}
\mathbf{E}(\mathbf{s}) \cdot \mathbf{n}(\mathbf{s})

• $$\sigma_b$$ is the induced charge density at the interface vertex $$\mathbf{s}$$.

• $$\bar{\epsilon}$$ is the mean dielectric constant at the interface vertex: $$\bar{\epsilon} = (\epsilon_1 + \epsilon_2)/2$$.

• $$\Delta \epsilon$$ is the dielectric constant difference at the interface vertex: $$\Delta \epsilon = \epsilon_1 - \epsilon_2$$

• $$\sigma_f$$ is the free charge density at the interface vertex

• $$\mathbf{E}(\mathbf{s})$$ is the electrical field at the vertex

• $$\mathbf{n}(\mathbf{s})$$ is the unit normal vector at the vertex pointing from medium with $$\epsilon_2$$ to that with $$\epsilon_1$$

Fix polarize/bem/gmres employs the Generalized Minimum Residual (GMRES) as described in (Barros) to solve $$\sigma_b$$.

Fix polarize/bem/icc employs the successive over-relaxation algorithm as described in (Tyagi) to solve $$\sigma_b$$.

Fix polarize/functional

## Restrictions¶

These fixes are part of the DIELECTRIC package. It is only enabled if LAMMPS was built with that package, which requires that also the KSPACE package is installed. See the Build package page for more info.

## Default¶

None.

(Barros) Barros, Sinkovits, Luijten, J. Chem. Phys, 140, 064903 (2014)

(Tyagi) Tyagi, Suzen, Sega, Barbosa, Kantorovich, Holm, J Chem Phys, 132, 154112 (2010)

(Jadhao) Jadhao, Solis, Olvera de la Cruz, J Chem Phys, 138, 054119 (2013)

(NguyenTD) Nguyen, Li, Bagchi, Solis, Olvera de la Cruz, Comput Phys Commun 241, 80-19 (2019)