# pair_style zbl command

Accelerator Variants: *zbl/gpu*, *zbl/kk*, *zbl/omp*

## Syntax

``` LAMMPS
pair_style zbl inner outer
```

-   inner = distance where switching function begins
-   outer = global cutoff for ZBL interaction

## Examples

``` LAMMPS
pair_style zbl 3.0 4.0
pair_coeff * * 73.0 73.0
pair_coeff 1 1 14.0 14.0
```

## Description

Style *zbl* computes the Ziegler-Biersack-Littmark (ZBL) screened
nuclear repulsion for describing high-energy collisions between atoms.
[(Ziegler)](Ziegler). It includes an additional switching function that
ramps the energy, force, and curvature smoothly to zero between an inner
and outer cutoff. The potential energy due to a pair of atoms at a
distance r_ij is given by:

$$\begin{aligned}
E^{ZBL}_{ij} & = \frac{1}{4\pi\epsilon_0} \frac{Z_i Z_j \,e^2}{r_{ij}} \phi(r_{ij}/a)+ S(r_{ij})\\
a & =  \frac{0.46850}{Z_{i}^{0.23} + Z_{j}^{0.23}}\\
\phi(x) & =  0.18175e^{-3.19980x} + 0.50986e^{-0.94229x} + 0.28022e^{-0.40290x} + 0.02817e^{-0.20162x}\\
\end{aligned}$$

where *e* is the electron charge, $\epsilon_0$ is the electrical
permittivity of vacuum, and $Z_i$ and $Z_j$ are the nuclear charges of
the two atoms. The switching function $S(r)$ is identical to that used
by [pair_style lj/gromacs](pair_gromacs). Here, the inner and outer
cutoff are the same for all pairs of atom types.

The following coefficients must be defined for each pair of atom types
via the [pair_coeff](pair_coeff) command as in the examples above, or in
the LAMMPS data file.

-   $Z_i$ (atomic number for first atom type, e.g. 13.0 for aluminum)
-   $Z_j$ (ditto for second atom type)

The values of $Z_i$ and $Z_j$ are normally equal to the atomic numbers
of the two atom types. Thus, the user may optionally specify only the
coefficients for each $i==i$ pair, and rely on the obvious mixing rule
for cross interactions (see below). Note that when $i==i$ it is required
that $Z_i == Z_j$. When used with [hybrid/overlay](pair_hybrid) and
pairs are assigned to more than one sub-style, the mixing rule is not
used and each pair of types interacting with the ZBL sub-style must be
included in a pair_coeff command.

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

The numerical values of the exponential decay constants in the screening
function depend on the unit of distance. In the above equation they are
given for units of Angstroms. LAMMPS will automatically convert these
values to the distance unit of the specified LAMMPS [units](units)
setting. The values of Z should always be given as multiples of a
proton\'s charge, e.g. 29.0 for copper.
::::

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

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.

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

## Mixing, shift, table, tail correction, restart, rRESPA info

For atom type pairs *i,j* and $i \neq i$, the $Z_i$ and $Z_j$
coefficients can be mixed by taking $Z_i$ and $Z_j$ from the values
specified for $i == i$ and $j == j$ cases. When used with
[hybrid/overlay](pair_hybrid) and pairs are assigned to more than one
sub-style, the mixing rule is not used and each pair of types
interacting with the ZBL sub-style must be included in a pair_coeff
command. The [pair_modify](pair_modify) mix option has no effect on the
mixing behavior

The ZBL pair style does not support the [pair_modify](pair_modify) shift
option, since the ZBL interaction is already smoothed to 0.0 at the
cutoff.

The [pair_modify](pair_modify) table option is not relevant for this
pair style.

This pair style does not support the [pair_modify](pair_modify) tail
option for adding long-range tail corrections to energy and pressure,
since there are no corrections for a potential that goes to 0.0 at the
cutoff.

This pair style does not write information to [binary restart
files](restart), so pair_style and pair_coeff commands must be specified
in an input script that reads a restart file.

This pair style can only be used via the *pair* keyword of the
[run_style respa](run_style) command. It does not support the *inner*,
*middle*, *outer* keywords.

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

## Restrictions

> none

## Related commands

[pair_coeff](pair_coeff)

## Default

none

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

::: {#Ziegler}
**(Ziegler)** J.F. Ziegler, J. P. Biersack and U. Littmark, \"The
Stopping and Range of Ions in Matter\", Volume 1, Pergamon, 1985.
:::