# pair_style lepton command

Accelerator Variants: *lepton/omp*, *lepton/coul/comp*,
*lepton/sphere/comp*

## Syntax

``` LAMMPS
pair_style style args
```

-   style = *lepton* or *lepton/coul* or *lepton/sphere*
-   args = list of arguments for a particular style

<!-- -->

    *lepton* args = cutoff
      cutoff = global cutoff for the interactions (distance units)
    *lepton/coul* args = cutoff keyword
      cutoff = global cutoff for the interactions (distance units)
      zero or more keywords may be appended
      keyword = *ewald* or *pppm* or *msm* or *dispersion* or *tip4p*
    *lepton/sphere* args = cutoff
      cutoff = global cutoff for the interactions (distance units)

## Examples

``` LAMMPS
pair_style lepton 2.5

pair_coeff  * *  "k*((r-r0)^2*step(r0-r)); k=200; r0=1.5" 2.0
pair_coeff  1 2  "4.0*eps*((sig/r)^12 - (sig/r)^6);eps=1.0;sig=1.0" 1.12246204830937
pair_coeff  2 2  "eps*(2.0*(sig/r)^9 - 3.0*(sig/r)^6);eps=1.0;sig=1.0"
pair_coeff  1 3  "zbl(13,6,r)"
pair_coeff  3 3  "(1.0-switch)*zbl(6,6,r)-switch*4.0*eps*((sig/r)^6);switch=0.5*(tanh(10.0*(r-sig))+1.0);eps=0.05;sig=3.20723"

pair_style lepton/coul 2.5
pair_coeff 1 1 "qi*qj/r" 4.0
pair_coeff 1 2 "lj+coul; lj=4.0*eps*((sig/r)^12 - (sig/r)^6); eps=1.0; sig=1.0; coul=qi*qj/r"

pair_style lepton/coul 2.5 pppm
kspace_style pppm 1.0e-4
pair_coeff 1 1 "qi*qj/r*erfc(alpha*r); alpha=1.067"

pair_style lepton/sphere 2.5
pair_coeff 1 * "k*((r-r0)^2*step(r0-r)); k=200; r0=radi+radj"
pair_coeff 2 2 "4.0*eps*((sig/r)^12 - (sig/r)^6); eps=1.0; sig=2.0*sqrt(radi*radj)"
```

## Description

::: versionadded
8Feb2023

added pair styles *lepton* and *lepton/coul*
:::

::: versionchanged
15Jun2023

added pair style *lepton/sphere*
:::

Pair styles *lepton*, *lepton/coul*, *lepton/sphere* compute pairwise
interactions between particles which depend on the distance and have a
cutoff. The potential function must be provided as an expression string
using \"r\" as the distance variable. With pair style *lepton/coul* one
may additionally reference the charges of the two atoms of the pair with
\"qi\" and \"qj\", respectively. With pair style *lepton/coul* one may
instead reference the radii of the two atoms of the pair with \"radi\"
and \"radj\", respectively; this is half of the diameter that can be set
in [data files](read_data) or the [set command](set).

Note that further constants in the expressions can be defined in the
same string as additional expressions separated by semicolons as shown
in the examples above.

The expression [\"200.0\*(r-1.5)\^2\"]{.title-ref} represents a harmonic
potential around the pairwise distance $r_0$ of 1.5 distance units and a
force constant *K* of 200.0 energy units:

$$U_{ij} = K (r-r_0)^2$$

The expression [\"qi\*qj/r\"]{.title-ref} represents a regular Coulombic
potential with cutoff:

$$U_{ij} = \frac{C q_i q_j}{\epsilon  r} \qquad r < r_c$$

The expression [\"200.0\*(r-(radi+radj)\^2\"]{.title-ref} represents a
harmonic potential that has the equilibrium distance chosen so that the
radii of the two atoms touch:

$$U_{ij} = K (r-(r_i+r_j))^2$$

The [Lepton library](https://simtk.org/projects/lepton)\_, that the
*lepton* pair style interfaces with, evaluates this expression string at
run time to compute the pairwise energy. It also creates an analytical
representation of the first derivative of this expression with respect
to \"r\" and then uses that to compute the force between the pairs of
particles within the given cutoff.

The following coefficients must be defined for each pair of atoms types
via the [pair_coeff](pair_coeff) command as in the examples above, or in
the data file or restart files read by the [read_data](read_data) or
[read_restart](read_restart) commands:

-   Lepton expression (energy units)
-   cutoff (distance units)

The Lepton expression must be either enclosed in quotes or must not
contain any whitespace so that LAMMPS recognizes it as a single keyword.
More on valid Lepton expressions below. The last coefficient is
optional; it allows to set the cutoff for a pair of atom types to a
different value than the global cutoff.

For pair style *lepton* only the \"lj\" values of the
[special_bonds](special_bonds) settings apply in case the interacting
pair is also connected with a bond. The potential energy will *only* be
added to the \"evdwl\" property.

For pair style *lepton/coul* only the \"coul\" values of the
[special_bonds](special_bonds) settings apply in case the interacting
pair is also connected with a bond. The potential energy will *only* be
added to the \"ecoul\" property.

For pair style *lepton/sphere* only the \"lj\" values of the
[special_bonds](special_bonds) settings apply in case the interacting
pair is also connected with a bond. The potential energy will *only* be
added to the \"evdwl\" property.

In addition to the functions listed below, both pair styles support in
addition a custom \"zbl(zi,zj,r)\" function which computes the
Ziegler-Biersack-Littmark (ZBL) screened nuclear repulsion for
describing high-energy collisions between atoms. For details of the
function please see the documentation for [pair style zbl](pair_zbl).
The arguments of the function are the atomic numbers of atom i (zi),
atom j (zj) and the distance r. Please see the examples above.

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

Lepton expression syntax and features
\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"\"

Lepton supports the following operators in expressions:

The following mathematical functions are available:

Numbers may be given in either decimal or exponential form. All of the
following are valid numbers: [5]{.title-ref}, [-3.1]{.title-ref},
[1e6]{.title-ref}, and [3.12e-2]{.title-ref}.

As an extension to the standard Lepton syntax, it is also possible to
use LAMMPS [variables](variable) in the format \"v_name\". Before
evaluating the expression, \"v_name\" will be replaced with the value of
the variable \"name\". This is compatible with all kinds of scalar
variables, but not with vectors, arrays, local, or per-atom variables.
If necessary, a custom scalar variable needs to be defined that can
access the desired (single) item from a non-scalar variable. As an
example, the following lines will instruct LAMMPS to ramp the force
constant for a harmonic bond from 100.0 to 200.0 during the next run:

``` LAMMPS
variable fconst equal ramp(100.0, 200)
bond_style lepton
bond_coeff 1 1.5 "v_fconst * (r^2)"
```

An expression may be followed by definitions for intermediate values
that appear in the expression. A semicolon \";\" is used as a delimiter
between value definitions. For example, the expression:

``` C
a^2+a*b+b^2; a=a1+a2; b=b1+b2
```

is exactly equivalent to

``` C
(a1+a2)^2+(a1+a2)*(b1+b2)+(b1+b2)^2
```

The definition of an intermediate value may itself involve other
intermediate values. Whitespace and quotation characters (\'\'\' and
\'\"\') are ignored. All uses of a value must appear *before* that
value\'s definition. For efficiency reasons, the expression string is
parsed, optimized, and then stored in an internal, pre-parsed
representation for evaluation.

Evaluating a Lepton expression is typically between 2.5 and 5 times
slower than the corresponding compiled and optimized C++ code. If
additional speed or GPU acceleration (via GPU or KOKKOS) is required,
the interaction can be represented as a table. Suitable table files can
be created either internally using the [pair_write](pair_write) or
[bond_write](bond_write) command or through the Python scripts in the
[tools/tabulate](tabulate) folder.

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

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

Pair styles *lepton*, *lepton/coul*, and *lepton/sphere* do not support
mixing. Thus, expressions for *all* I,J pairs must be specified
explicitly.

Only pair style *lepton* supports the [pair_modify shift](pair_modify)
option for shifting the energy of the pair interaction so that it is 0
at the cutoff, pair styles *lepton/coul* and *lepton/sphere* do *not*.

The [pair_modify table](pair_modify) options are not relevant for the
these pair styles.

These pair styles do not support the [pair_modify tail](pair_modify)
option for adding long-range tail corrections to energy and pressure.

These pair styles write their information to [binary restart
files](restart), so pair_style and pair_coeff commands do not need to be
specified in an input script that reads a restart file.

These pair styles can only be used via the *pair* keyword of the
[run_style respa](run_style) command. They do not support the *inner*,
*middle*, *outer* keywords.

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

## Restrictions

These pair styles are part of the LEPTON package and only enabled if
LAMMPS was built with this package. See the [Build
package](Build_package) page for more info.

Pair style *lepton/coul* requires that atom atoms have a charge
property, e.g. via [atom_style charge](atom_style).

Pair style *lepton/sphere* requires that atom atoms have a radius
property, e.g. via [atom_style sphere](atom_style).

## Related commands

[pair_coeff](pair_coeff), [pair_style python](pair_python), [pair_style
table](pair_table), [pair_write](pair_write)

## Default

none