# bond_style lepton command

Accelerator Variants: *lepton/omp*

## Syntax

``` LAMMPS
bond_style lepton
```

## Examples

``` LAMMPS
bond_style lepton

bond_coeff  1  1.5 "k*r^2; k=250.0"
bond_coeff  2  1.1 "k2*r^2 + k3*r^3 + k4*r^4; k2=300.0; k3=-100.0; k4=50.0"
bond_coeff  3  1.3 "k*r^2; k=350.0"
```

## Description

::: versionadded
8Feb2023
:::

Bond style *lepton* computes bonded interactions between two atoms with
a custom function. The potential function must be provided as an
expression string using \"r\" as the distance variable relative to the
reference distance $r_0$ which is provided as a bond coefficient. For
example [\"200.0\*r\^2\"]{.title-ref} represents a harmonic potential
with a force constant *K* of 200.0 energy units:

$$U_{bond,i} = K (r_i - r_0)^2 = K r^2 \qquad r = r_i - r_0$$

The [Lepton library](https://simtk.org/projects/lepton)\_, that the
*lepton* bond 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 atom pairs
forming bonds as defined by the topology data.

The following coefficients must be defined for each bond type via the
[bond_coeff](bond_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)
-   $r_0$ (distance)

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 $r_0$ is the \"equilibrium
distance\". The potential energy function in the Lepton expression is
shifted in such a way, that the potential energy is 0 for a bond length
$r_i == r_0$.

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

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.

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

## Restrictions

This bond style is 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.

## Related commands

[bond_coeff](bond_coeff), [bond_style table](bond_table),
[bond_write](bond_write), [angle_style lepton](angle_lepton),
[dihedral_style lepton](dihedral_lepton)

## Default

none