# bond_style quartic command

Accelerator Variants: *quartic/omp*

## Syntax

``` LAMMPS
bond_style quartic
```

## Examples

``` LAMMPS
bond_style quartic
bond_coeff 2 1200 -0.55 0.25 1.3 34.6878
```

## Description

The *quartic* bond style uses the potential

$$\begin{aligned}
E      & = E_q + E_{LJ} \\
E_q    & = K (r - R_c)^ 2 (r - R_c - B_1) (r - R_c - B_2) + U_0 \\
E_{LJ} & = \left\{ \begin{array} {l@{\quad:\quad}l}
4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^6 \right] + \epsilon & r < 2^{\frac{1}{6}}, \epsilon = 1, \sigma = 1 \\
                                               0 & r >= 2^{\frac{1}{6}}
                      \end{array} \right.
\end{aligned}$$

to define a bond that can be broken as the simulation proceeds (e.g. due
to a polymer being stretched). The $\sigma$ and $\epsilon$ used in the
LJ portion of the formula are both set equal to 1.0 by LAMMPS and the LJ
portion is cut off at its minimum, i.e. at $r_c = 2^{\frac{1}{6}}$.

The following coefficients must be defined for each bond type via the
[bond_coeff](bond_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/distance\^4)
-   $B_1$ (distance)
-   $B_2$ (distance)
-   $R_c$ (distance)
-   $U_0$ (energy)

This potential was constructed to mimic the FENE bond potential for
coarse-grained polymer chains. When monomers with $\sigma =
\epsilon = 1.0$ are used, the following choice of parameters gives a
quartic potential that looks nearly like the FENE potential:

$$\begin{aligned}
K &= 1200 \\
B_1 &= -0.55 \\
B_2 &= 0.25 \\
R_c &= 1.3 \\
U_0 &= 34.6878
\end{aligned}$$

Different parameters can be specified using the [bond_coeff](bond_coeff)
command, but you will need to choose them carefully so they form a
suitable bond potential.

$R_c$ is the cutoff length at which the bond potential goes smoothly to
a local maximum. If a bond length ever becomes $> R_c$, LAMMPS
\"breaks\" the bond, which means two things. First, the bond potential
is turned off by setting its type to 0, and is no longer computed.
Second, a pairwise interaction between the two atoms is turned on, since
they are no longer bonded. See the [Howto](Howto_broken_bonds) page on
broken bonds for more information.

LAMMPS does the second task via a computational sleight-of-hand. It
subtracts the pairwise interaction as part of the bond computation. When
the bond breaks, the subtraction stops. For this to work, the pairwise
interaction must always be computed by the [pair_style](pair_style)
command, whether the bond is broken or not. This means that
[special_bonds](special_bonds) must be set to 1,1,1, as indicated as a
restriction below.

Note that when bonds are dumped to a file via the [dump local](dump)
command, bonds with type 0 are not included. The
[delete_bonds](delete_bonds) command can also be used to query the
status of broken bonds or permanently delete them, e.g.:

``` LAMMPS
delete_bonds all stats
delete_bonds all bond 0 remove
```

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

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 can only be used if LAMMPS was built with the MOLECULE
package. See the [Build package](Build_package) page for more info.

The *quartic* style requires that [special_bonds](special_bonds)
parameters be set to 1,1,1. Three- and four-body interactions (angle,
dihedral, etc) cannot be used with *quartic* bonds.

## Related commands

[bond_coeff](bond_coeff), [delete_bonds](delete_bonds)

## Default

none