# fix spring command

## Syntax

    fix ID group-ID spring keyword values

-   ID, group-ID are documented in [fix](fix) command

-   spring = style name of this fix command

-   keyword = *tether* or *couple*

        *tether* values = K x y z R0
          K = spring constant (force/distance units)
          x,y,z = point to which spring is tethered
          R0 = equilibrium distance from tether point (distance units)
        *couple* values = group-ID2 K x y z R0
          group-ID2 = 2nd group to couple to fix group with a spring
          K = spring constant (force/distance units)
          x,y,z = direction of spring
          R0 = equilibrium distance of spring (distance units)

## Examples

``` LAMMPS
fix pull ligand spring tether 50.0 0.0 0.0 0.0 0.0
fix pull ligand spring tether 50.0 0.0 0.0 0.0 5.0
fix pull ligand spring tether 50.0 NULL NULL 2.0 3.0
fix 5 bilayer1 spring couple bilayer2 100.0 NULL NULL 10.0 0.0
fix longitudinal pore spring couple ion 100.0 NULL NULL -20.0 0.0
fix radial pore spring couple ion 100.0 0.0 0.0 NULL 5.0
```

## Description

Apply a spring force to a group of atoms or between two groups of atoms.
This is useful for applying an umbrella force to a small molecule or
lightly tethering a large group of atoms (e.g. all the solvent or a
large molecule) to the center of the simulation box so that it does not
wander away over the course of a long simulation. It can also be used to
hold the centers of mass of two groups of atoms at a given distance or
orientation with respect to each other.

The *tether* style attaches a spring between a fixed point *x,y,z* and
the center of mass of the fix group of atoms. The equilibrium position
of the spring is R0. At each timestep the distance R from the center of
mass of the group of atoms to the tethering point is computed, taking
account of wrap-around in a periodic simulation box. A restoring force
of magnitude K (R - R0) Mi / M is applied to each atom in the group
where *K* is the spring constant, Mi is the mass of the atom, and M is
the total mass of all atoms in the group. Note that *K* thus represents
the spring constant for the total force on the group of atoms, not for a
spring applied to each atom.

The *couple* style links two groups of atoms together. The first group
is the fix group; the second is specified by group-ID2. The groups are
coupled together by a spring that is at equilibrium when the two groups
are displaced by a vector *x,y,z* with respect to each other and at a
distance R0 from that displacement. Note that *x,y,z* is the equilibrium
displacement of group-ID2 relative to the fix group. Thus (1,1,0) is a
different spring than (-1,-1,0). When the relative positions and
distance between the two groups are not in equilibrium, the same spring
force described above is applied to atoms in each of the two groups.

For both the *tether* and *couple* styles, any of the x,y,z values can
be specified as NULL which means do not include that dimension in the
distance calculation or force application.

The first example above pulls the ligand towards the point (0,0,0). The
second example holds the ligand near the surface of a sphere of radius 5
around the point (0,0,0). The third example holds the ligand a distance
3 away from the z=2 plane (on either side).

The fourth example holds 2 bilayers a distance 10 apart in z. For the
last two examples, imagine a pore (a slab of atoms with a cylindrical
hole cut out) oriented with the pore axis along z, and an ion moving
within the pore. The fifth example holds the ion a distance of -20 below
the z = 0 center plane of the pore (umbrella sampling). The last example
holds the ion a distance 5 away from the pore axis (assuming the
center-of-mass of the pore in x,y is the pore axis).

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

The center of mass of a group of atoms is calculated in \"unwrapped\"
coordinates using atom image flags, which means that the group can
straddle a periodic boundary. See the [dump](dump) doc page for a
discussion of unwrapped coordinates. It also means that a spring
connecting two groups or a group and the tether point can cross a
periodic boundary and its length be calculated correctly.
::::

## Restart, fix_modify, output, run start/stop, minimize info

No information about this fix is written to [binary restart
files](restart).

The [fix_modify](fix_modify) *energy* option is supported by this fix to
add the energy stored in the spring to the global potential energy of
the system as part of [thermodynamic output](thermo_style). The default
setting for this fix is [fix_modify energy no](fix_modify).

The [fix_modify](fix_modify) *respa* option is supported by this fix.
This allows to set at which level of the [r-RESPA](run_style) integrator
the fix is adding its forces. Default is the outermost level.

This fix computes a global scalar which can be accessed by various
[output commands](Howto_output). The scalar is the spring energy = 0.5
\* K \* r\^2.

This fix also computes global 4-vector which can be accessed by various
[output commands](Howto_output). The first 3 quantities in the vector
are xyz components of the total force added to the group of atoms by the
spring. In the case of the *couple* style, it is the force on the fix
group (group-ID) or the negative of the force on the second group
(group-ID2). The fourth quantity in the vector is the magnitude of the
force added by the spring, as a positive value if (r-R0) \> 0 and a
negative value if (r-R0) \< 0. This sign convention can be useful when
using the spring force to compute a potential of mean force (PMF).

The scalar and vector values calculated by this fix are \"extensive\".

No parameter of this fix can be used with the *start/stop* keywords of
the [run](run) command.

The forces due to this fix are imposed during an energy minimization,
invoked by the [minimize](minimize) command.

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

If you want the spring energy to be included in the total potential
energy of the system (the quantity being minimized), you MUST enable the
[fix_modify](fix_modify) *energy* option for this fix.
::::

## Restrictions

> none

## Related commands

[fix drag](fix_drag), [fix spring/self](fix_spring_self), [fix
spring/rg](fix_spring_rg), [fix smd](fix_smd)

## Default

none