# fix spring/rg command

## Syntax

    fix ID group-ID spring/rg K RG0

-   ID, group-ID are documented in [fix](fix) command
-   spring/rg = style name of this fix command
-   K = harmonic force constant (force/distance units)
-   RG0 = target radius of gyration to constrain to (distance units)

<!-- -->

    if RG0 = NULL, use the current RG as the target value

## Examples

``` LAMMPS
fix 1 protein spring/rg 5.0 10.0
fix 2 micelle spring/rg 5.0 NULL
```

## Description

Apply a harmonic restraining force to atoms in the group to affect their
central moment about the center of mass (radius of gyration). This fix
is useful to encourage a protein or polymer to fold/unfold and also when
sampling along the radius of gyration as a reaction coordinate (i.e. for
protein folding).

The radius of gyration is defined as RG in the first formula. The energy
of the constraint and associated force on each atom is given by the
second and third formulas, when the group is at a different RG than the
target value RG0.

$$\begin{aligned}
{R_G}^2 & = \frac{1}{M}\sum_{i}^{N}{m_{i}\left( x_{i} -
\frac{1}{M}\sum_{j}^{N}{m_{j}x_{j}} \right)^{2}} \\
E & = K\left( R_G - R_{G0} \right)^{2} \\
F_{i} & = 2K\frac{m_{i}}{M}\left( 1-\frac{R_{G0}}{R_G}
\right)\left( x_{i} - \frac{1}{M}\sum_{j}^{N}{m_{j}x_{j}} \right)
\end{aligned}$$

The ($x_i$ - center-of-mass) term is computed taking into account
periodic boundary conditions, $m_i$ is the mass of the atom, and *M* is
the mass of the entire group. Note that K is thus a force constant for
the aggregate force on the group of atoms, not a per-atom force.

If $R_{G0}$ is specified as NULL, then the RG of the group is computed
at the time the fix is specified, and that value is used as the target.

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

This fix writes the currently used reference RG ($R_{G0}$) to [binary
restart files](restart). See the [read_restart](read_restart) command
for info on how to re-specify a fix in an input script that reads a
restart file, so that the fix continues in an uninterrupted fashion.

None of the [fix_modify](fix_modify) options are relevant to this fix.

This fix computes a global scalar which can be accessed by various
[output commands](Howto_output). The scalar is the reference radius of
gyration $R_{G0}$ used by the fix. energy change due to this fix. The
scalar value calculated by this fix is \"intensive\".

No parameter of this fix can be used with the *start/stop* keywords of
the [run](run) command. This fix is not invoked during [energy
minimization](minimize).

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.

## Restrictions

This fix is part of the EXTRA-FIX package. It is only enabled if LAMMPS
was built with that package. See the [Build package](Build_package) page
for more info.

## Related commands

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

## Default

none