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fix spring command :h3

[Syntax:]

fix ID group-ID spring keyword values :pre

ID, group-ID are documented in "fix"_fix.html command :ulb,l
spring = style name of this fix command :l
keyword = {tether} or {couple} :l
  {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) :pre
:ule

[Examples:]

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 :pre

[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 doesn't 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 total force on the group of atoms, not a
per-atom force.

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).

IMPORTANT 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.html
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.
One exception is for rigid bodies, which should not be used with the
fix spring command, if the rigid body will cross a periodic boundary.
This is because image flags for rigid bodies are used in a different
way, as explained on the "fix rigid"_fix_rigid.html doc page.

[Restart, fix_modify, output, run start/stop, minimize info:]

No information about this fix is written to "binary restart
files"_restart.html.

The "fix_modify"_fix_modify.html {energy} option is supported by this
fix to add the energy stored in the spring to the system's potential
energy as part of "thermodynamic output"_thermo_style.html.

This fix computes a global scalar which can be accessed by various
"output commands"_Section_howto.html#howto_8.  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"_Section_howto.html#howto_8.  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 2nd group (group-ID2).  The 4th 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.html command.

The forces due to this fix are imposed during an energy minimization,
invoked by the "minimize"_minimize.html command.

IMPORTANT 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.html {energy} option for
this fix.

[Restrictions:] none

[Related commands:]

"fix drag"_fix_drag.html, "fix spring/self"_fix_spring_self.html,
"fix spring/rg"_fix_spring_rg.html, "fix smd"_fix_smd.html

[Default:] none
