lammps/doc/fix_neb.txt

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fix neb command :h3

[Syntax:]

fix ID group-ID neb kspring :pre
  
ID, group-ID are documented in "fix"_fix.html command
neb = style name of this fix command
kspring = inter-replica spring constant :ul

[Examples:]

fix 1 active neb 10.0 :pre

[Description:]

Add inter-replica forces to atoms in the group for a multi-partition
simulation run via the "neb"_neb.html command to perform a nudged
elastic band (NEB) calculation for transition state finding.  Hi-level
explanations of NEB are given with the "neb"_neb.html command and in
"this section"_Section_howto.html#neb of the doc pages.  The fix neb
command is used to define how inter-replica forces are computed.

Atoms in the two end-point replicas do not experience inter-replica
forces, but those in intermediate replicas do.  The 3N-length vector
of interatomic forces Fi = -Grad(V) acting on the atoms of each
intermediate replica I is altered to become:

Fi = -Grad(V) + (Grad(V) dot That) That + Kspring (|Ri+i - Ri| - |Ri - Ri-1|) That :pre

Ri are the atomic coordinates of replica I; Ri-1 and Ri+1 are the
coordinates of its neighbor replicas.  That (t with a hat over it) is
the unit "tangent" vector for replica I which is a function of Ri,
Ri-1, Ri+1, and the potential energy of the 3 replicas; it points
roughly in the direction of (Ri+i - Ri-1).  The first two terms in the
above equation are the component of the interatomic forces
perpendicular to the tangent vector.  The last term is a spring force
between replica I and its neighbors, parallel to the tangent vector
direction with the specified spring constant.

NOTE: That is defined in what papers?

The effect of the first two terms is to push the atoms of each replica
toward the minimum energy path (MEP) of conformational states that
transition over the energy barrier.  The MEP for an energy barrier is
defined as a sequence of 3N-dimensional states which cross the barrier
at its saddle point, each of which has a potential energy gradient
parallel to the MEP itself.

The effect of the last term is to push each replica away from its two
neighbors in a direction along the MEP, so that the final set of
states are equidistant from each other.

A NEB calculation is performed in two stages, as described by the neb
command.  In the second stage, the forces on atoms in the replica
nearest the top of the energy barrier are altered so that it climbs to
the top of the barrier and finds the saddle point.  The forces on
atoms in this replica become:

Fi = -Grad(V) + 2 (Grad(V) dot that) that :pre

The inter-replica forces for the other replicas are unchanged from the
first equation. 

NOTE: discuss how to do NEB on a subset of atoms - group ID of fix neb
command.

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

No information about this fix is written to "binary restart
files"_restart.html.  None of the "fix_modify"_fix_modify.html options
are relevant to this fix.  No global or per-atom quantities are stored
by this fix for access by various "output
commands"_Section_howto.html#4_15.  No parameter of this fix can be
used with the {start/stop} keywords of the "run"_run.html command.
This fix is not invoked during "energy minimization"_minimize.html.

[Restrictions:]

This command can only be used if LAMMPS was built with the "replica"
package.  See the "Making LAMMPS"_Section_start.html#2_3 section for
more info on packages.

[Related commands:]

"neb"_neb.html

[Default:] none

:link(HJ1)
[(Henkelman1)] Henkelman and Jonsson, J Phys Chem, 113, 9978-9985 (2000).

:link(HJ2)
[(Henkelman2)] Henkelman and Jonsson, J Phys Chem, 113, 99019904 (2000).