.. index:: neb

neb command
===========

Syntax
""""""

.. code-block:: LAMMPS

   neb etol ftol N1 N2 Nevery file-style arg keyword values

* etol = stopping tolerance for energy (dimensionless)
* ftol = stopping tolerance for force (force units)
* N1 = max # of iterations (timesteps) to run initial NEB
* N2 = max # of iterations (timesteps) to run barrier-climbing NEB
* Nevery = print replica energies and reaction coordinates every this many timesteps
* file-style = *final* or *each* or *none*

  .. parsed-literal::

       *final* arg = filename
         filename = file with initial coords for final replica
           coords for intermediate replicas are linearly interpolated
           between first and last replica
       *each* arg = filename
         filename = unique filename for each replica (except first)
           with its initial coords
       *none* arg = no argument all replicas assumed to already have
           their initial coords

* zero or more keyword/value pairs may be appended
* keyword = *verbosity*

  .. parsed-literal::

     *verbosity* value = *verbose* or *default* or *terse*
       *verbose* = very detailed per-replica output
       *default* = some per-replica output
       *terse* = only global state output

Examples
""""""""

.. code-block:: LAMMPS

   neb 0.1 0.0 1000 500 50 final coords.final
   neb 0.0 0.001 1000 500 50 each coords.initial.$i
   neb 0.0 0.001 1000 500 50 none verbose

Description
"""""""""""

Perform a nudged elastic band (NEB) calculation using multiple
replicas of a system.  Two or more replicas must be used; the first
and last are the end points of the transition path.

NEB is a method for finding both the atomic configurations and height of
the energy barrier associated with a transition state, e.g. for an atom
to perform a diffusive hop from one energy basin to another in a
coordinated fashion with its neighbors.  The implementation in LAMMPS
follows the discussion in these 4 papers: :ref:`(HenkelmanA)
<HenkelmanA>`, :ref:`(HenkelmanB) <HenkelmanB>`, :ref:`(Nakano)
<Nakano3>` and :ref:`(Maras) <Maras2>`.

Each replica runs on a partition of one or more processors.  Processor
partitions are defined at run-time using the :doc:`-partition
command-line switch <Run_options>`.  Note that if you have MPI
installed, you can run a multi-replica simulation with more replicas
(partitions) than you have physical processors, e.g you can run a
10-replica simulation on just one or two processors.  You will simply
not get the performance speed-up you would see with one or more physical
processors per replica.  See the :doc:`Howto replica <Howto_replica>`
doc page for further discussion.

.. note::

   As explained below, a NEB calculation performs a damped dynamics
   minimization across all the replicas.  The minimizer uses whatever
   timestep you have defined in your input script, via the
   :doc:`timestep <timestep>` command.  Often NEB will converge more
   quickly if you use a timestep about 10x larger than you would normally
   use for dynamics simulations.

When a NEB calculation is performed, it is assumed that each replica
is running the same system, though LAMMPS does not check for this.
I.e. the simulation domain, the number of atoms, the interaction
potentials, and the starting configuration when the neb command is
issued should be the same for every replica.

In a NEB calculation each replica is connected to other replicas by
inter-replica nudging forces.  These forces are imposed by the
:doc:`fix neb <fix_neb>` command, which must be used in conjunction
with the neb command.  The group used to define the fix neb command
defines the NEB atoms which are the only ones that inter-replica springs
are applied to.  If the group does not include all atoms, then non-NEB
atoms have no inter-replica springs and the forces they feel and their
motion is computed in the usual way due only to other atoms within
their replica.  Conceptually, the non-NEB atoms provide a background
force field for the NEB atoms.  They can be allowed to move during the
NEB minimization procedure (which will typically induce different
coordinates for non-NEB atoms in different replicas), or held fixed
using other LAMMPS commands such as :doc:`fix setforce <fix_setforce>`.
Note that the :doc:`partition <partition>` command can be used to invoke
a command on a subset of the replicas, e.g. if you wish to hold NEB or
non-NEB atoms fixed in only the end-point replicas.

The initial atomic configuration for each of the replicas can be
specified in different manners via the *file-style* setting, as
discussed below.  Only atoms whose initial coordinates should differ
from the current configuration need be specified.

Conceptually, the initial and final configurations for the first
replica should be states on either side of an energy barrier.

As explained below, the initial configurations of intermediate
replicas can be atomic coordinates interpolated in a linear fashion
between the first and last replicas.  This is often adequate for
simple transitions.  For more complex transitions, it may lead to slow
convergence or even bad results if the minimum energy path (MEP, see
below) of states over the barrier cannot be correctly converged to
from such an initial path.  In this case, you will want to generate
initial states for the intermediate replicas that are geometrically
closer to the MEP and read them in.

----------

For a *file-style* setting of *final*, a filename is specified which
contains atomic coordinates for zero or more atoms, in the format
described below.  For each atom that appears in the file, the new
coordinates are assigned to that atom in the final replica.  Each
intermediate replica also assigns a new position to that atom in an
interpolated manner.  This is done by using the current position of
the atom as the starting point and the read-in position as the final
point.  The distance between them is calculated, and the new position
is assigned to be a fraction of the distance.  E.g. if there are 10
replicas, the second replica will assign a position that is 10% of the
distance along a line between the starting and final point, and the
9th replica will assign a position that is 90% of the distance along
the line.  Note that for this procedure to produce consistent
coordinates across all the replicas, the current coordinates need to
be the same in all replicas.  LAMMPS does not check for this, but
invalid initial configurations will likely result if it is not the
case.

.. note::

   The "distance" between the starting and final point is
   calculated in a minimum-image sense for a periodic simulation box.
   This means that if the two positions are on opposite sides of a box
   (periodic in that dimension), the distance between them will be small,
   because the periodic image of one of the atoms is close to the other.
   Similarly, even if the assigned position resulting from the
   interpolation is outside the periodic box, the atom will be wrapped
   back into the box when the NEB calculation begins.

For a *file-style* setting of *each*, a filename is specified which is
assumed to be unique to each replica.  This can be done by using a
variable in the filename, e.g.

.. code-block:: LAMMPS

   variable i equal part
   neb 0.0 0.001 1000 500 50 each coords.initial.$i

which in this case will substitute the partition ID (0 to N-1) for the
variable I, which is also effectively the replica ID.  See the
:doc:`variable <variable>` command for other options, such as using
world-, universe-, or uloop-style variables.

Each replica (except the first replica) will read its file, formatted
as described below, and for any atom that appears in the file, assign
the specified coordinates to its atom.  The various files do not need
to contain the same set of atoms.

For a *file-style* setting of *none*, no filename is specified.  Each
replica is assumed to already be in its initial configuration at the
time the neb command is issued.  This allows each replica to define
its own configuration by reading a replica-specific data or restart or
dump file, via the :doc:`read_data <read_data>`,
:doc:`read_restart <read_restart>`, or :doc:`read_dump <read_dump>`
commands.  The replica-specific names of these files can be specified
as in the discussion above for the *each* file-style.  Also see the
section below for how a NEB calculation can produce restart files, so
that a long calculation can be restarted if needed.

.. note::

   None of the *file-style* settings change the initial
   configuration of any atom in the first replica.  The first replica
   must thus be in the correct initial configuration at the time the neb
   command is issued.

----------

A NEB calculation proceeds in two stages, each of which is a
minimization procedure, performed via damped dynamics.  To enable
this, you must first define a damped dynamics
:doc:`min_style <min_style>`, such as *quickmin* or *fire*\ .  The *cg*,
*sd*, and *hftn* styles cannot be used, since they perform iterative
line searches in their inner loop, which cannot be easily synchronized
across multiple replicas.

The minimizer tolerances for energy and force are set by *etol* and
*ftol*, the same as for the :doc:`minimize <minimize>` command.

A non-zero *etol* means that the NEB calculation will terminate if the
energy criterion is met by every replica.  The energies being compared
to *etol* do not include any contribution from the inter-replica
nudging forces, since these are non-conservative.  A non-zero *ftol*
means that the NEB calculation will terminate if the force criterion
is met by every replica.  The forces being compared to *ftol* include
the inter-replica nudging forces.

The maximum number of iterations in each stage is set by *N1* and
*N2*\ .  These are effectively timestep counts since each iteration of
damped dynamics is like a single timestep in a dynamics
:doc:`run <run>`.  During both stages, the potential energy of each
replica and its normalized distance along the reaction path (reaction
coordinate RD) will be printed to the screen and log file every
*Nevery* timesteps.  The RD is 0 and 1 for the first and last replica.
For intermediate replicas, it is the cumulative distance (normalized
by the total cumulative distance) between adjacent replicas, where
"distance" is defined as the length of the 3N-vector of differences in
atomic coordinates, where N is the number of NEB atoms involved in the
transition.  These outputs allow you to monitor NEB's progress in
finding a good energy barrier.  *N1* and *N2* must both be multiples
of *Nevery*\ .

In the first stage of NEB, the set of replicas should converge toward
a minimum energy path (MEP) of conformational states that transition
over a barrier.  The MEP for a transition is defined as a sequence of
3N-dimensional states, each of which has a potential energy gradient
parallel to the MEP itself.  The configuration of highest energy along
a MEP corresponds to a saddle point.  The replica states will also be
roughly equally spaced along the MEP due to the inter-replica nudging
force added by the :doc:`fix neb <fix_neb>` command.

In the second stage of NEB, the replica with the highest energy is
selected and the inter-replica forces on it are converted to a force
that drives its atom coordinates to the top or saddle point of the
barrier, via the barrier-climbing calculation described in
:ref:`(HenkelmanB) <HenkelmanB>`.  As before, the other replicas rearrange
themselves along the MEP so as to be roughly equally spaced.

When both stages are complete, if the NEB calculation was successful,
the configurations of the replicas should be along (close to) the MEP
and the replica with the highest energy should be an atomic
configuration at (close to) the saddle point of the transition. The
potential energies for the set of replicas represents the energy
profile of the transition along the MEP.

----------

A few other settings in your input script are required or advised to
perform a NEB calculation.  See the NOTE about the choice of timestep
at the beginning of this doc page.

An atom map must be defined which it is not by default for :doc:`atom_style atomic <atom_style>` problems.  The :doc:`atom_modify map <atom_modify>` command can be used to do this.

The minimizers in LAMMPS operate on all atoms in your system, even
non-NEB atoms, as defined above.  To prevent non-NEB atoms from moving
during the minimization, you should use the :doc:`fix setforce <fix_setforce>` command to set the force on each of those
atoms to 0.0.  This is not required, and may not even be desired in
some cases, but if those atoms move too far (e.g. because the initial
state of your system was not well-minimized), it can cause problems
for the NEB procedure.

The damped dynamics :doc:`minimizers <min_style>`, such as *quickmin*
and *fire*\ ), adjust the position and velocity of the atoms via an
Euler integration step.  Thus you must define an appropriate
:doc:`timestep <timestep>` to use with NEB.  As mentioned above, NEB
will often converge more quickly if you use a timestep about 10x
larger than you would normally use for dynamics simulations.

----------

Each file read by the neb command containing atomic coordinates used
to initialize one or more replicas must be formatted as follows.

The file can be ASCII text or a gzipped text file (detected by a .gz
suffix).  The file can contain initial blank lines or comment lines
starting with "#" which are ignored.  The first non-blank, non-comment
line should list N = the number of lines to follow.  The N successive
lines contain the following information:

.. parsed-literal::

   ID1 x1 y1 z1
   ID2 x2 y2 z2
   ...
   IDN xN yN zN

The fields are the atom ID, followed by the x,y,z coordinates.  The
lines can be listed in any order.  Additional trailing information on
the line is OK, such as a comment.

Note that for a typical NEB calculation you do not need to specify
initial coordinates for very many atoms to produce differing starting
and final replicas whose intermediate replicas will converge to the
energy barrier.  Typically only new coordinates for atoms
geometrically near the barrier need be specified.

Also note there is no requirement that the atoms in the file
correspond to the NEB atoms in the group defined by the :doc:`fix neb <fix_neb>` command.  Not every NEB atom need be in the file,
and non-NEB atoms can be listed in the file.

----------

Four kinds of output can be generated during a NEB calculation: energy
barrier statistics, thermodynamic output by each replica, dump files,
and restart files.

When running with multiple partitions (each of which is a replica in
this case), the print-out to the screen and master log.lammps file
contains a line of output, printed once every *Nevery* timesteps.  The
amount of information printed in this line can be selected with the
*verbosity* keyword.  Available options are *terse*, *default*, and
*verbose*.

With the *terse* setting, it contains the timestep, the maximum force of
a replica, the maximum force per atom (in any replica), potential
gradients in the initial, final, and climbing replicas, the forward and
backward energy barriers, the total reaction coordinate (RDT).

With the *default* setting, additionally the normalized
reaction coordinate and potential energy of each replica are printed.

With the *verbose* setting, additional per-replica properties are
printed: the "path angle" (pathangle), the angle between the 3N-length
tangent vector and the 3N-length force vector at image *i*
(angletangrad), the angle between the 3N-length energy gradient vector
of replica *i* and that of replica *i*\ +1 (anglegrad), the norm of the
energy gradient (gradV), the the two-norm of the 3N-length force vector
(RepForce), and the maximum force component of any atom (MaxAtomForce).

The "maximum force per replica" is the two-norm of the 3N-length force
vector for the atoms in each replica, maximized across replicas, which
is what the *ftol* setting is checking against.  In this case, N is
all the atoms in each replica.  The "maximum force per atom" is the
maximum force component of any atom in any replica.  The potential
gradients are the two-norm of the 3N-length force vector solely due to
the interaction potential i.e.  without adding in inter-replica
forces.

The "reaction coordinate" (RD) for each replica is the two-norm of the
3N-length vector of distances between its atoms and the preceding
replica's atoms, added to the RD of the preceding replica. The RD of
the first replica RD1 = 0.0; the RD of the final replica RDN = RDT,
the total reaction coordinate.  The normalized RDs are divided by RDT,
so that they form a monotonically increasing sequence from zero to
one. When computing RD, N only includes the atoms being operated on by
the fix neb command.

The forward (reverse) energy barrier is the potential energy of the
highest replica minus the energy of the first (last) replica.

The "path angle" (pathangle) for the replica i which is the angle
between the 3N-length vectors :math:`(R_{i-1} - R_i)` and
:math:`(R_{i+1} - R_i)` (where :math:`R_i` is the atomic coordinates of
replica *i*). A "path angle" of 180 indicates that replicas *i*\ -1, *i*
and *i*\ +1 are aligned.  "angletangrad" is the angle between the
3N-length tangent vector and the 3N-length force vector at image
*i*. The tangent vector is calculated as in :ref:`(HenkelmanA)
<HenkelmanA>` for all intermediate replicas and at R2 - R1 and RM - RM-1
for the first and last replica, respectively.  "anglegrad" is the angle
between the 3N-length energy gradient vector of replica *i* and that of
replica *i*\ +1. It is not defined for the final replica and reads nan.
gradV is the norm of the energy gradient of image *i* (:math:`\nabla
V`).  ReplicaForce is the two-norm of the 3N-length force vector
(including nudging forces) for replica *i*.  MaxAtomForce is the maximum
force component of any atom in replica *i*.

When a NEB calculation does not converge properly, the supplementary
information can help understanding what is going wrong. For instance
when the path angle becomes acute, the definition of tangent used in
the NEB calculation is questionable and the NEB cannot may diverge
:ref:`(Maras) <Maras2>`.

When running on multiple partitions, LAMMPS produces additional log
files for each partition, e.g. log.lammps.0, log.lammps.1, etc.  For a
NEB calculation, these contain the thermodynamic output for each
replica.

If :doc:`dump <dump>` commands in the input script define a filename
that includes a *universe* or *uloop* style :doc:`variable <variable>`,
then one dump file (per dump command) will be created for each
replica.  At the end of the NEB calculation, the final snapshot in
each file will contain the sequence of snapshots that transition the
system over the energy barrier.  Earlier snapshots will show the
convergence of the replicas to the MEP.

Likewise, :doc:`restart <restart>` filenames can be specified with a
*universe* or *uloop* style :doc:`variable <variable>`, to generate
restart files for each replica.  These may be useful if the NEB
calculation fails to converge properly to the MEP, and you wish to
restart the calculation from an intermediate point with altered
parameters.

There are 2 Python scripts provided in the tools/python directory,
neb_combine.py and neb_final.py, which are useful in analyzing output
from a NEB calculation.  Assume a NEB simulation with M replicas, and
the NEB atoms labeled with a specific atom type.

The neb_combine.py script extracts atom coords for the NEB atoms from
all M dump files and creates a single dump file where each snapshot
contains the NEB atoms from all the replicas and one copy of non-NEB
atoms from the first replica (presumed to be identical in other
replicas).  This can be visualized/animated to see how the NEB atoms
relax as the NEB calculation proceeds.

The neb_final.py script extracts the final snapshot from each of the M
dump files to create a single dump file with M snapshots.  This can be
visualized to watch the system make its transition over the energy
barrier.

To illustrate, here are images from the final snapshot produced by the
neb_combine.py script run on the dump files produced by the two
example input scripts in examples/neb.


.. |neb1| image:: img/hop1.jpg
   :width: 48%

.. |neb2| image:: img/hop2.jpg
   :width: 48%

|neb1|  |neb2|

.. raw:: html

   Click on them to see a larger image.

----------

Restrictions
""""""""""""

This command can only be used if LAMMPS was built with the REPLICA
package.  See the :doc:`Build package <Build_package>` doc
page for more info.

----------

Related commands
""""""""""""""""

:doc:`prd <prd>`, :doc:`temper <temper>`, :doc:`fix langevin <fix_langevin>`,
:doc:`fix viscous <fix_viscous>`, :doc:`fix neb <fix_neb>`

Default
"""""""

*verbosity* = *default*

----------

.. _HenkelmanA:

**(HenkelmanA)** Henkelman and Jonsson, J Chem Phys, 113, 9978-9985 (2000).

.. _HenkelmanB:

**(HenkelmanB)** Henkelman, Uberuaga, Jonsson, J Chem Phys, 113,
9901-9904 (2000).

.. _Nakano3:

**(Nakano)** Nakano, Comp Phys Comm, 178, 280-289 (2008).

.. _Maras2:

**(Maras)** Maras, Trushin, Stukowski, Ala-Nissila, Jonsson,
Comp Phys Comm, 205, 13-21 (2016)
