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# neb/spin command

## Syntax

    neb/spin etol ttol N1 N2 Nevery file-style arg keyword

- etol = stopping tolerance for energy (energy units)

- ttol = stopping tolerance for torque ( 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

      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

- keyword = verbose

      verbose = print supplemental information

## Examples

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

## Description

Perform a geodesic nudged elastic band (GNEB) 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.

GNEB is a method for finding both the spin configurations and height of the energy barrier associated with a transition state, e.g. spins to perform a collective rotation from one energy basin to another. The implementation in LAMMPS follows the discussion in the following paper: (Bessarab).

Each replica runs on a partition of one or more processors. Processor partitions are defined at run-time using the -partition command-line switch. 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 Howto replica doc page for further discussion.

Note

As explained below, a GNEB calculation performs a minimization across all the replicas. One of the spin style minimizers has to be defined in your input script.

When a GNEB 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 magnetic atoms, the interaction potentials, and the starting configuration when the neb command is issued should be the same for every replica.

In a GNEB calculation each replica is connected to other replicas by inter-replica nudging forces. These forces are imposed by the fix neb/spin command, which must be used in conjunction with the neb command. The group used to define the fix neb/spin command defines the GNEB magnetic atoms which are the only ones that inter-replica springs are applied to. If the group does not include all magnetic atoms, then non-GNEB magnetic atoms have no inter-replica springs and the torques they feel and their precession motion is computed in the usual way due only to other magnetic atoms within their replica. Conceptually, the non-GNEB atoms provide a background force field for the GNEB atoms. Their magnetic spins can be allowed to evolve during the GNEB minimization procedure.

The initial spin configuration for each of the replicas can be specified in different manners via the file-style setting, as discussed below. Only atomic spins whose initial coordinates should differ from the current configuration need to 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 spin 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 and spin 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 spin to that atom in an interpolated manner. This is done by using the current direction of the spin at the starting point and the read-in direction as the final point. The “angular distance” between them is calculated, and the new direction is assigned to be a fraction of the angular distance.

Note

The “angular distance” between the starting and final point is evaluated in the geodesic sense, as described in (Bessarab).

Note

The angular interpolation between the starting and final point is achieved using Rodrigues formula:

\[\vec{m}_i^{\nu} = \vec{m}_i^{I} \cos(\omega_i^{\nu}) + (\vec{k}_i \times \vec{m}_i^{I}) \sin(\omega_i^{\nu}) + (1.0-\cos(\omega_i^{\nu})) \vec{k}_i (\vec{k}_i\cdot \vec{m}_i^{I})\]

where \(\vec{m}_i^I\) is the initial spin configuration for spin i, \(\omega_i^{\nu}\) is a rotation angle defined as:

\[\omega_i^{\nu} = (\nu - 1) \Delta \omega_i \mathrm{~~and~~} \Delta \omega_i = \frac{\omega_i}{Q-1}\]

with \(\nu\) the image number, Q the total number of images, and \(\omega_i\) the total rotation between the initial and final spins. \(\vec{k}_i\) defines a rotation axis such as:

\[\vec{k}_i = \frac{\vec{m}_i^I \times \vec{m}_i^F}{\left|\vec{m}_i^I \times \vec{m}_i^F\right|}\]

if the initial and final spins are not aligned. If the initial and final spins are aligned, then their cross product is null, and the expression above does not apply. If they point toward the same direction, the intermediate images conserve the same orientation. If the initial and final spins are aligned, but point toward opposite directions, an arbitrary rotation vector belonging to the plane perpendicular to initial and final spins is chosen. In this case, a warning message is displayed.

For a file-style setting of each, a filename is specified which is assumed to be unique to each replica. See the neb documentation page for more information about this option.

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 read_data, read_restart, or 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. To enable this, you must first define a min_style, using either the spin, spin/cg, or spin/lbfgs style (see min_spin for more information). The other styles cannot be used, since they relax the lattice degrees of freedom instead of the spins.

The minimizer tolerances for energy and force are set by etol and ttol, the same as for the minimize command.

A non-zero etol means that the GNEB 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 ttol means that the GNEB calculation will terminate if the torque criterion is met by every replica. The torques being compared to ttol 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 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 angular distance (normalized by the total cumulative angular distance) between adjacent replicas, where “distance” is defined as the length of the 3N-vector of the geodesic distances in spin coordinates, with N the number of GNEB spins involved (see equation (13) in (Bessarab)). 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 GNEB, 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 spin 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 fix neb command.

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

When both stages are complete, if the GNEB calculation was successful, the configurations of the replicas should be along (close to) the MEP and the replica with the highest energy should be a spin 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.

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

An initial value can be defined for the timestep. Although, the spin minimization algorithm is an adaptive timestep methodology, so that this timestep is likely to evolve during the calculation.

The minimizers in LAMMPS operate on all spins in your system, even non-GNEB atoms, as defined above.

Each file read by the neb/spin command containing spin 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:

    ID1 g1 x1 y1 z1 sx1 sy1 sz1
    ID2 g2 x2 y2 z2 sx2 sy2 sz2
    ...
    IDN gN yN zN sxN syN szN

The fields are the atom ID, the norm of the associated magnetic spin, followed by the x,y,z coordinates and the sx,sy,sz spin 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 GNEB calculation you do not need to specify initial spin coordinates for very many atoms to produce differing starting and final replicas whose intermediate replicas will converge to the energy barrier. Typically only new spin 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 GNEB atoms in the group defined by the fix neb command. Not every GNEB atom need be in the file, and non-GNEB atoms can be listed in the file.

Four kinds of output can be generated during a GNEB 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. It contains the timestep, the maximum torque per replica, the maximum torque 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), and the normalized reaction coordinate and potential energy of each replica.

The “maximum torque per replica” is the two-norm of the 3N-length vector given by the cross product of a spin by its precession vector omega, in each replica, maximized across replicas, which is what the ttol setting is checking against. In this case, N is all the atoms in each replica. The “maximum torque per atom” is the maximum torque component of any atom in any replica. The potential gradients are the two-norm of the 3N-length magnetic precession vector solely due to the interaction potential i.e. without adding in inter-replica forces, and projected along the path tangent (as detailed in Appendix D of (Bessarab)).

The “reaction coordinate” (RD) for each replica is the two-norm of the 3N-length vector of geodesic distances between its spins and the preceding replica’s spins (see equation (13) of (Bessarab)), 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 spins being operated on by the fix neb/spin command.

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

Supplementary information for all replicas can be printed out to the screen and master log.lammps file by adding the verbose keyword. This information include the following. The “GradVidottan” are the projections of the potential gradient for the replica i on its tangent vector (as detailed in Appendix D of (Bessarab)). The “DNi” are the non normalized geodesic distances (see equation (13) of (Bessarab)), between a replica i and the next replica i+1. For the last replica, this distance is not defined and a “NAN” value is the corresponding output.

When a NEB calculation does not converge properly, the supplementary information can help understanding what is going wrong.

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

If dump commands in the input script define a filename that includes a universe or uloop style variable, then one dump file (per dump command) will be created for each replica. At the end of the GNEB 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, restart filenames can be specified with a universe or uloop style variable, to generate restart files for each replica. These may be useful if the GNEB calculation fails to converge properly to the MEP, and you wish to restart the calculation from an intermediate point with altered parameters.

A c file script in provided in the tool/spin/interpolate_gneb directory, that interpolates the MEP given the information provided by the verbose output option (as detailed in Appendix D of (Bessarab)).

## Restrictions

This command can only be used if LAMMPS was built with the SPIN package. See the Build package doc page for more info.

For magnetic GNEB calculations, only the spin_none value for the line keyword can be used when minimization styles spin/cg and spin/lbfgs are employed.

## Related commands

min/spin, fix neb/spin

## Default

none

(Bessarab) Bessarab, Uzdin, Jonsson, Comp Phys Comm, 196, 335-347 (2015).