minor changes to NEB doc pages and examples

ID, group-ID are documented in "fix"_fix.html command :ulb,l

neb = style name of this fix command :l

Kspring = parallel spring constant (force/distance units or force units, see nudge keyword) :l

Kspring = spring constant for parallel nudging force (force/distance units or force units, see parallel keyword) :l

zero or more keyword/value pairs may be appended :l

keyword = {nudge} or {perp} or {ends} :l

  {nudge} value = {neigh} or {ideal}

keyword = {parallel} or {perp} or {end} :l

  {parallel} value = {neigh} or {ideal}

    {neigh} = parallel nudging force based on distance to neighbor replicas (Kspring = force/distance units)

    {ideal} = parallel nudging force based on interpolated ideal position (Kspring = force units)

  {perp} value = {Kspring2}

all intermediate replicas (i.e. for 1 < I < N, except the climbing

replica) the force vector becomes:

Fi = -Grad(V) + (Grad(V) dot T') T' + Fnudge_parallel + Fspring_perp :pre

Fi = -Grad(V) + (Grad(V) dot T') T' + Fnudge_parallel + Fnudge_perp :pre

T' is the unit "tangent" vector for replica I and 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); see the

"(Henkelman1)"_#Henkelman1 paper for details.  Ri gives the atomic

"(Henkelman1)"_#Henkelman1 paper for details.  Ri are the atomic

coordinates of replica I; Ri-1 and Ri+1 are the coordinates of its

neighbor replicas.  The term (Grad(V) dot T') is used to remove the

component of the gradient parallel to the path which would tend to

distribute the replica unevenly along the path.  Fnudge_parallel is an

artificial nudging force which is applied only in the tangent

direction and which maintains the equal spacing between replicas (see

below for more information).  Fspring_perp is an optional artificial

spring which is applied only perpendicular to the tangent and which

prevent the paths from forming acute kinks (see below for more

information).

below for more information).  Fnudge_perp is an optional artificial

spring which is applied in a direction perpendicular to the tangent

direction and which prevent the paths from forming acute kinks (see

below for more information).

In the second stage of the NEB calculation, the interatomic force Fi

for the climbing replica (the replica of highest energy after the

:line

The keyword {nudge} specifies how the parallel nudging force is

The keyword {parallel} specifies how the parallel nudging force is

computed.  With a value of {neigh}, the parallel nudging force is

computed as in "(Henkelman1)"_#Henkelman1 by connecting each

intermediate replica with the previous and the next image:

:line

The keyword {perp} adds a spring force perpendicular to the path in

order to prevent the path from becoming too kinky. It

can significantly improve the convergence of the NEB calculation when

the resolution is poor.  I.e. when too few replicas are used; see

The keyword {perp} specifies if and how a perpendicual nudging force

is computed.  It adds a spring force perpendicular to the path in

order to prevent the path from becoming too kinky.  It can

significantly improve the convergence of the NEB calculation when the

resolution is poor.  I.e. when few replicas are used; see

"(Maras)"_#Maras1 for details.

The perpendicular spring force is given by

Fspring_perp = {Kspring2} * F(Ri-1,Ri,Ri+1) (Ri+1 + Ri-1 - 2 Ri) :pre

Fnudge_perp = {Kspring2} * F(Ri-1,Ri,Ri+1) (Ri+1 + Ri-1 - 2 Ri) :pre

where {Kspring2} is the specified value.  F(Ri-1 Ri R+1) is a smooth

scalar function of the angle Ri-1 Ri Ri+1.  It is equal to 0.0 when

:line

By default, no nudging forces act on the first and last replicas during 

the NEB relaxation, so these replicas simply relax toward their 

respective local minima.  By using the key word {end}, additional forces 

can be applied to the first or last replica, to enable them to relax 

toward a MEP while constraining their energy.

By default, no additional forces act on the first and last replicas

during the NEB relaxation, so these replicas simply relax toward their

respective local minima.  By using the key word {end}, additional

forces can be applied to the first and/or last replicas, to enable

them to relax toward a MEP while constraining their energy.

The interatomic force Fi for the specified replica becomes:

than the first replica.  This should effectively prevent the

intermediate replicas from over-relaxing.

After converging a NEB calculation using an {estyle} of {last/efirst/middle},

you should check that all intermediate replicas have a larger energy than the

first replica. If this is not the case, the path is probably not a MEP.

After converging a NEB calculation using an {estyle} of

{last/efirst/middle}, you should check that all intermediate replicas

have a larger energy than the first replica. If this is not the case,

the path is probably not a MEP.

Finally, note that if the last replica converges toward a local

minimum which has a larger energy than the energy of the first

mpirun -np 8 lmp_g++ -partition 4x2 -in in.neb.hop1

mpirun -np 8 lmp_g++ -partition 4x2 -in in.neb.hop2

mpirun -np 8 lmp_g++ -partition 4x2 -in in.neb.hop1.end

mpirun -np 6 lmp_g++ -partition 3x2 -in in.neb.sivac

mpirun -np 9 lmp_g++ -partition 3x3 -in in.neb.sivac

mpirun -np 8 lmp_g++ -partition 4x2 -in in.neb.sivac

Note that more than 4 replicas should be used for a precise estimate 

of the activation energy corresponding to a transition.

group		nonneb subtract all nebatoms

fix		1 lower setforce 0.0 0.0 0.0

fix		2 nebatoms neb 1.0 #nudge ideal

fix		2 nebatoms neb 1.0 parallel ideal

fix		3 all enforce2d

thermo		100

group		nonneb subtract all nebatoms

fix		1 lower setforce 0.0 0.0 0.0

fix		2 nebatoms neb 1.0 nudge ideal end first 1.0

fix		2 nebatoms neb 1.0 parallel ideal end first 1.0

fix		3 all enforce2d

thermo		100