# convergence issue with neb

Hello

I am running neb calculation with lammps for a large system (with 80000 atoms) and I have a convergence issue and I am not sure that I understand well what's going on.

When my convergence criterion is on force (with a ftol of 0.1), the NEB never converges. After 2000 steps of NEB and 2000 steps of CI-NEB the calculation is still not converged. I still have values of the MaxReplicaForce which are usually larger than 1eV/A and can be as large as 20eV/A depending on the system and timestep.
I could of course increase the maximum number of steps but it does not look like MaxReplicaForce will ever converge since it is not really decreasing (for some simulations it's almost constant for some other it changes kind of randomly).

If I got it right MaxReplicaForce will be dependent on the system size : if we have N atoms all having a force of 1eV/A we will have MaxReplicaForce = Sqrt(N) eV/A right? So having 80000 atoms I should maybe have a larger ftol. But I think that even with a small ftol it should converge after some time....
Plus when I check MaxAtomForce it has values which can be larger than 1eV/A which is large. Does this MaxAtomForce includes the spring forces (if not it would be normal to have relatively large values for MaxAtomForce)?

Then when I use a convergence criterion on energy it is converged very quickly. For instance with etol=0.0001eV it is converged in 56 steps. But the energy profile is very different from the one I get after 4000 steps (when I have etol=0).
The energy criterion is met when the maximum energy change of on atom is larger than etol. Right?

Well as you must have now understood, all this is not so clear for me.
Any help is welcome.

Emile

PS : I use lammps1Feb14.
I enclose the output I get with
neb 0. 0.1 2000 2000 100 final FinalImage #: slurm-13024084.out
neb 0.00001 0.1 2000 2000 100 final FinalImage #:slurm-13049634.out

Here is my input file :

slurm-13024084.out (17.6 KB)

slurm-13049634.out (1.95 KB)

Hello again

So my neb calculations are still not converging for large systems. It really is a size issue since I have no problem with a small system (up to around 1000 atoms).
Has anybody been running neb for large system (more than 10000 atoms)?

Regarding my previous post, I now understand the convergence energy criterion. The etol I chose previously was too large. When I put smaller values, the calculations do not converge.

Well, I have to say that I do not really know what to do now...
Thank you for any help or suggestion.

Emile

Most of your questions are explicitly answered in this paragraph of neb.html:

"""
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.
Note that inter-replica forces are zero in the initial and final
replicas, and only affect the direction in the climbing replica. For
this reason, the "maximum force per replica" is often equal to the
potential gradient in the climbing replica. In the first stage of NEB,
there is no climbing replica, and so the potential gradient in the
highest energy replica is reported, since this replica will become the
climbing replica in the second stage of NEB.
"""

The maximum force per replica is an extensive property. That is, if
you were to increase the number of atoms N by adding periodic images
to each replica, MaxReplicaForce should increase as O(N), not
O(sqrt(N)) as you suggested earlier. This is confirmed by looking at
the following piece of code from neb.cpp

double fnorm2 = sqrt(update->minimize->fnorm_sqr());
double fmaxreplica;
MPI_Allreduce(&fnorm2,&fmaxreplica,1,MPI_DOUBLE,MPI_MAX,roots);

1. If N is increased in the trivial manner that I describe above, it
might happen that NEB would evolve identically, independent of Natoms,
so that MaxReplicaForce/Natoms was the same on each iteration,
independent of N. However, you are probably increasing Natoms in a
non-trivial manner, so that the number of independent degrees of
freedom is truly increasing. This will probably require more NEB
iterations to achieve the same value of MaxReplicaForce/Natoms. How
much more? Hard to say, it might be O(logNatoms), or O(Natoms), or
worse.

2. You might want to turn off the climbing phase until you are sure
your NEB calculation is converging to a stable pathway.

3. It is possibly that there is something qualitatively different in
the behaviors of 1000 and 10,000 atoms. The larger system may be
picking up a different pathway that did not appear. What about 2000,
or 5000? More study required on your part.

Aidan