applicability of dimer/lanczos/etc (min-mode methods)

[perez]

hello

I would like to enquiry about the applicability or the min-mode methods, particularly regarding the type of problem I am working with
Let me please explain in detail (coming from a non-expert..). I am trying to determine energy barriers which vary within the range
10-100 eV. To me, this is probably much higher that is commonly seen in chemistry, even in atomic diffusion in solids/surfaces (never higher than 4 eV or so?)
Please correct me if I am wrong, I am just talking about the literature I personally know

Those high barriers take place in a particular experimental situation, ie ion bombardent. There is the concept of threshold displacement energy, which corresponds to
the barrier for a particular atom in the solid to get displaced (kicked) to usually form a Frenkel defect. The idea is that you start from a minimum (equilibrium configuration of the solid)
and end up in a different minimum, and the barrier between them is huge

Now, will you please inform me whether either the dimer or the lanczos method, as numerical methods, and we know that numerical methods have limitations, do they have a limit towards
determining really large energy barriers? Or else, the performance of the min-mode methods is unrelated to the height of the barrier?

thanks for your kind support

Manuel

[perez]

hi again

I would like to add one point to my previous message. The literature on threshold displacement energies of solids, from the point of view of ab-initio calculations, concentrates on ab-initio molecular dynamics (mostly siesta, there are probably no more than 2 papers on vasp using ab-initio molecular dynamics for TDEs). The question I submitted in the previous message is related to this point: is it possible that the reason for saddle-point search methods not appearing in the TDE literature is the numerical limitations of saddle-point search methods? Usually, ab-initio molecular dynamics is very expensive, so you need a good reason not to try first saddle-point search methods, dont' you?

regards

Manuel
PS I could send the reference for one or more of those papers to anyone interested

[graeme]

In high energy collision events, I would not expect the atoms to react by crossing near to saddle points. In the framework of transition state theory, we assume that the reactants are in thermal equilibrium so that the probability of crossing a barrier is related to the Boltzmann factor, exp(-dE/kT), where dE is the energy of the saddle with respect to the minimum. In the high-energy collision scenario, the initial system is far from equilibrium. During the collision, energy is dissipated to the system and so a much higher incident energy is required (tens of eV) than a typical barrier energy (a few eV).

There may, however, be some relationship between the barrier energy and the incident energy. We have done a little work in this regard, in this publication:
http://theory.cm.utexas.edu/henkelman/p ... 074706.pdf

[perez]

thanks a lot for your reply and your paper

"non-equilibrium effects" is then the key physics in ion-bombardment

regards

Manuel

[perez]

hi

further to this discussion and to the paper kindly provided by Graeme (rare event MD dynamics simulations of plasma induced surface ablation), I would like to mention that this paper is a really clear evidence of the need for dissipation in treating this type of physics, rendering equilibrium barriers useless in high energy ion experiments

In fact, I have tried to sample the literature further (more specifically on ion irradiation rather than plasma) and have been unable to locate anything as convincing, or with any more theory or explanations than Graeme's paper. Certainly there are many ab-initio MD papers providing the final number (threshold displacement energy), which seems to be reliable and comparable to experiment; it seems to be the "standard" if I may say so...

Now, my question is this (apologies for my poor knowledge in MD): why does the Nose-Hoover thermostat contain the right physics in order to treat dissipation?

According to the literature, the two main sources (the highest contribution) of dissipation in "swift heavy ion" irradiation of solids are given by 1- highly excited electronic states/impact ionisation/redistribution of hot electrons and 2- non-equilibrium electron-phonon interaction

My intuition tells me that point number 1- is not present in any form of ab-initio MD threshold displacement energy published work, although there are some explicit ways of including it. Point 2- seems to be the type of dissipation that Graemes paper refers to (via the Noose-Hooever thermostat)?

Incidentally, I would like to refer to a couple of empirical corrections which seem to take care of dissipation in theoretical threshold displacement energy work and do the trick as corrections (I do not think they provide very convincing evidence for the physics of dissipation in ion bombardment):
- the "sudden approximation", it is something appearing in a few papers; apparently considering phonons via constrained geometry optimisation, ie fixing the positions of all atoms in the supercell, except for the recoiling atom, and following the energy surface. It is not clear to me, although it seems related to reaction dynamics...
- some form of geometry optimisation whilst fixing the core electrons gives the second correction; this sounds like the type of effect that is needed in point 1- (see above)

If someone has any comments I would appreciate them (I am happy to send references)

regards

Manuel

[graeme]

I don't think there is any particularly special about the Nose-Hoover thermostat. It allows for coupling of a small system to a bath, but the details of the interactions are not physical. I view it as a tradeoff between messing up the dynamics vs getting the right canonical distribution. So in that paper relating to ablation the thermostat was used to adsorb any heat that would dissipate to the bulk, if we had explicitly modeled more bulk atoms. The details of the thermostat should not have any significant impact on the results, but some thermostat with an appropriate time constant is needed to prevent artificial reflection of phonons back to the surface and a heating of the sample.

The comments about electronic states is good. None of the electronic contributions to dissipation were considered. If there is some empirical way of treating these effects with a thermostat, I'm not aware of them.