Can I tune EHT to match LDA+U?

[pippin]

I understand that LDA+U is still on the to-do list of VNL product development.  Meanwhile, is it possible to tune the extended Huckel Theory parameters in VNL to fit to LDA+U?  If it is possible, what are possible pitfalls?  Also, I followed the link in your Reference manual for J. Cerda's fitting program called "green".  But it took me to a web page of a start-up company and I cannot seem to find any reference to "green".  Is there an alternative tool available?  Thanks!

[Anders Blom]

The question is kind of backwards The reason you need LDA+U in DFT is that there are no fitting parameters to get e.g. the bandgap right. However, in Huckel we have no such problem - since we do have fitting parameters. So, there is no real point to fit the Huckel model to LDA+U - just fit it to experiments (or GW or similar)!

Of course, if you have a particular reason to, say, compare an EHT calculation with an LDA+U calculation, then, perhaps... But otherwise I don't really see any compelling reason for intermixing LDA+U and EHT.

The point is rather, how transferable the EHT parameters are. The fitted parameters might only work well for a subset of problems, while DFT is a much more generic. However, as soon as you introduce LDA+U you again fit, and thus restrict things. In both cases (EHT/LDA+U) the hope is naturally that you can go a little bit, or a lot, outside of the configuration space in which you fitted, and hopefully the parameters don't change too much.

Taking something like ZrB2 as an example, we have EHT parameters for Zr, and for B, but that doesn't necessarily (or rather probably!) work for ZrB2. So you'd want to do a fit for Zr and B in ZrB2, but again the reference is best chosen as something like GW or experiments.

[Anders Blom]

A very relevant side point is, how can we fit the EHT parameters ourselves, without relying on Cerda?! That is something we will have to return to later on...

[pippin]

Thanks for your response.  In my case, I have an LDA+U for a binary compound from another program that fits to experimental data well enough.  I'd like to use VNL to study transport property but am limited to LDA, which is widely known to underestimate the band gap energy.  So, I'm thinking that if I can fit the EHT parameters to my LDA+U (~= experimental data), I can better related my LDA+U study to VNL transport simulations.  It is O.K. for me if the fitted parameters do not transfer to any other compounds.  Does this make sense or am I totally off?  Thanks!  

[Anders Blom]

Ok, that is certainly a useful idea. Absolutely possible, with the caveat noted in my additional comment about how to actually perform the fitting. But there are, after all, not that many parameters, and once you have a reference, from whereever it comes, there are a multitude of general fitting methods.

Let us know how it works out, maybe it has wider applications!

[Nordland]

Hey pippin.

I think your approach is correct. The idea behind Huckel, is that you have a bandstructure or similar quantity that comes from a more exact method or an experiment.

So if you want to do like Cerda, does the following would be the procedure to getting EHT parameters:

-> Select a couple of symmetry points from the reference calculation.
-> Setup a starting point for EHT parameters. ( If you need a help here, I can provide a good starting guess.)
-> Perform a calculation ( non-selfconsistent that is ) of the bandstructure, and calculate the error in the symmetry points
according to your reference calculation.
-> What I would do here, ( simply because it is the simplest and first attempt at it for you ) is to do a parameter sweep of the
parameters to see, and find the parameters that gives you the best fit.

And then you will have a parameters set for this system.

If you need a little assistance, getting started, so just write back to me.

[pippin]

Thanks, Nordland, for your comment.  The suggested steps make sense.  I have a question for you.  For my system, I get Eg from EHT that is pretty close to the experimental value.  This is good.  But if I sweep lattice perimeter length (a in SimpleTetragonal with constant a/c) and compute total energy (Etot) at each point, the perimeter length at minimum Etot is way off from the experimental data.  Is this common in EHT?  If I fit my EHT parameters for the relaxed structure, do I get reasonable simulation result (band gap, transmission, etc.) for structure other than the relaxed one?

[Nordland]

You should never determine a lattice constant from a EHT calculation, since it will be very off. EHT parameters are fitted to give an exact bandstructure, but not a correct lattice determination when calculating the total energy.

The transferability of your EHT parameters are usually quite good, but of course it has it limitations. So it depends on what you mean by other structures. If your introduce complex new elements changing the fundamental appearance for the geometry and environment, then the EHT parameters might not be good enough. But the Cerda parameter for Gold which is fitted to a bulk FCC calculation is quite good for making molecular junctions, and the graphite parameters for carbon is perfect for ribbons, nanotubes, and junctions.

So in short. Unless you want to make it not work, it will mostly like be quite transferable.

[pippin]

Thanks again for your response.  I'm interested in looking at the impact of introducing a small amount of defects (vacancies, self-doping, etc. but not foreign species) to my system.  Can the EHT, fitted to LDA+U of a perfect lattice, be used to predict creation of defect levels?  Or is it better to use LDA+U on the defect system?

[Anders Blom]

The hope and expectation is indeed that it should work quite nicely to perform this kind of study with EHT. Whether or not that is the case must perhaps be checked from case to case, so once we have the LDA+U it will be interesting to compare the results. The idea is that you do this once, for a test system (with defect), and if the agreement is good you can trust the EHT and use it instead of more time-consuming LDA for the rest of the calculations.