RCORE vs MIN DIST

[mark]

Hi team,

I'm a new user of Bader and am using it to look at charges on metal coordination complexes. I've read your web site and several of the discussions here, but I'm still unclear: should the minimum distance given in the ACF.dat file (which I presume is in angstroms) be greater or less than RCORE in the POTCAR file (which is in Bohr radii)?

Thanks for your help!

[graeme]

Hi Mark,

Rcore is given in Bohr, and the minimum distance from a Bader surface to each atom should be larger than Rcore.

The issue here is that the pseudopotentials alter the charge density inside of a radial cutoff, Rcore. In general, the charge density in the core region does not affect properties of chemical bonding, so the potential can be artificially modified to smooth out electron wavefunctions in the core region.

The Bader analysis uses the surfaces of minimum charge density between atoms (in the bonding region) to separate the atoms. If a pseudopotential is too aggressive, it is possible for these surfaces to cut inside the core region, where the charge density can not be trusted. In this case, we want to caution users that there could be problems with the Bader analysis.

[mark]

Thanks! So it looks like maybe the pseudopotentials I'm using are too agressive. I'm looking at complexes of Zinc with carboxylic acids, and in all cases (i.e., for all atoms, which include H, C, O, and Zn) MIN DIST is less than RCORE. I tried increasing the size of the NG(XYZ)F grid, per one of the other messages, but this didn't make much difference (e.g., MIN DIST for Zn went from 0.9136 w/ a 140^3 grid to 0.9635. RCORE = 2.650 Bohr = 1.40 A). Any suggestions?

Also, the BADER charges I'm getting for Zn are of order 10.7. Should I be subtracting these from 12 (number of valence electrons) to get the correct charge?

Thanks again!

[graeme]

Yes, that's right; you need to subtract the valance charge to find the net charge.

I'm a little surprised that you are seeing many cases in which the distance from the atomic surfaces to the nuclei is within Rcore. The sum of Rcore for two bonding atoms should be less than the bonding distance. This means that a Bader surface will at most cut into one of the atom's core. But perhaps you mean that there are several instances in which it happens.

One thing to try, in order to see how sensitive your results are to the pseudopotentials, is to try a harder potential. I only see one Zn potential, but the PAW version has a smaller core radius of 2.3 Bohr. If the Bader charges do not change significantly as you change potentials, I think you have more grounds to trust them.

Ultimately, we need to find a way of putting the core charges back into the CHGCAR file.

It's good to hear that your results do not depend upon the grid size. That should always be the case when the calculation is converged.

[aarondesk]

[quote="graeme"]I'm a little surprised that you are seeing many cases in which the distance from the atomic surfaces to the nuclei is within Rcore. [/quote]

I'd like to follow-up on the above discussion. I have been looking at TiO2 and am having problems with my RCORE and minimum Bader distances. I've been modelling bulk Rutile and have tried all the Ti PAW pseudopotentials (LDA, GGA, PBE - _sv, _pv) and in all cases I consistently see RCORE greater than the Bader minimum. I'm seeing MIN DIST typically ~0.9-0.95 Ang. All the PAW Ti potentials use RCORE 2.8-2.3 Bohr (1.48-1.22 Ang).

I'm also going to look at anatase to see if there is a similar problem. I'll also look try using the US pseudopotentials, but I'm guessing that I'll see a similar problem because the US RCORE values are similar to the PAW RCORE values for Ti.

At this point I think I can:

1) Develop new pseudopotentials with smaller cutoffs. I honestly don't see myself doing this.

or

2) Live with the error in the Bader charges and just realize that there is some error due to too large cut-offs in the pseudopotentials.

Any other ideas/suggestions?

Aaron

[andri]

How are the charge coming out? Are they totally off mark or are the reasonable? I guess at least one more item on your list could be that we are not calculating the minimum distances correctly. At least it is point to consider, given the frequency which this problems seems to arise.

[graeme]

I think that a bug in the minimum distance calculation is unlikely (although of course it's always possible). I checked the values given by the bader code against a manual measurement for several chgcar files, and found them to be consistent. Perhaps a few more checks would be in order, but I doubt this is the problem.

To put this discussion into context, we added the minimum distance calculation to address the problem of missing core charges in the pseudopotentials. The criteria that the bader surface should be outside rcore is just a crude way to determine if the analysis is unaffected by the missing core charge. In practice, rcore is a parameter of the pseudopotential fitting procedure. The density is neither perfect outside rcore, nor does it go crazy immediately inside the rcore radius. Perhaps a better way to determine if the bader charges are sensitive to the pseudopoential approximation is to compare different potentials (as Aaron has done). If potentials with different rcore radii (hardness) result in similar bader charges, one gains confidence in the measurement, even if the Bader surface falls somewhat inside the core region.

To second Andri's question, how do the TiO2 charges vary with different pseudopotentials?

[aarondesk]

[quote="andri"]How are the charge coming out? Are they totally off mark or are the reasonable? [/quote]

Here's a summary of some of my results.


PAW-LDA(s_v) Ti: +2.22 O: -1.11 RMIN: 0.94 RCORE: 1.22
PAW-GGA Ti: +2.62 O: -1.31 RMIN: 0.77 RCORE: 1.48
PAW-GGA(p_v) Ti: +2.31 O: -1.15 RMIN: 0.92 RCORE: 1.32
PAW-GGA(s_v) Ti: +2.25 O: -1.13 RMIN: 0.93 RCORE: 1.22
PAW-PBE(s_v) Ti: +2.26 O: -1.13 RMIN: 0.95 RCORE: 1.22
US-GGA Ti: +2.53 O: -1.26 RMIN: 0.83 RCORE: 1.48

The results do appear reasonable and consistent with other work. For example, Bandura et al. (J.Phys. Chem B, 108,7844) found charges of +2.44 and -1.22 for bulk TiO2 using CASTEP.

The valence electron scheme seems a dominant factor for the charges, i.e. potentials with two s orbital sets (s_v) give similar charges, as do the normal potentials. It appears that even the potential with valence p electrons (p_v) gives similar charges to the s_v potentials and may be sufficient.

[sindbad]

Perhaps some more bad news.
for
VH2:
PAW_GGA V_sv (13e-) : RCORE=1.217 Angstrom , Min Dist =1.046 Angstrom , Charge on Vanadium = + 1.146 (its VH2 vandium hydride)
PAW_GGA V_pv (11e-) : RCORE=1.217 Angstrom , Min Dist =1.046 Angstrom , Charge on Vanadium = + 1.136 (its VH2 vandium hydride)
PAW_GGA V (5e-) : RCORE=1.429 Angstrom , Min Dist =1.046 Angstrom , Charge on Vanadium = + 1.059 (its VH2 vandium hydride)
TiH2
PAW_GGA Ti_sv (12e-) : RCORE=1.217 Angstrom , Min Dist =1.073 Angstrom , Charge on Titanium = + 1.326 (its TiH2 titanium hydride)
PAW_GGA Ti_pv (10e-) : RCORE=1.323 Angstrom , Min Dist =1.073 Angstrom , Charge on Titanium = + 1.309 (its TiH2 titanium hydride)
PAW_GGA Ti (5e-) : RCORE=1.482 Angstrom , Min Dist =1.073 Angstrom , Charge on Titanium = + 1.212 (its TiH2 titanium hydride)
ScH2
PAW_GGA Sc_sv (11e-) : RCORE=1.323 Angstrom , Min Dist =1.130 Angstrom , Charge on Scandium = + 1.326 (its ScH2 Scandium hydride)

FFT grid was sufficient for the convergence.

Do you think these results can be trusted?

Regards
Sindbad

[graeme]

It is now possible to write the core charges within vasp. This essentially eliminates the core charge problem. There are instructions about how to do this on the page http://theory.cm.utexas.edu/bader/vasp.php

With core charges, the analysis should not be particularly sensitive to how many electrons are treated explicitly (_sv and _pv potentials).

[sindbad]

I already used LAECHG=.TRUE. and the instructions given on the Bader page as suggested .

[graeme]

Ok, it's good that you are using the core charge.

Now, what exactly are you concerned about: the difference in the V/Ti/Sc as you go from the _pv to _sv potentials (0.01-0.02 e), or that Rcore is less than Min Dist? If the former, I would suggest that this is related to the systematic error intrinsic to the pseudopotential. I'm sure that you would find this or greater errors going to an all-electron code. If the second, remember that the MinDist>Rcore is a rule of thumb. Rcore is a radius in which you trust your pseudopotential, but it doesn't go completely crazy inside that distance. If you have short bonds with H so that you care about the charge density inside Rcore, you might want to worry about the quality of your calculation. But this is unrelated to the analysis - it is a matter of the accuracy of the charge density.

[sindbad]

Thank you, for the reply

regards

Sindbad