Fictitious Hydrogen Charges: 0.5 & 1.5 - What's the Difference?

[saray1360]

Hi,

I would like to have some information about the fictitious hydrogens with charges of 0.5 and 1.5 for example.

What are their differences with real hydrogens. Do they make "hydrogen bonds" as well or not?

I would be thankful if you suggest a reference for me to read about this subject.

Regards,
Sara

 

[alxm]

I've never heard the term 'fictitious hydrogen'. Do you mean a hydrogen-like (or hydrogenic) atom, which is a single-electron system with any nuclear charge, Z, or do you mean a hydrogen atom where both the nuclear and electron charge have changed?

In the latter case, changing the charge amounts to scaling the system. (See the definitions of Atomic Units, and how the elementary charge is included, via the fine-structure constant)

In the former case you no longer have a neutral atom but an ion (or pseudo-ion). For all intents and purposes, it'd be an altogether different element (since an element is defined by Z). Only hydrogen forms hydrogen bonds. (hence the name) so it wouldn't. If Z > 1 then it could perhaps interact in a similar way, but that wouldn't really be hydrogen bonding. More like a π-cation interaction.

You could predict the chemistry of 'non-integer Z' compounds using ordinary quantum-chemical methods (in fact, existing codes might even be able to do so as-is. It's just a number in an equation). But I doubt that anyone actually has. There's little point in studying a fictional system unless you can learn something from it; and there isn't much to be learned from hydrogen-with-a-non-integer-Z. (You can learn something from Helium and other many-electron atoms by varying Z. But that would be to gain insight into electron-electron interactions under different conditions, rather than studying the actual chemistry of the fictional atoms, which would be of little or no use in explaining real chemistry)

 

[saray1360]

As you know the dangling bonds of material are saturated by what they call it "fictitious hydrogen", "hydrogen-like atoms" or "pseudo hydrogens". I have read all these names in the literature, but, I am working with the pseudopotential of this "hydrogen-like atoms" with charge of 1.5 and 0.5. But I do not know the reason why we have to use thes hydrogen like atoms to saturate the dangling bonds?

Also, I have not yet found the papers related to the proposed idea of generating the pseudopotential and the basic idea why they have come to the idea of saturating these bonds with hydrogen-like atoms.

I would be thankful if you help me.

 

[alxm]

As you know the dangling bonds of material are saturated by what they call it "fictitious hydrogen", "hydrogen-like atoms" or "pseudo hydrogens". I have read all these names in the literature, but, I am working with the pseudopotential of this "hydrogen-like atoms" with charge of 1.5 and 0.5. But I do not know the reason why we have to use thes hydrogen like atoms to saturate the dangling bonds? Also, I have not yet found the papers related to the proposed idea of generating the pseudopotential and the basic idea why they have come to the idea of saturating these bonds with hydrogen-like atoms.

Actually, as I don't know - as it turns out. :) Seems I spoke too soon or rather, too specifically, in saying the chemistry of such 'hydrogens' isn't interesting. It's not interesting in itself but as a pseudopotential, it's of course a valid application. Googling for it seems to turn up work by Dumont and Chaquin. I believe it's their method. I don't think it's a general thing, or I'd have heard about it before.

That said, looking at what Dumont & Chaquin did, it makes good sense. The idea is to study/replicate substitutent effects in organic chemistry. I'll have to refer you to a textbook on organic chem if you're not acquainted with it, but the basic concept is that if you substitute a hydrogen on a benzene for another atom/functional group it will act as an http://en.wikipedia.org/wiki/Activating_group" group, depending on the electronegativity of the group relative benzene. That, in turn, greatly affects the reactivity of the substituted benzene.

So by varying the Z of one of the hydrogens, you change its electronegativity and can thereby use it to mimic (to an extent) the effects of different substituents. For instance, you might wish to figure out which substituent would give the lowest transition-state barrier in some organic reaction. You could (probably) just find the transition-state and then vary the charge of your 'ficticious hydrogen', and then identify a real substituent with the desired value. Which would be more efficient than building separate models for a large number of trial substituents.

Note though, that the fake hydrogen is merely acting as a 'dummy substitutent'. It's not actually involved directly in the reaction, but just acting to add or remove charge density from the benzene (or whatever it's attached to).

Here's a ref on the method:
"The H* Method : Hydrogen Atoms with a fictitious nuclear charge. A versatile theoretical tool for study of atom and group properties as substituents : electronegativity and partition of σ and π contributions"
E. Dumont and P. Chaquin Journal of Molecular Structure (Theochem) 680 (2004) 99-106.

 

[saray1360]

Unfortunately I have no access to that paper :( But works of Dr. Jim Chelikowsky are interesting as well.
I do thank you for your useful description.

 

[bpsbps]

This is a trick used in DFT methods to remove the surface states.

My experience with these is that you essentially pick the Z of the H-like atom to ensure that the surfaces have bulk-like bonds.

For example in GaAs each As has 5 valence electron and each Ga has 3. In the bulk this essentially means that each As brings 1.25 e to each bond and Ga brings 0.75 e.

If you create a surface you then will want to "cap" the dangling As atoms with H having Z=0.75 and the dangling Ga with H having Z=1.25.

If you instead use Z=1.0 you'll find that the surface will buckle. There are experimental papers that study this surface buckling.

Also the H pseudopotentials used for surfaces will have a much larger r_cut than for modeling true H. You'll want to create a pseudpotential with r_cut around 2 a.u.. To create a true H pseudopotential (to reproduce the vibrational properties of H) you will want r_cut to be 0.75 a.u. or even smaller.

 

[saray1360]

For example in GaAs each As has 5 valence electron and each Ga has 3. In the bulk this essentially means that each As brings 1.25 e to each bond and Ga brings 0.75 e.

This is exactly mentioned in paper PRB 71, 165328. It came to my mind that we calculate the share of each electron like this (considering GaAs again): 5x+3x=2, then x would be 1/4 therefore As would have 1.25e of the share and Ga 0.75e. Is it right? But we do not do so for those atoms that have d orbitals right?

In that paper the fraction of the Z of hydrogen is suitably chosen with calculating the homo-lumo gap, but they've done it for the semiconductors, is it only applicable for the semiconductors?

If you instead use Z=1.0 you'll find that the surface will buckle. There are experimental papers that study this surface buckling.

Yes you are right, I've had the experience of passivating the surfaces with true hydrogen, but I would be grateful if you address me to a better detail of surface buckling.

Also the H pseudopotentials used for surfaces will have a much larger r_cut than for modeling true H. You'll want to create a pseudpotential with r_cut around 2 a.u.. To create a true H pseudopotential (to reproduce the vibrational properties of H) you will want r_cut to be 0.75 a.u. or even smaller.

I am somehow familiar with the pseudogenerators, but do not know the reason for increasing R_cut, would be grateful to know the reason or references about that.

 

[bpsbps]

The choice of Z comes from drawing a simple Lewis structure diagram. The d-electrons of the potentials are ignored because in the simplest world view it is the sp electrons that are important. In practice, when creating pseudopotentials for Ga and As you need the d electrons -- you can include them explicitly as semi-core electrons or by including a partial core charge (pcc) in the potential.

In the paper the HOMO-LUMO gap is maximized to show that the H-surface states have been removed. An easier way to show for yourself that the potentials you've selected are far from the band edges is to perform a localized DOS calculation and the plot the DOS for the H atoms versus the DOS for the interior of the nanostructure.

Regarding buckling, the paper that I remember is:

K. N. Ow and X. W. Wang, Surface Science 337, 109 (1995).

I haven't read it for years so maybe my memory is wrong.

Regarding pseudopotentials, I use Opium

http://sourceforge.net/projects/opium/

You can generate modified (fractional) Z atoms but need to hack the periodic table data in the source.

Regarding selecting Rcut the smaller Rcut the harder the potential, and the more of the core that is included in the calculation. If you have too hard of a H then they become an important part of the calculation, whereas here we just want nice soft H that passivates the charge, but does little else. Also using hard H means that you will need a very large cutoff energy. Presumably you're looking at a large number of atoms so you don't want the surface passivation, which you aren't even getting useful data from, to mess up your overall calculation.

Regarding metals... I'm not certain how one would treat a surface to remove surface effects from metal structures... in semiconductors you're thinking about directional bonding -- mostly covalent, but slightly polar. In metals the bonding is completely different. I'll think about this and if I come up with an idea I'll post is later.