Calculating ESP charges for a molecule fragment using Gaussian

[angura]

Hi there,

I'm trying to reconstruct the ESP charges that have been determined in a paper using a Gaussian-like quantum chemistry program. While I understand the basic notion of the iterative procedures to approximate the wavefunctions etc., I'm not a chemist and so I'm having problems with simple chemical stuff, that probably every undergraduate student would know :(

The problem: I have taken out a cluster of a crystal structure, which is now a Zinc(II) that has 4 nitrogens of imidazole molecules coordination-bonded to it (which is not a "real" bond, as far as i understand). For this structure (Zn+4*imidazole), I want to perform a Gaussian geometry optimization and get ESP charges for the atoms.

Now I have to give the total charge of this molecule and I'm not sure what it is. A friend suggested that it is 2(Zinc) - 4*1 = -2, because the imidazolate units have -1. I also found an article which agreed with that suggestion.
So I did that and eventually got ESP and also RESP charges. But when I apply these charges to the full network (instead of the smaller cluster to compute these charges) this crystal is heavily charged and not neutral, because - roughly spoken - the imidazolates are too negative, while the Zn is not positive enough. (Although the charges properly add up to -2 for the cluster)
Oddly, when I use the published charges, the crystal IS neutral, but the cluster does NOT have a charge of -2, but -1.1.

How does that fit together? What am I doing wrong?

greetings, angu

PS: I can go further into detail, but I wanted to make the first post as small as possible, so I won't frighten you off ;)

 

[alxm]

Okay. Well an imidazole can have the charge:
-1 - nothing bound to either nitrogen atom
0 - a proton (or other cation) bound to one of the nitrogen atoms and no bond to the other (except as a ligand)
+1 - a proton or cation covalently bound to both nitrogens.

Now, the question is what the crystal structure looks like? You have four imidazoles bound (either as a ligand or covalently) to a Zn(II). What are the other nitrogen atoms on the imidazoles bound to? Neighboring zinc atoms? I suspect this is the case.

If that is indeed the case, then you can view each Zinc has having two bonded imidazoles (i.e. where the bonding nitrogen has charge -1), and two coordinating imidazoles (i.e. where the bonding nitrogen has charge 0).

Of course, due to symmetry and the fact that imidazole is aromatic, in actuality both bonds are equivalent. You could view it as each imidazole sharing -1/2 a charge with the zinc atom, and -1/2 with the other zinc it's bound to. (and then, the whole cluster will have a charge of -2, but the crystal as a whole will be neutral)

Chemically that'd be resonance between the forms: Zn..Im-Zn <-> Zn-Im..Zn
(where the dots are liganding, and the dashes are bonds)

You say the charge should be -1.1, which is noninteger and can't possibly be the simple total charge of the system. What is it? The sum of the Mulliken charges on the nitrogens or similar?
A model with a net charge isn't a good model. One idea is (if the structure is as described) that you'd try adding H+ or perhaps Na+ or K+ to two of the imidazoles, to try to emulate the effect of the neighboring Zn(II). (whichever does a better job of replicating the electrostatic potential from the neighboring Zn). This would unfortunately have the drawback of breaking the symmetry; the four ligands would no longer be equivalent.

Or you could make your model include more than one unit cell.. If you had five Zinc atoms and 16 imidazoles (which is big, but not too big). One symmetric and the outer four zinc-complexes asymmetric, it should probably get the middle complex right.

Feel free to link to the paper in question.

 

[angura]

Hi alxm,

first of all many thanks for your quick and detailed reply!
I also thought about somehow "terminating" some of these free nitrogens with something similar to Zn, but I wasn't sure, if this would be valid.

Here is a http://www3.interscience.wiley.com/journal/123204011/abstract?CRETRY=1&SRETRY=0" to the paper I was referring to. The details on the calculations are in the Supporting material on page S4.
They used such a larger system with more Zn's and then referred to the calculated charges near the center of the cluster, just like you suggested. However they don't seem to have added any atoms and therefore kept the symmetric structure. (Here again I wouldn't be sure what charge to use, If I wanted to reproduce that. I don't think that this cluster would be neutral). So - on a bigger scale - this would rise the same questions like my smaller cluster.

And there is one more thing, that I have trouble with understanding. You mentioned two ways to interpret this bonding (which I also both found in some literature):
- two bonded IM and two coordinated IM at one Zn
- but actually the bonds are all equivalent
How can both be true at the same time?
Or asked differently from a modelling point of view: Would there be a difference in the behaviour of a "bonded IM" and a "coordinated IM"? Please forgive my lack of knowledge, I'm a physicist on more or less unknown territory

Thanks again for your help,
greetings, angu

 

[alxm]

Here is a http://www3.interscience.wiley.com/journal/123204011/abstract?CRETRY=1&SRETRY=0" to the paper I was referring to. The details on the calculations are in the Supporting material on page S4.
They used such a larger system with more Zn's and then referred to the calculated charges near the center of the cluster, just like you suggested. However they don't seem to have added any atoms and therefore kept the symmetric structure.

Ah, nice to see they modeled it exactly like I thought they should!
But if you look carefully, they have 'capped' imidazoles in the outer four clusters with protons/hydrogens, so that there are two neutral and two negative imidazoles in each cluster. The total charge of the system should be zero.

And there is one more thing, that I have trouble with understanding. You mentioned two ways to interpret this bonding (which I also both found in some literature):
- two bonded IM and two coordinated IM at one Zn
- but actually the bonds are all equivalent
How can both be true at the same time?

Well, only the latter is true. It's due to quantum mechanics of course, the electrons don't have any problem being in more than one place at once. But chemists discovered this way before quantum mechanics and rationalized it as http://en.wikipedia.org/wiki/Resonance_%28chemistry%29" . So you draw it as if it were switching back and forth between the two different forms, although the reality (which everyone agrees on) is that it's actually in-between, or in both states at once.

Or asked differently from a modelling point of view: Would there be a difference in the behaviour of a "bonded IM" and a "coordinated IM"?

Yes! Now if you think about a single complex, where you have Zn(II) with two Im_- and two ImH (neutral). These four bonds are not equivalent - the two negatively charged bind much more strongly to the zinc, because it's a proper ionic bond (which is viewed as the imidazole 'donating' its entire surplus charge to the positive zinc).

But in your crystal, you do have four equivalent bonds due to resonance. Each imidazole resonates between coordinating to one zinc and binding to the other, and vice versa. Obviously this chain has to be terminated somewhere (at the edge of the crystal) but from the chemical standpoint, that's infinitely far away and the contributions from it are negligible.

So in a 1-zinc, 4-imidazole model, you wouldn't be able to make it have four equivalent bonds while keeping it neutral (and having a model with an overall charge would very likely cause even bigger errors). But with 5 zincs and 16 imidazoles, all the imidazoles on the innermost zinc are (mostly) free to resonate.

 

[angura]

Hi alexm,

thanks once again for your explanations.
I looked at the structure in that paper and really seem to have overlooked these capping hydrogens. Thanks a lot, I will prepare a similar system and try it out :)

The reason I asked about the difference of these bonds for modelling purposes was that I was wondering, If one should then also incorporate 2 different bond types in simulations of a flexible network of this structure. But since it seems to be always "both at the same time" I guess that wouldn't make sense.

So now I will submit this to our computing cluster and hope for the best ;)

greetings, angu

 

[angura]

Update:

I now have the results of the Gaussian job and computed the ESP (actually RESP) charges.
Since I only have a cluster and not the extended structure, there are some differences between the charges on the atoms near the center and at the edge.

In the paper I quoted, they say they took the charges from the atoms near the center, because the outer ones show clustering effects. However, when I do that, is also end up with a charged structure for the whole extended system, although this time not as bad as with the small cluster at the beginning.
When I adjust these charges very slightly, I can make the crystal neutral, but I would have to justify this adjustment. Or is this something, that is commonly done, but not directly said and just silently implied?

greetings, angu

 

[alxm]

Hmm, do you mean that Zn + 2 Imidazoles or Zn + 4 Imidazoles? I'd expect the former to be near-neutral but the latter should have a -2 charge.

Other than that I don't really know; I'd suggest asking the guys who did the original work.