The post on applying VSEPR ("valence shell electron pair repulsion") theory to the geometry of ClF3 has proved perennially popular. So here is a follow-up on another little molecue, F3SN. As the name implies, it is often represented with an S≡N bond. Here I take a look at the conventional analysis.
This is as follows:
Now for a calculation[1]; ωB97XD/Def2-TZVP, where the wavefunction is analysed using ELF (electron localisation function), which is a useful way of locating the centroids of bonds and lone pairs (click on diagram below to see 3D model).
So we have achieved the same result as classical VSEPR, but using partial rather than full electron pairs to do so. We got the same result with ClF3 before. So perhaps this variation could be called "valence shell partial electron pair repulsions" or VSPEPR.
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Just to show that this picture can be obtained from QTAIM, I made one graph for you.
To make this figure, I removed sigma orbitals from the wavefunction of molecule (MOs #10, 13, and 23). Sigma orbitals are usually highly concentrated so do not permit that the topology of pi electrons to be detected. The molecular graph evidently shows three equivalent pi-interactions. I have to mention that delocalization index of the S-N bond is 1.99 electrons, comparable with a double bond C-C bond. However, since the S-N bond is polar, the magnitude of DI is reduced from ideal number expected from VSEPR that is 3. Finally, I think it is legitimate to remind of the latest works of Ronald Gillespie in which he explained that VSEPR is in fact a buzz name for Pauli Exclusion Principle. The real factor that determines geometry of a molecule is not valence shell electron repulsion but is Pauli exclusion that pushes electrons with same spin as far as possible from each other.
The real factor that determines geometry of a molecule is not valence shell electron repulsion but is Pauli exclusion that pushes electrons with same spin as far as possible from each other.
Yes indeed it is the Pauli exclusion we are really discussing here (and ELF is another way of tracking that). But most student-level examples do not teach it like that, and instead focus on the electron-pair. This leads to eg the consideration of five pairs (ten electrons) for F3Cl, or if you take the Lewis structure shown for NSF3 at face value, 12 electrons (four σ-bonds and two π-bonds).
Yes, unfortunately, at student's level VSEPR is defined as electron pair repulsion. Again unfortunately, those who study in less-theory-oriented branches of chemistry have no idea about the role of PEP. They keep the notion of electron-pair repulsion as a sacred rule. PEP should be entered into general chemistry text books, I believe.
And to add one further electron localization method, NBO (natural bond orbitals). I will merely summarise the results (DOI: 10.14469/ch/191808) here:
1. Two orthogonal S-N π-NBOs
2. One S-N σ-NBO
3. Three equivalent F-S σ-NBOs.
Which seems to point to six electron-pair bonds around S (NBO integrates these to 11.39e) and very much the Lewis structure shown at the head of the post.
BUT:
4. There are three equivalent F lone pairs each with some F-S antibonding character.
5. There is one N lone pair, again with a node along the N-S bond.
Overall then, one might conclude that there are LESS than six bonding electron pairs surrounding the central atom, attenuated by antibonding character from another four pairs.
This is certainly a fascinating little molecule.
One can reduce this last example down to the di-anion of methane (DOI: 10.14469/ch/191811). It has tetrahedral symmetry (no Jahn-Teller effect), with four equivalent C-H bonds/NBOs and one (spherical) carbon lone pair/NBO. Ten valence electrons surrounding carbon? Of course, this carbon lone pair is antibonding in the four C-H regions. This does help remind us that the octet rule applies to bonding electron pairs.
To make this figure, I removed σ orbitals from the wavefunction of molecule (MOs #10, 13, and 23) ... The molecular graph evidently shows three equivalent π-interactions.
So if you QTAIM using only MOs 10,13 and 23, do you then get a N-S σ line critical point (vis BCP) back?
Although no longer seen much, an alternative non-symmetry-adapted represention of double bonds is two equivalent banana bonds. Is NSF3 a three-fold version of that, or something new?
First, I think I should say that the figure in my previous comment is a trap! It does not demonstrate a triple π-bond + one σ bond that is removed, making altogether 4 bonds. It is merely curvature of pi-electrons that look like banana bonds.
Then I should say yes, using those orbitals I get one LCP between S and N.
Please remember that according to IUPAC definition the bond order (on the basis of Muliken MO theory) is sum of all overlap matrices between two atoms. In practice there are many MOs in which S and N have at least a minor overlap -here I had to remove 3 of them to remove σ S-N bond. The sum of all MOs is manifested in the magnitude of the delocalization index that is 1.99 in this case.
If I remove sigma-type orbitals from the system and rerun QTAIM computations, I get DI = 1.33 e that is ~ 0.66 e less than the all-electron wavefunction. This means that those 3 σ orbitals had 0.66 e contribution to the S-N bonding.
The π contribution (1.33 electrons) is the sum of contributions of MOs 15, 16, 20, 21, 24, and 25.
One can play the same game with FNPF3, with a NF higher bond order than one (DOI: 10.14469/ch/191812). The coordination is square pyramidal, with three P-F basins and two N-P basins.
Here are two maxima in π-framework of FNPF3:
Responding to the drop in the DI for the N=P bond due to F on the nitrogen, the obvious system to try next is NPF2 (DOI: 10.14469/ch/191814).
The angle subtended at P for the N-P basins is 149.6° (basin integration 1.82e), closing the angle subtended at P for the P-F basins (integration 1.22e) to 91.2°. The phosphorus is now ~tetrahedral. The NP bond is therefore ~double, and not triple as shown in the Lewis representation. Does QTAIM replicate this?
Another homology of the above would be NClF4. It is a stable species with all-real normal modes and C2v symmetry (doi: 10.14469/ch/191817) but the ELF analysis as well as standard QTAIM make little sense. NBO analysis however does suggest two π bonds between N and Cl. Not sure what is going on here.
The Br analogue NBrF4. (DOI: 10.14469/ch/191818) however is normal, with ~double-bond N-Br character.
I get normal results for F5ClN (wB97XD/def2-TZVP but Cs symmetry ... C2v symmetry is found with a little higher threshold). NBO6 analysis with Natural Resonance Theory stuff says, that there are no other important Lewis structures above the threshold ... which is different to the first structure in this blog entry, F3SN (there are six and the "main" one has only 29% weight). (I missed to show it, but the bond critical points are only on the "middle" of all five bonds and there is also only one BCP per bond.)
Well ... I hope, the picture is included this time.
Thanks Philipp.
1. It is unfortunately not possible in the security model for Wordpress blogs, for comments to include images. This is because they could include executable code which is a virus. So I have to manually get the image and insert it as "administrator".
2. MultiWFN (as discussed elsewhere on this blog) is a highly capable wavefunction analyser. Unfortunately, I am running OS X El Capitan which has a new security model. One of the key graphics libraries required to make MultiWFN work on a Mac (OpenMotif) no longer works with El Capitan (even the installer will not install). So my MultiWFN capability has (I hope temporarily) gone.
Amongst the significant differences in the ELF function between MultiWFN and TopMod09 is how lone pairs at halogens are treated. TopMod09 produces normally a pair of localisations basins, whereas MultWFN produces a torus; I think the latter is more accurate and can be seen above!.
Just a note to say I have now got Multiwfn working again. The solution was rather tedious, but involves over-riding El Capitan's System Integrity protection ( http://www.imore.com/el-capitan-system-integrity-protection-helps-keep-malware-away ) and the use of Pacifist to then install the OpenMotif libraries. There are quite a few other non-standard operations, and if anyone reading this wants more details, do please contact me directly.
re BCPs (better perhaps called line critical points or LCPs) are in the middle of all five bonds and there is one BCP per bond only if one looks at the total density. If one removes σ MOs leaving only π-looking MOs, the QTAIM picture is different. This is because the σ density induces annihilations of the π contributions and leaves only an LCP along the bond. See the graphs produced by Cina here!
Both systems were pretty interesting. In case of PNF2 I checked the DI for PN bond; it is 1.89 e for full electron density, which is more than twice the magnitude of DI for PN bond in FNPF3. I think it confirms my speculation about the role of fluoride substituent in polarizing the PN bond. I also removed the σ electrons. The DI droped to 1.25 e. Two LCPs appeared, corresponding to two electron concentration in the topology of electron density of π framework. Also in line with ELF picture.
Yes, the π topology is indeed fascinating; a four-fold banana bond. One might even be tempted to equate it to a quadruple bond (although I suspect the analogy is false).
I do not know why the WFN file was corrupted (it clearly was), since it works for eg NBrF4 and even NClF3Cl. I did run the calculation three times, changing eg the integral accuracy and the grid size, but all failed in this manner. A deep seated Gaussian bug?
I ran the π-only WFN file you created through TopMod09; it has the advantage that it integrates the basins for electron density (If I remember, MultiWFN does not do this?) and it shown below (π-only).
If I understand the desired calculation correctly, yes, MultiWFN is able to integrate the electron density in the ELF basins:
* Main menu option 17 (basin analysis)
* Generate basins (option 1 in 1st menu) on ELF (option 9 in 2nd menu)
* Once generated, integrate real space function (option 2 in 1st menu) selecting electron density (option 1 in 2nd menu) as the function
One of the frustrating aspects of MultiWFN, though, is tracing back which basin # corresponds to which nucleus and/or non-nuclear ELF attractor. I have plans to write a Python wrapper for it at some point to automate collation of such results, but I've not yet started coding it.
I am unable to use MultiWFN any more. It is built using an OpenMotif graphics library for OS X. Since I updated OS X to El Capitan, that library (which is no longer maintained) does not install (the installer simply now fails) and MultiWFN does not execute.
MultiWFN has many advantages:
1. It is parallelised, and so runs very much faster than TopMod09.
2. Accordingly, it can generate very much finer meshes
3. Basin collection seems to be more accurate than TopMod09.
4. But its graphic interface is relatively simple and it can be quite difficult to orient a molecule interactively.
If anyone has any advice on how to get MultiWFN working again on OS X, I would much appreciate it.
Hm, well, that's irritating.
I looked at the MultiWFN website; there is apparently a new version as of last week, 3.3.9 - but, it appears still to have openMotif as a dependency. No help there.
I would contact the development lead, Tian Lu, at Sobereva--at--sina--dot--com to notify regarding the incompatibility and to solicit advice for resolving it. Hopefully there's another library to which it can be ported.
As re #4, yes, this is a tremendous disadvantage of MultiWFN. I think one can export basins, paths, etc. in various forms (.cube, pdb, etc.) that might be importable to other software (Avogadro, VMD... perhaps Chemcraft?), but it's an annoyance to have to go through the additional steps.
A slight change of tack, but I checked the crystal database for any instances of e.g. N=Cl or N≡Cl (ie higher than a single bond order). There are none.
There are however 35 instances of S≡N (no disorder or error in data). One should remember that the designation ≡ is to a large extent entered into the database by a human and probably does not have any theoretical meaning.
A histogram of SN distances is shown below, revealing there are examples below 1.4Å!
This entry (VEPVES, doi: 10.5517/CCNJ6V6) is the shortest (1.364Å) and is Me-N≡SF3+. SbF6-. This in turn reminds me that if one takes N≡N and protonates it to H-N≡N+, the N≡N bond contracts significantly!
Interesting results! I am not much aware of experimental work on hyper-coordinated halogens but I doubt anyone have tried to synthesize NClF4. It should be very instable, almost an explosive! What you think about publishing NClF4 as the first example of Cl-N triple bond? :)
Whilst a Cl≡N triple bond is quite esoteric, the route taken to arrive at that point is perhaps more interesting. Thus the article entitled "One Molecule, Two Atoms, Three Views, Four Bonds?" (coined by the way by Roald) sets out a trialogue almost in the manner of the script for a play (see DOI: 10.1002/anie.201208206). I think its always interesting to experiment with the form of the "journal article". So food for thought there.
I noted above that defining a triple N≡S bond in the crystal search is rather subject to arbitrary classification, and so got to wondering what a search with a double bond specified might come up with. Here it is. Again, there are a few hits < 1.4Å, although the most frequent value is now ~1.55Å, longer than with N≡S.
Back to the start! Here is the ELF analysis for MeNSF3+ (doi: 10.14469/ch/191820). The triple bond basins are now highly populated, and as per usual in this trialogue your π-dissected QTAIM Cina would be useful. And what is going on with that little basin integrating to 0.4e along the SN axis?
This new molecule is really hot! First, though the S-N bond in CH3NSF3 is shorter than that of NSF3, the delocalization index between S and N is "less" than that of SN bond in NSF3. Here the DI is 1.35 e, compared with 1.99 for the SN bond of NSF3.
So, I might say that some sort of ionic interaction between S and N is decreasing the bond length. Or, something is going on that I cannot understand at the moment. I need to think more. I see a short bond with less covalency. Maybe we cannot compare NSF3 and Me-NSF3+...
Anyhow, there are even more interesting things to see. Please see the molecular graph without σ electrons:
Here not only I can see the familiar banana shaped curvatures, but I see also something between methyl group and N that I would like to call it the effect of hyperconjugation! This is fascinating! I think this is the first example that someone showed an electron-density based representation of hyperconjugation.
The DI without σ-framework is 1.18 e that suggests the σ-electrons have a minor effect on the S-N covalency. While in NSF3 σ-electrons had a contribution of 0.66 e, here the σ-framework has only 0.17 e contribution to S-N bond. Where are those electrons? Maybe are shared with carbon. Finally, nothing comes out of electron density analysis to unveil the nature of that attractor near the sulphur atom. Can that attractor explain lower covalency between S and N? Many things to think about till tomorrow!
Cina,
I thought I would have a go at computing QTAIM on just the π manifold. The most obvious thing to try first was to obtain a WFX file (this is a human-readable version of the standard WFN file, + some additions) where the MO occupancy numbers can be easily edited down to zero as desired. But running this edited WFX file through AIMALL produces nonsense.
So might I ask how you dissect the contributions of the MOs to the QTAIM analysis?
In fact WFX is not as easy to work as WFN for disection. I do not use WFX unless 1- I want to check magnetic properties; 2- Deal with an atom with ECP. To remove MOs from WFN you just have to set occupation number of MOs in WFN equal to zero. I am working on your samples. But unfortunately, I catch a cold, stayed in bed and thus computation is slow... Please see one example of manipulated WFN here: https://dl.dropboxusercontent.com/u/51599297/cf3clfn-pi.wfn If in some cases like this species &;sigma; and π are mixed. It's better to remove whatever that resembles a σ orbital.
The normal canonical MOs often mix σ and π very extensively. I am wondering whether one could instead use localised wavefunctions such as NBOs? The trick would be to get eg Gaussian to write out NBOs into the WFN file rather than MOs. This should result in σ NBOs that project out π contaminations and vice versa.
Do you know if the WFN write can be manipulated like this (perhaps via an IOP command?)