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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I forgot to mention about the DI value for F2. I looked at my old data and found F2 optimized at B3LYP/aug-cc-pVTZ level. Its DI was pretty large (~1.2 au). Of course, DFT is not comparable with CASSCF but in general DI for F2 is bigger than that of ethane at DFT level. DI of ethane is almost unity.
A CASSCF(14,14)/Def2-TZVPP calculation with optimized geometry for F2 (doi: 10.14469/ch/191869) gives a value for DI = 0.88637, or rather less than unity.
I am not surprised about small DI of fluorine molecule. As I mentioned before by inclusion of correlation between alpha and beta electrons they tend to localize more and more thus the delocalization index drops significantly. Therefore, for a meaningful comparison one must compute DI for two molecules at the same level of theory. If we want to compare DI of F2 with that of ethane as a stereotype of singly bonded system we must have DI of ethane at a CASSCF level comparable with that for F2.
I have done a CASSCF(6,6)/Def2-TZVPP calculation on [1.1.1] propellane, which is perhaps the most analogous system to C2. DI for the central C-C bond is .546 whilst that for a normal "covalent" C-C bond is .965. A CASSCF(12,12) calculation is running (added: central DI, 0.531, Normal CC 0.964)
I am not sure we can ever find a molecule that is a real analogous of C2. Please see my comment above.
One test for my hypothesis that fourth electrons localize bonding electrons:
How the C-CH2 bond lengths change between [1.1.1] propellane and tricyclo [1.1.1] pentane (I am not sure about name please forgive me if I use a wrong name; I mean the hydrogenated analogous of propellane).
If the weakly coupled electron localizes bonding electrons of C-CH2 bonds, then the C-CH2 bond lengths must increase and their DI should decrease from tricyclo [1.1.1] pentane to the propellane analogous.
Hi Cina, If you ge me an eamil I will be happy to send you the last paper on C2 (to be published in Chemistry Eur. J). If you have time to read it, you may be convinced that there is a quadruple bond and this quadruple bond reproduces the properties of the molecule. And you may find out that the model of Frenking (double bond with some weak dative bonds) collapses to the quadruple bond. As I told Henry, VB gives you a snapshot of the bonds as electron pairs, each lowering the energy of the molecule. I am less convinced by bond indices of various types. Sason
Hi Prof. Shaik, It's my pleasure to know more about this molecule from your point of view. What do you think of my idea of interfering fourth electron? I am almost sure that C2 is not a 2 +1 bonded system as Frenking et. al. say. But it is highly possible that a fourth electron can localize bonding electrons so C2 has 3 moderate + 1 weak bonds not 2 strong + 1 moderate bonds. Discussions on the basis of bond energy can be misleading because bond order-bond energy relationships are not that straighforward. Here is my e-mail address: canyslopus[-at-]yahoo.co.uk. I just replaced @ with [-at-] to minimize risk of receiving spams from machines that look for email addresses on web.
It is a pleasure to read the curiosity-driven conversations of my colleagues!
I also concur in that we need to understand what a "bond index" means, and that it might not always mean what it seems. Thus, Sason reminded of a quintuple bonded Cr-Cr system I had taken a look at a few years back. At the CASSCF(14,14)/Def2-TZVPP level, this ultra-short "quintuple" bond has a DI(A,B) = 2.195, practically the same as C2. So again driven by curiousity, I am runnning a CASSCF of the type we have been discussing on Cr2 (a molecule notoriously driven by electron correlation). The result might not be directly comparable to the molecules here, but it should be interesting!
It is indeed an interesting coinsidence. I should mention that the magnitude of DI cannot be used as a measure of bond order in the same sense that one cannot use bond energy as a measure of bond order. In both cases we need a reference system. For a detailed discussion please see this paper (DOI:10.1039/C5CP05777A) on the nature of anion-pi bonding (a supposedly noncovalent interaction that seems to be pretty covalent).
Yes, reference systems (or states) are always unsatisfactory, perhaps especially so with any molecule that has unusual/unique bonding that is not directly comparable.
Here are a belated two further systems, NArF3 (doi: 10.14469/ch/191878) and NKrF3. (doi: 10.14469/ch/191877). The ELF analysis gives both octahedral coordination, and as with the previous systems the delocalisation index DI(A,B) is large. One may again presume multiple NAr and NKr bonding.
Henry, Is there a take home summary about DI, Laplacian, ELF, etc.? May be time to summarize. .. Sason
Yes Sason, lots of results on two basic types of molecule, the X~ZFn systems (X=C, N, Z = P,S,Cl,Ar,Kr) and then the very different C2 (with its own problems). As you say, a summary is needed.