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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Yet another transform; CF3CSF3 is a known crystal structure (doi: 10.1021/ja00050a027), where the neutral CF3C replaces the charged CH3N+. The calculation (doi: 10.14469/ch/191821) shows C3v symmetry, but the out of plane deformation is a low energy one. The C≡S bond length is calculated as 1.430Å.
The CF3N+SF3 isoelectronic isomer of CF3CSF3 (doi: 10.14469/ch/191823) is now bent (156.8°) and the C≡N length is 1.395Å. This bending reminds of Lewis' 1916 representation of the triple bond in three isomeric forms, one linear and two bent. Whilst C≡C is always found in a linear form, SiSi bonds are bent, and this system is clearly on the edge between the two.
Next, CF3NClF4+ (doi: 10.14469/ch/191824)
And to complete the set, here is CF3CClF4 (doi: 10.14469/ch/191826).
This is a nice idea indeed. In 2009 I searched a lot to do so because I wanted to check the effect of electron density on dissected-NICS. But, couldn't find any trick to do that. Anyhow, for most of your examples σ-π separation was achievable. These non-linear molecules are making a bit of trouble. Meanwhile, please see molecular graph of CF3NCl4: N-Cl DI for full electron density wavefunction is 1.76 e and for π-framework is 1.3 e. Molecular graph seems fine to me, although the molecule is nonlinear.
Here is CF3-CSF3; the C-S DI for the full electron density is 1.99 e, and that of π-density is 1.41 e. I see three banana-shaped π-interactions.
The last example that I checked today is CF3-NSF3. It seems that when molecule is bent, σ-π separation distorts the molecular graph. Please see the MG here: https://dl.dropboxusercontent.com/u/51599297/cf3-nsf6-pi.png The DI of S-N bond is 1.30 e that drops to 0.83 e after removing σ-electrons. I am not happy with the MG of this species. It is a catastrophic MG in Bader's terminology, i.e. a small change in the molecular geometry changes the MG. Please note how close are RCP and BCP in CF3 side. A minor change in the geometry will merge these points.
Yes, it is a topological feature that appropriate pairs of critical points can annihiliate each-other, and so geometric catastrophies are possible. ELF at least is stable to this sort of effect.
P.S. 1; I will check the last system tomorrow. P.S. 2; I am almost sure you have seen this paper but just in case. 10.1039/C5SC04608D
Finally, here are data for CF3CClF4. The π-electron density has a pattern pretty similar to what you obtained from ELF analysis. I noticed that there are some CMOs formed from combination of p-orbitals of fluorine atoms on Cl and σ-type Cl-C MOs. If I keep them in the wavefunction, the final molecular graph looks perfect and those anomalous critical points do not appear. So, it means that I may play with the molecular graphs of the other systems to make them stable (in terms of topology).
It does not affect on the magnitude of DI considerable because the overlap matrix is not big enough to affect the magnitude of the DI. The DI for C-Cl bond in CF3CClF4 is 1.63 e. Removing the σ electrons decreases the DI to 1.12e. What do you think about examining molecules with a negative carbon? This is iso-electronic with nitrogen. Someone may synthesize them as a cesium salt perhaps!
Cina,
The C(-) analogue of N is a known motif in crystal structures; there are four examples known to metals.
1. SIVREV to Os (doi: 10.5517/CCN9Z41 )
2. ROJVOB to Mo (no doi)
3. OGONON to Ru (a Kate Bush song! Almost) (doi: 10.5517/CC6CYL2 )
4. IDOZOQ to Ru (doi: 10.5517/CC61WVY)
Now there is a suggestion. Since single-coordinated carbon (in e.g. C2) can (controversially it has to be said, see 10.1002/chem.201400356 for one interpretation) sustain a quadruple bond, are any of these examples thus? I suspect we might be about to find out!
Now for (-)CSF3 (doi: 10.14469/ch/191831)
Well, I analyzed this system. For the full electron density DI is quite high (2.50 e), comparable with C2. At that time when C2 was in spot light, I checked it with AIM for my curiosity and came to this conclusion that it can't be a quaduply bonded carbon-carbon bond but didn't publish anything. In fact, ethyne has a DI of ~ 3.0. Anyhow, when it comes to heteronuclear bonds polarity of the bond decreases the DI. The DI for π-electron density is 1.84 e. Thus, σ contribution is 0.66, exactly similar to the original molecule, NSF3. Now, let me be a dreamer for a moment. If we imagine that the π contribution to delocalization is comparable with the σ contribution then I should say that my analysis suggests that this molecule has a quadruple C-S bond since 1.84/0.66 = ~ 3 that is three π bonds and one σ bond.
10.14469/ch/191831)
Remember that with C2 itself, the 4th bond can only manifest when multireference character is included. Any density derived from single reference methods will not reveal the 4th bond. There is also very direct experimental thermodynamic evidence that over and above three normal bonds, there is an additional stabilisation of ~17 kcal/mol in C2, and the simplest way of understanding that stabilization is to ascribe it to 4th bond worth 17 kcal/mol. This is strong enough to be called a bond rather than an interaction.
With metals, ie Cr-Cr and other high multiple bonds, again it is correlation only recovered from multireference methods that describe such species properly.
I did check its CAS density indeed but as far as I can remember from the original paper in Nature Chemistry, that 17 kcal/mol stability is with respect to an arbitrary electronic state, i.e. an excited electronic state of carbon with four unpaired electrons in the valence shell. Excitation needs a large energy (perhaps ~ 80 to 90 kcal/mol) that absolutely compensates that 17 kcal/mol. Then, is it really meaningful to call C2 a quadruply bonded carbon? I feel uncomfortable with it. To me MO picture with two bonds is perfect. One can compare C2 with C2H and HC2H to see how the bond length is changing; very simple and clearly the trend is in favour of a doubly bonded C2. Also C2 is isoelectronic with N2(2+); does anyone in chemical community accepts that N2(2+) has quadruple bond?
The topic of higher multiple bonds between C or N and metals is perhaps rather straying from the theme here. But having flagged quadruple bonds, I cannot resist showing one metal system, VADBAD (a nitridocyanomanganese metallate, doi: 10.1021/ic971377h). This has C4v symmetry, and the ELF is shown below (doi: 10.14469/ch/191834). Notice how the ELF basins in the C≡N regions are split into two because of the π contributions. Normally, this splitting may not be observed.
10.14469/ch/191831)
The caveat is that this is a single reference method describing the Mn-N multiple bond character, and should probably be taken with a pinch of salt.
Here is the beautiful π-molecular graph of this complex:
The DI between Mn and N is amazingly large for a polar metal-nitride. It is 2.49 e with 0.72e σ contribution and 1.77e π-contribution. These examples are indeed fascinating due to their large DIs. What do you call these bonds? A triple bond? A quadruple bond?
re I did check its CAS density indeed but as far as I can remember from the original paper in Nature Chemistry, that 17 kcal/mol stability is with respect to an arbitrary electronic state, i.e. an excited electronic state of carbon with four unpaired electrons in the valence shell
Sorry Cina, that is wrong. The 17 kcal/mol is an experimental value for bond dissociation energies leading to C2. The dissociation energy of HCC(.) to CC is measured as 17 kcal/mol less than the dissociation energy of HCCH to HCC(.). The HCC(.) radical is σ state, and localised on just one carbon, and the stabilisation arises from new spin coupling between this radical and the new electron liberated from the second dissociation. In character, it is similar to the spin coupling in [1.1.1] propellane which forms a weak central C-C bond, ie much "longer" than normal C-C bonds. Because this "bond" is longer, its effect on the total electron density is likely to be small, and probably masked. Sason Shaik has gone through other arguments such as Badger's rule for bond length/force constants etc, and resolved them all.
Then I obviously missed this part. No one can argue against the bond energy, I think. I read the original article in Nature Chem. and few follow ups one by you and Roald Hoffmann and the other by Gernot Frenking. The excited C atom was introduced in the original work I remember. So, let's go back to our business; let me check the latest molecule.
I rechecked my old AIM computations on C2. There is something weird there. I am rechecking everything from the beginning by a huge basis set. My old interpretations seem wrong to me.
Time I think to collect all these results into a single table to see if further patterns emerge. Whether this is best done here or elsewhere we might discuss.
Absolutly agree. I am just working on C2. I checked my old data, there was an NNA in between carbons. I also realized I had studied C2 at a DFT level that produces the same geometry as CAS, not at CAS level. Then, I was trying to get it optimized at CAS(8,8)/def2-TZVP level with Gaussian. But, I realized that G09 rev. D02 has a bug with CAS; if you sepcify CASSCF instead of CAS, though technically these methods are the same, Gaussian fills the memory of computer with something that I don't know what it is! Even, CAS(4,4) for ethyne does not proceed with specifying CASSCF with 1.5 TB memory! So, I am now redoing them after realizing how to fix that bug. I hope I can get the data before tonight. Tonight, I am going to Iran and there I will have limited access to Worldpress blogs since they are surprisingly filtered! I can be in touch with you via email.
Finally, analysis of C2 finished. I got it optimized at CAS(6,6)/def2-TZVP level. Concerning the results obtained by Frenking et al (doi: 10.1002/anie.201301485), CAS(6,6) should describe the main part of the wavefunction according to their analysis, performed at CAS(8,8)/cc-pVTZ computational level. I also did the same with ethyne as a reference system (optimized at CAS(6,6)/def2-TZVP). The DI for CC bond in ethyne is 2.20 e. IN C2 the situation is indeed very complicated and open for debate! I found two NNA in between C atoms. Please see the MG and plot of del^2Rho for this system here:
These NNAs contain 0.83 e. One may say these electrons are indeed a part of shared electrons between two carbons. Then the DI betwen two carbon atoms is 1.48 e. Of course less than that of ethyne. Each carbon shares some electrons with each NNA too. Also, NNAs share some electrons with each other. The sum of all shared electrons in the molecule is 2.91 e but this includes NNA-NNA and C-NNA interactions too that I have no idea what to say about them. However, if we say since NNAs are in between two carbons then their sharing can affect CC bonding and increase the CC bond order. I cannot manipulate WFN of CAS since orbital populations are evidently fractional. So, I can just speculate that these NNAs might be related to those free electrons of the C2 molecule. One may look at the situation differently. You can say the bond order is sum of DI between CC and the population of NNAs because NNAs are between C atoms, thus have characteristics of the "shared electrons". Then total number of shared electrons will be 2.31 e, again larger than that of ethyne.
I will perform one final analysis within the context of IQA theory of Pendas et al. Let's see what may come out of that one.
I have seen NNA (non-nuclear attractors) between atoms previously (most famously in F-F), but never two. As you say, interpreting QTAIM with fractional orbital occupancies coming from multireference states is "unexplored". But clearly C2 is different from HCCH, and continues to spring surprises!
I had seen examples with more than one NNA between two atoms. B3+ at DFT level has a strange molecular graph with more than one NNA between two atoms. But again, such cases are not systematically studied. I cannot say that those NNAs are not just an artifact in the electron density of B3+. Even here who knows, increasing the basis set size may removes these NNAs. Or an FCI treatment or even CASPT2 may results in a different molecular graph. There are many unexplored things about tiny molecules like C2. Unfortunately, grant agencies do not pay for such studies!
In chemistry we are application-oriented as you know well; but in physics, they know how to admire the elegance of phenomena and do not care how much it may cost to build a megamachine like LHC.
One technical comment; it is always worth increasing all program accuracies on SCF and two electron integrals for such cases.
I can fully replicate Cina's CASSCF(6,6)/Def2-TZVP QTAIM result for C2 (below, all electrons included, doi: 10.14469/ch/191848). The two NNA's are surrounded by three LCPs, but they are quite close and two annihilations would indeed leave just a single LCP (BCP), which is the normal result along a bond. So there is little doubt that C2 is most unusual in this regard.
A similar result is obtained for the isoelectronic B22- (doi: 10.14469/ch/191847)
The equally isoelectronic N22+ is however different (doi: 10.14469/ch/191846):
We also did AIM for C2. C2 has at least two charge-shift bonds (the π bonds) if not three (the weak bond). Charge shift bonds have these strange AIM features.
Sason
May I ask you if you have published your results, let me have its DOI?
I have to add that the pattern in the Laplacian plot is related to the atomic shells. Each atomic shell has a charge concentration and a charge depletion region. The best examples to check are noble gases. You see these regions for helium to any noble gas that has an all electron basis set. Besides, I checked delocalization index for C2 at CAS (8, 8)/def2-TZVP. It has basically the same values as that of CAS (6, 6). The DI differs in the second digit after the point.
It's a good point. The small effects we are looking for may indeed be masked by the larger effects of the atomic shells.
I am not sure how the VB concept of charge shift bonding can be defined within the context of AIM but if you are looking for charge concentration/depletion regions, you may look at the ∇4ρ(r), Laplacian of the Laplacian, to see minute changes in the electron density distribution. It is available in AIMAll, I think. Though, no one used it yet for such a purpose.