Hypervalence revisited. The odd case of hexamethyl selenium.

November 7th, 2017

One thread that runs through this blog is that of hypervalency. It was therefore nice to come across a recent review of the concept[1] which revisits the topic, and where a helpful summary is given of the evolving meanings over time of the term hypervalent. The key phrase “it soon became clear that the two principles of the 2-centre-2-electron bond and the octet rule were sometimes in conflict” succinctly summarises the issue. Two molecules that are discussed in this review caught my eye, CLi6 and SeMe6. The former is stated as “anomalous in terms of the Lewis model“, but as I have shown in an earlier post, the carbon is in fact not anomalous in a Lewis sense because of a large degree of Li-Li bonding. When this is taken into account, the Lewis model of the carbon becomes more “normal”. Here I take a look at the other cited molecule, SeMe6.

I should start by summarising what I think are two fundamental ways in which electrons can be added to the valence shell of a main group element.

  • If an s/p basis only is used for the (main group) valence shell, then once eight electrons have populated the four bonding molecular orbitals constructed from this basis, additional electrons can then go into the four antibonding orbitals. This simple concept is often taught as an explanation for why the bond orders across the range N≡N, O=O, F-F and Ne…Ne decrease regularly (in fact one could also add CC to the left of this series, which is thought to have a weak quadruple bond). The Lewis octet is maintained throughout.
  • The second fundamental possibility is to expand the valence shell basis set to s/p/d or s/s/p/p (the second s or p-shell is the Rydberg level, i.e. 3s for carbon) or even s/s/p/p/d. That would be a true Lewis octet expansion, which depends on identifying significant Rydberg occupancy. This latter is in fact very rare, and few examples have been conclusively identified. One such as been discussed on this blog  and more examples were presented at the Aachen bond Slam in September 2017. Unlike the first mechanism (which reduces bond orders), this one actually increases bond orders and any bonds where the atomic orbital contributions have a significant Rydberg component can be considered as “Hyperbonds“.

One can then address the issue of hypervalency (and any octet expansion) by analysing the basis set contributions of the orbitals. These orbitals can be either canonical molecular orbitals or localised (NBO) orbitals. If a single determinant wavefunction is appropriate, then the orbitals would be doubly occupied (for closed shell species). If the molecule has multi-reference character, then of course fractional electron occupancy of these orbitals may be required (as would e.g. be the case for ozone, O3, another molecule asserted in the review as hypervalent[1]).

There are other ways of analysing the wavefunction. The one discussed at length in the review[1] is from an atomic charge map, but also mentioned is an ELF partitioning. This derives not from an orbital population but from the distribution of a function (ELF) calculated from the electron density itself. It was this latter method that was cited for SeMe6. The ELF method partitions electrons into so-called basins, which can be monosynaptic (lone pairs and ionic bonds), disynaptic (covalent bonds) and more rarely trisynaptic (3-centre bonds). Using this analysis, six disynaptic octahedrally-arranged ELF basins were located for  SeMe6  (“in which the Se–C bonds are relatively non-polar, can have electron populations exceeding 8 at the central atom”[1]) and for which the total integration cames to 11.34e (FAIR Data DOI for this calculation can be see at 10.14469/hpc/3219).

The key phrase is “non-polar”, since the Lewis concept relates to shared electron pair or covalent hypervalency. It was this aspect that I focused on seven years back in looking at whether e.g. IF7 was hypervalent (along with I(CN)7). These were too ionic to reveal disynaptic covalent ELF basins. So in an effort to reduce the polarity, I tried II7 and At.At7, on the grounds that these homonuclear molecules might be less polar. The seven I-I or At-At ELF disynaptic basins integrated to totals of 6.55 and 6.47e respectively; there was no evidence of “octet expansion” for either central halogen. Instead of course, the six electrons in the octet-excess needed to create seven I-I bonds actually populate I-I antibonding orbitals, as per method 1 above. Accordingly the I-I bond orders reduce from 1.0 to e.g. 0.47 for the axial substituents and 0.37 for the five equatorial groups.

One interesting property of the centroid of the ELF basins is that you can infer the polarity of the bond from its position along the bond axis. For II7, the centroids are displaced towards the central iodine, indicating it is more electronegative, and away from the terminal iodine, indicating it is the electropositive partner. I mention this since the ELF basins for SeMe6 show the centroids to be strongly displaced towards the carbon and away from the Se (0.38/0.62), indicating that this molecule is in fact polar and NOT non-polar as was asserted. 

To follow-up this latter observation, I did an NBO analysis of the wavefunction for SeMe6 (FAIR Data DOI: 10.14469/hpc/3220). This reveals the following properties.

  • Se populations: [core]4S( 1.30)4p( 3.04)4d( 0.06)5p( 0.01) of which Rydberg = 0.06516, natural charge on Se, 1.60224
  • C populations:  [core]2S( 1.20)2p( 3.65)3S( 0.01)3p( 0.01) of which Rydberg = 0.01838, natural charge on C -0.86670
  • H populations:  1S( 0.80)
  • Total Rydberg population: 0.20556
  • Wiberg Se-C bond orders:  0.6689
  • Wiberg bond indices:  Se 4.0431, C 3.8252,  H 0.9621

So according to this orbital-based analysis, SeMe6 is in effect a partially ionic compound with no evidence of significant Rydberg occupancies and hence no evidence of any octet expansion at Se. Thus we see two different interpretations emerging, depending on the analytical method used:

  1. SeMe6 is a polar molecule with no hypervalent attributes as judged using orbital analysis.
  2. As a polar molecule, it has six methyl carbanion-like substituents in which the carbon “lone pairs” all point towards the Se, manifesting as disynaptic ELF basins and indicating a total valence-basin octet-expanded population of 11.34e at Se. Even though this octet expansion originates mostly from the carbon atomic orbitals, the disynaptic nature of these valence basins means that the Se could indeed be defined as hypervalent.

Well, SeMe6 has turned out to be rather less clear-cut than implied by the assertion “in which the Se–C bonds are relatively non-polar”. There are however possible modifications to SeMe6 that might yet make it less polar. These may be the subject of a follow-up post.

References

  1. M.C. Durrant, "A quantitative definition of hypervalency", Chemical Science, vol. 6, pp. 6614-6623, 2015. https://doi.org/10.1039/c5sc02076j

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Posted in Hypervalency | 4 Comments »

Elongating an N-B single bond is much easier than stretching a C-C single bond.

October 24th, 2017

An N-B single bond is iso-electronic to a C-C single bond, as per below. So here is a simple question: what form does the distribution of the lengths of these two bonds take, as obtained from crystal structures? 

The Conquest search query is very simple (no disorder, no errors).

When applied to the Cambridge structure database (CSD) the following two distributions are obtained. That for carbon is pretty symmetric with the peak at ~1.53Å but with rather faster decay in the region >1.6Å compared with the region <1.46Å (the latter may be caused by hyperconjugation shortening the C-C bond).

In contrast, the iso-electronic N-B distribution is more asymmetric about the peak of 1.56Å, exhibiting a long tail beyond 1.63Å, up to a value of 1.825Å.

The molecule with that longest N-B bond (1.825Å) is shown below; UWOHUK, Data DOI: 10.5517/ccwcwlp. This by the way is no crystal artefact; a calculation (ωB97XD/6-311G(d,p), Data DOI: 10.14469/hpc/3202) gives a calculated length of 1.81Å, with a N-B bond order of 0.48.

Stretching a C-C bond heterolytically requires charge separation (a relatively unfavourable process) and likewise homolytic stretching would tend to form a biradical, in effect an excited state and again not favourable. In contrast, elongating the N-B bond reduces (at least formally) any charge separation and allows this heteronuclear pair to sustain (single) bond lengths over the much wider range of ~0.4Å without requiring biradical formation.

One might wonder what other single-bonded atoms pairs give such unusually large spans in their bond length distributions.

 
 

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Posted in crystal_structure_mining | 3 Comments »

Two stories about Open Peer Review (OPR), the next stage in Open Access (OA).

October 5th, 2017

We have heard a lot about OA or Open Access (of journal articles) in the last five years, often in association with the APC (Article Processing Charge) model of funding such OA availability. Rather less discussed is how the model of the peer review of these articles might also evolve into an Open environment. Here I muse about two experiences I had recently.

Organising the peer review of journal articles is often now seen as the single most important activity a journal publisher can undertake on behalf of the scientific community; the very reputation of the journal depends on this process being conducted responsibly, thoroughly and with integrity by the selected reviewers. Reviewers conduct this process voluntarily, mostly anonymously, without remuneration or recognition and often with short deadlines for completion. After one such process, I recently received an interesting follow-up email from the journal, suggesting I register my activity with Publons.com, a site set up to register and give non-anonymous credit for reviewing activities. I should say that Publons is a commercial company, set up in 2012 to to “address the static state of peer-reviewing practices in scholarly communication, with a view to encourage collaboration and speed up scientific development”. Worthy aims, but like many a .com company nowadays, one might ask what the back-story might be. Thus many of the Internet giants, Google, Facebook, Twitter etc, do have back-stories, which often underpin their business models, but which may only emerge years after their founding. With only a hazy idea of what Publons’ back-story might be, I went ahead and registered my reviewing activity.

After doing so, I then accessed my entry. You only learn that I have reviewed for a particular journal, but nothing about the actual process itself. I did not really think that this experiment had done much to encourage collaboration and speed up scientific development. It might be useful for early career researchers to get their name exposed however.

I can almost understand why the review itself might not be publicly displayed, but as a result you learn nothing about the factual basis of the review and whether it might have been conducted responsibly, thoroughly and with integrity. Instead, I now suspect that the presence of my name on this site might merely encourage other publishers to deluge me with requests for further (freely donated) refereeing.

Discussing this at lunch, a colleague (thanks Ed!) reminded me of a veritable journal called Organic Syntheses. Here, authors submit a synthetic procedure and open identified “checkers” are invited to repeat the procedure and comment on it. The two roles are kept separate (i.e. the checkers do not become co-authors), but they could get credit for their activity. Thus if you view a typical recent entry[1] you will see a full biography and affiliation of the checkers given at the end, with footnotes often describing their own observations if they differ from those of the authors. 

This set me thinking whether an open peer review process might also contain such an element of checking, as well as informed comment, nay opinion, about the article itself and the conclusions it makes. The opportunity arose when I was contacted by an author who was about to submit a computational article to a journal. This journal allowed open peer review. If I agreed to review, my name would be attached to the article if accepted for publication. I undertook this on the basis that I would use this review to conduct some limited checking of the computations and other assumptions underpinning the conclusions in the submitted article. I also wanted this open process to include the data on which my review was based. Most importantly if anyone wished to replicate my replication, the barriers to doing so should be as low as is possible. Shortly thereafter, I received a formal invitation from the journal and I set about my task. Crucially, all my own calculations supporting the review were archived in a data repository, albeit under embargo. In my cover letter I included the DOI for my data and the embargo access code, so that the authors (and the editor of the journal if they so wished) could inspect the data against which I wrote my review.

Then followed standard procedures, whereby the authors took my comments into consideration, revised the article and the final version was indeed accepted and published.[2] You will find the two referees/checkers listed, although unlike Organic Syntheses,  there is no bibliographic information about them or their affiliation. I did ask the journal if they could at least link my ORCID identifier to my name, but that request was refused. If my name had been a common one, then disambiguating it into a unique identity could be a challenge. There was also no mechanism to associate my identity on the journal with any data on which I had based my review. Really, the only open aspect of this process was just my (potentially ambiguous) name, nothing else. No follow-up was received from the journal to add the review to Publons. 

The next stage was to contact the author who had originally set the process under way to ask them if they would mind my releasing the data on which my review had been based. They agreed, as also they did to my telling this story. The overall outcome is thus a published article with the reviewers (if not their reviews or any supporting evidence for their review) openly named. In this specific case, there is also an open dataset with a formal link back to the article in the form of a DOI (10.14469/hpc/2640, although I suspect this aspect is unique, even precedent setting), but one driven by the reviewer and not the journal. It would be nice to have bidirectional links between both article and the review data, but I do not know any publishers currently operating such a mechanism (if anyone knows such, please tell).

Now to the broader questions about the process described above. I think that the aspiration to encourage collaboration and speed up scientific development may indeed have been promoted by this association between article and the data assembled by the reviewer. Whether the final article was improved as a result of the processes described here I will leave the authors to comment if they wish. As with the checkers employed by Organic Syntheses, such a review process takes not just time, but resources. Resources that currently have to be freely donated by the reviewers and their host institution and which clearly cannot become expensive, time-consuming or onerous. That was not the case as it happens here; my contributions were facilitated by my having sufficient expertise to perform the tasks I undertook really quite quickly.

I will raise one more issue; that of whether to add my review to the dataset which is now openly available. In fact it is not included, in part because it related to the initially submitted version of the MS. The final MS version has been revised and so many of the comments in my review may only make sense if you have the first version to hand. It would be perhaps unreasonable to make the first drafts of manuscripts routinely available (although historians of science would probably love that!) alongside the reviews of that first draft. But I could also see a case for doing so if the community agreed to it. One to discuss for the future I think. There is also the associated issue of what should happen to any dataset associated with a review in the event that the final article is rejected and not accepted. Should the data remain permanently under embargo and the reviewer’s identity permanently anonymous? Perhaps opening up even such datasets might nevertheless  encourage collaboration and speed up scientific development, but I fancy some would consider that a step too far!

References

  1. J. Zhu, "Preparation of N-Trifluoromethylthiosaccharin: A Shelf-Stable Electrophilic Reagent for Trifluoromethylthiolation", Organic Syntheses, vol. 94, pp. 217-233, 2017. https://doi.org/10.15227/orgsyn.094.0217
  2. L. Li, M. Lei, Y. Xie, H.F. Schaefer, B. Chen, and R. Hoffmann, "Stabilizing a different cyclooctatetraene stereoisomer", Proceedings of the National Academy of Sciences, vol. 114, pp. 9803-9808, 2017. https://doi.org/10.1073/pnas.1709586114

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Posted in Chemical IT, General | 5 Comments »

Dyotropic Ring Expansion: more mechanistic reality checks.

October 1st, 2017

I noted in my WATOC conference report a presentation describing the use of calculated reaction barriers (and derived rate constants) as mechanistic reality checks. Computations, it was claimed, have now reached a level of accuracy whereby a barrier calculated as being 6 kcal/mol too high can start ringing mechanistic alarm bells. So when I came across this article[1] in which calculated barriers for a dyotropic ring expansion observed under mild conditions in dichloromethane as solvent were used to make mechanistic inferences, I decided to explore the mechanism a bit further.

Shown in blue above is the reported outcome, a dyotropic transposition of a OMs group with a ring CH2 group. Shown in red are my additions.

The observed product is a 6,6-bicyclic ring system, for which various calculated mechanistic pathways were reported (R=H)[1].

  1. The first involved dyotropic-like [1,2] transposition of the neutral molecule, for which barriers >39 kcal/mol were calculated[1]. These are certainly too high to be viable and the warning bells were certainly heeded.
  2. These bells led the authors to the hypothesis that protonation of the OMs group would facilitate the reaction (Figure 7[1]). Their model included the proton, but did not include any counter-ion. A barrier of 5.6 kcal/mol for this system was estimated and considered “fully compatible with the mild experimental conditions“. However, as they also noted, “a singular transition structure could not be located due to the topology of the potential energy surface” and “A nudged elastic band method (was) employed to explore how the reaction proceeds“. This latter method was new to me, but in fact since I now thought the barrier might be too low; warning bells started to ring for me now.
  3. I thought the answer might relate to the lack of a negative counter-ion to the positive proton and so I added HCl instead of H+ (red above) to create a more physically realistic model of an acid catalyst; an isolated cation is an un-physical model, unless found in e.g. a mass spectrometer. Also included were two explicit water molecules, waters that were also included in the reported models[1], to help stabilise what was likely to be an ion-pair like system, labelled HI in the diagram above. I will explain what HI means shortly.
  4. I used the same ωB97XD/Def2-SVPP/SCRF=DCM method as originally reported[1]. The inclusion of explicit HCl instead of H+ now readily allowed a transition state to be located and an IRC (intrinsic reaction coordinate) could be computed (FAIR data DOI: 10.14469/hpc/3016) as a replacement for nudged elastic bands! This profile turned out to have some remarkable features, as I will discuss below.
    • I also recomputed the reactant and transition state at the Def2-TZVPPD basis set level, which allows for a better description of negative ions (FAIR data DOI: 10.14469/hpc/3095,10.14469/hpc/3140)  and this results in a calculated ΔG‡195 of ~16 kcal/mol, less than the original computed transition state barriers of >39 kcal/mol and closer to the barrier required for mild experimental conditions at -78°C.
  5. An animation of the IRC at the ωB97XD/Def2-SVPP/SCRF=DCM level (10.14469/hpc/3016) is shown below. It is a concerted formally dyotropic process, albeit very asynchronous in nature in which C-OMs bond breaking precedes C migration, which in turn precedes C-OMs bond formation.
  6. The energy profile is shown below. 

    • Between IRC -13 and IRC -6, the reaction prepares for a proton transfer from HCl to the mesityl oxygen, which occurs ~IRC -4.
    • From IRC -3 to IRC +1, the profile is very flat, which probably is the cause of the original failure[1] to locate a transition state.
    • The region IRC -3 to +2 is where the CH2 group starts to migrate, reaching the half way point at ~ IRC 0, the transition state.
    • At IRC +4, the alkyl [1,2] migration is complete and a hidden ion-pair intermediate has formed.
    • From IRC +5 to +17, this hidden ion-pair collapses to form the final non-ionic product. In the process a second proton transfer occurs back to the chloride anion (~IRC +5).
  7. The hidden ion-pair intermediate can be seen more clearly in this plot of the energy derivative gradient norm at IRC +4. The two proton transfers can be seen very clearly as sharp features at IRC -4 and +5. 
  8. The zone of the hidden ion-pair intermediate can also be seen in this dipole moment plot.
  9. This next plot charts the changes in the length of the bond labelled (a) in the diagram above. As the CH2 migration starts to create a carbocation-mesityl anion pair, the bond connecting the two rings is now tempted to also migrate. Doing so would create a more stable tertiary carbocation centre.
  10. This is mirrored by the length of the bond labelled (b). As (a) lengthens, so (b) contracts. But then at IRC +4, the aspirations of both bonds are cruelly frustrated. The methane sulfonic acid has just lost its proton (which has returned to its original home, the chloride anion) and, as an anion, is now voraciously seeking a cation. It out-competes bond (b) and forms a C-O bond. The rejected bond (b) rapidly retreats.
  11. The knock-on effects of this battle between two electron donors can be see further afield. Here is a plot of one C-H bond length (shown above as R-C; R=H). In the expectation that bond (b) will depart, it starts to increase its hyperconjugation with the adjacent carbon, but then retreats along with bond (b).

There are lots more fun to be had with these IRC plots, but I will stop there and try to summarise. This [1,2] dyotropic transposition only has a reasonably low barrier if an ion-pair can be formed. This in turn requires a proton as catalyst, which starts off life attached to Cl, then migrates to O to enhance the ion-pair formation, and finally returns back home to the Cl. By using just a proton (without chloride) in the original study[1], in effect only the region of the reaction coordinate not involving the proton transfers was studied, i.e. IRC -4 to IRC +5. That would indeed give the misleading impression of a very small barrier for the reaction. By including a larger region of the reaction coordinate with the addition of chloride, we get a more realistic model for the reaction.

More importantly, we learn a lot more about the reaction from this better model. The most important new insights are:

  1. Beyond the transition state at IRC = 0, we have pathways for both the formation of a 6,6 bicyclic ring (the blue route in the scheme above) and an alternative 5,7 bicyclic ring product (red route above). The 6,6 product was isolated in 70% yield, which leaves open the possibility that some 5,7 product was formed but was not identified. It would be worth repeating the original synthesis to see if any such product could in fact be detected.
  2. The fact that remote substituents such as R have a response to the reaction suggests that they could be used to mediate between 6,6 and 7,5 ring formation. Perhaps some modification could be found that would lead to only 5,7 product? I will explore this computationally and report my results back presently.
  3. This may represent yet another example where reaction dynamics play a role in determining the product outcome. One transition state but two possible products!  So, as also noted in the previous post, yet another candidate for a molecular dynamics study?

References

  1. H. Santalla, O.N. Faza, G. Gómez, Y. Fall, and C. Silva López, "From Hydrindane to Decalin: A Mild Transformation through a Dyotropic Ring Expansion", Organic Letters, vol. 19, pp. 3648-3651, 2017. https://doi.org/10.1021/acs.orglett.7b01621

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Posted in pericyclic, reaction mechanism | 3 Comments »

Hydrogen capture by boron: a crazy reaction path!

September 21st, 2017

A recent article reports, amongst other topics, a computationally modelled reaction involving the capture of molecular hydrogen using a substituted borane (X=N, Y=C).[1] The mechanism involves an initial equilibrium between React and Int1, followed by capture of the hydrogen by Int1 to form a 5-coordinate borane intermediate (Int2 below, as per Figure 11).‡ This was followed by assistance from a proximate basic nitrogen to complete the hydrogen capture via a TS involving H-H cleavage. The forward free energy barrier to capture was ~11 kcal/mol and ~4 kcal/mol in the reverse direction (relative to the species labelled Int1), both suitably low for reversible hydrogen capture. Here I explore a simple variation to this fascinating reaction.∞


This variation involves transposing X and Y such that Y=N+ and X=C– to form a carbon ylide such that X=C becomes much more nucleophilic than the original nitrogen nucleophile. An animation of the full IRC† (intrinsic reaction coordinate computed at ωB97XD/cc-pvtz; FAIR data doi: 10.14469/hpc/2704) is shown below.

The profile shows that the reaction is concerted between the species labelled React and Prod; no sign of Int1 and Int2!

  1. The region IRC -12 to -5 involves B-C bond cleavage. Because the C is so very nucleophilic, the 4-ring species labelled React becomes very stable and opening it requires a high barrier.
  2. Between IRC -5 and 0, the BH2 group rotates, losing its original interaction with the C to slowly create an empty acceptor orbital on the boron which can then interact with the incoming hydrogen.
  3. At IRC= 0 (the transition state) the hydrogen has been captured by the boron to form a 5-coordinate species, in a manoeuvre that reminds one of the orbital capture of satellites by planets on their way to the outer reaches of the solar system. If the barrier to this capture is computed from IRC= -4 (the region of Int2) it is very much lower than the original system[1], again a reflection of the higher nucleophilicity of X=C–.
  4. The fly past continues until IRC= +7, at which point one end of the bound hydrogen has become suitably orientated to interact with the nucleophilic carbon via lone-pair donation into the acceptor H-H σ* orbital, thus helping to break it.
  5. By IRC= +9, the H-H cleavage is complete.
  6. By IRC= +13 the reaction has reached Prod, being overall ~ -12 kcal/mol exothermic.
  7. The overall thermochemistry is dominated by the potent carbon nucleophile in the reactant, which in turn makes this modification entirely useless for the purposes of a hydrogen-capture system!


The evolution of the dipole moment along the IRC shows very non-linear behaviour (such plots are rarely shown in most published IRC analyses; they should be!), ending of course with the ionic zwitterion that is the imminium borohydride Prod. Indeed the entire reaction coordinate is an unusually vivid example of a non-least motion path!

This simple atom transposition has given us a very instructive exercise in reaction paths, by-passing entirely both  Int1 and Int2 (making them hidden intermediates), and converting React → Prod into a concerted reaction. It would be great to probe this convoluted journey using reaction dynamics!

∞Archived as DOI: 10.14469/hpc/3096

‡ Such a species can be seen as a hidden intermediate in the mechanism of reduction of a carboxylic acid by diborane.

†None were shown in the original study.[1]

References

  1. L. Li, M. Lei, Y. Xie, H.F. Schaefer, B. Chen, and R. Hoffmann, "Stabilizing a different cyclooctatetraene stereoisomer", Proceedings of the National Academy of Sciences, vol. 114, pp. 9803-9808, 2017. https://doi.org/10.1073/pnas.1709586114

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Posted in reaction mechanism | 1 Comment »

The di-anion of dilithium (not the Star Trek variety): Another "Hyper-bond"?

September 16th, 2017

Early in 2011, I wrote about how the diatomic molecule Be2 might be persuaded to improve upon its normal unbound state (bond order ~zero) by a double electronic excitation to a strongly bound species. I yesterday updated this post with further suggestions and one of these inspired this follow-up.

The standard molecular orbital diagram for Be2 below shows two electrons in both the 2s Σg and Σu levels, the first being considered bonding and the second antibonding. By exciting the two electrons from the Σu into the Πu MO to form a triplet, one converts one antibonding occupancy into two bonding occupancies, in the process changing the total formal bond order from zero to two.

 

The triplet excited state of diberyllium

You can see the results of my playing with these ideas both in my appended comments to the original post and the table below. This shows that the calculated bond order for the excited triplet state of Be2 is actually closer to 1.50 rather than to two, but definitely not zero!

System Wiberg bond order Bond length FAIR Data
Be2 singlet 0.15 2.805 10.14469/hpc/3082
Be2 excited triplet 1.50 1.785 10.14469/hpc/3075
Be22+ 1.00 2.135 10.14469/hpc/3076
Be22- triplet 0.89 2.242 10.14469/hpc/3074
Be22- excited singlet 3.00 1.817 10.14469/hpc/3083

The games above represent isoelectronic substitutions and here I try one more, namely that Li22- is isoelectronic with Be2. Unlike the latter, there is no need to force an electronic excitation (ωB97XD/Def2-QZVPPD/SCRF=water) to achieve the required occupancies with Li22-.

System Wiberg bond order Bond length FAIR Data
Li22- triplet 1.501 2.381 10.14469/hpc/3087

I also checked what crystal structures could tell us about Li-Li bonds and it seems 2.38Å is about as short as they get.

At this point, the NBO analysis of the Li22- localised orbitals alerted me to another feature, which is that the Rydberg occupancy amounted to 2.18e. This in turn reminded me of the previous post which dealt with such occupancy in another small molecule, CH3F2-, but here the Rydberg occupancy involved the 3s/3p AOs of the carbon and the fluorine. With Li22- triplet, it is of the lithium 2p AO (2.18e) and only a tiny occupancy of 3d (0.03). By definition, for alkali metals such as Li the normal valence shell is just 2s, whereas 2p occupancy is considered a Rydberg state; a hypervalent state if you will. So Li22- triplet has a Li-Li hyper-bond!‡ Of course, by this definition most Li compounds are then hypervalent, since many have populated 2p shells.

Even if use of the term hyper-bond to describe Li22- triplet is rather artificial, this example does reveal the games one can play with the first row elements Li-B (see table above). Given that most introductory text books on bonding normally only explain the diatomics formed from N-Ne (occasionally including C), I might suggest that these earlier elements are equally instructive and fun to play with.

‡ This species is 36.0 kcal/mol higher in free energy than two separated Li– anions.

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Posted in Interesting chemistry | 3 Comments »

The di-anion of dilithium (not the Star Trek variety): Another “Hyper-bond”?

September 16th, 2017

Early in 2011, I wrote about how the diatomic molecule Be2 might be persuaded to improve upon its normal unbound state (bond order ~zero) by a double electronic excitation to a strongly bound species. I yesterday updated this post with further suggestions and one of these inspired this follow-up.

The standard molecular orbital diagram for Be2 below shows two electrons in both the 2s Σg and Σu levels, the first being considered bonding and the second antibonding. By exciting the two electrons from the Σu into the Πu MO to form a triplet, one converts one antibonding occupancy into two bonding occupancies, in the process changing the total formal bond order from zero to two.

 

The triplet excited state of diberyllium

You can see the results of my playing with these ideas both in my appended comments to the original post and the table below. This shows that the calculated bond order for the excited triplet state of Be2 is actually closer to 1.50 rather than to two, but definitely not zero!

System Wiberg bond order Bond length FAIR Data
Be2 singlet 0.15 2.805 10.14469/hpc/3082
Be2 excited triplet 1.50 1.785 10.14469/hpc/3075
Be22+ 1.00 2.135 10.14469/hpc/3076
Be22- triplet 0.89 2.242 10.14469/hpc/3074
Be22- excited singlet 3.00 1.817 10.14469/hpc/3083

The games above represent isoelectronic substitutions and here I try one more, namely that Li22- is isoelectronic with Be2. Unlike the latter, there is no need to force an electronic excitation (ωB97XD/Def2-QZVPPD/SCRF=water) to achieve the required occupancies with Li22-.

System Wiberg bond order Bond length FAIR Data
Li22- triplet 1.501 2.381 10.14469/hpc/3087

I also checked what crystal structures could tell us about Li-Li bonds and it seems 2.38Å is about as short as they get.

At this point, the NBO analysis of the Li22- localised orbitals alerted me to another feature, which is that the Rydberg occupancy amounted to 2.18e. This in turn reminded me of the previous post which dealt with such occupancy in another small molecule, CH3F2-, but here the Rydberg occupancy involved the 3s/3p AOs of the carbon and the fluorine. With Li22- triplet, it is of the lithium 2p AO (2.18e) and only a tiny occupancy of 3d (0.03). By definition, for alkali metals such as Li the normal valence shell is just 2s, whereas 2p occupancy is considered a Rydberg state; a hypervalent state if you will. So Li22- triplet has a Li-Li hyper-bond!‡ Of course, by this definition most Li compounds are then hypervalent, since many have populated 2p shells.

Even if use of the term hyper-bond to describe Li22- triplet is rather artificial, this example does reveal the games one can play with the first row elements Li-B (see table above). Given that most introductory text books on bonding normally only explain the diatomics formed from N-Ne (occasionally including C), I might suggest that these earlier elements are equally instructive and fun to play with.

‡ This species is 36.0 kcal/mol higher in free energy than two separated Li– anions.

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Two new types in the chemical bonding zoo: exo-bonds and hyper-bonds?

September 6th, 2017

The chemical bond zoo is relatively small (the bond being a somewhat fuzzy concept, I am not sure there is an actual count of occupants). So when two new candidates come along, it is worth taking notice. I have previously noted the Chemical Bonds at the 21st Century-2017: CB2017 Aachen conference, where both were discussed.

  1. The first now has a name, the exo-bond, one example of which is the C2 diatomic. The hint that a quadruple bond could be formulated between the two carbon atoms goes back a little while[1] (see Table 1), but revived interest really took off after ~2010, around the time my blog on the topic also appeared. You can see the abundance of post 2010 articles in the bibliography at the Aachen bond-slam. At the conference, four speakers all agreed using rather different methods that there was indeed “something” additional to a C≡C triple bond and that this “something” might be worth ~15-30 kcal/mol of stabilization.† The debate centered around whether this term deserved to be called a bond, or whether it should be downgraded to merely that of biradicaloid stabilizations.‡ The more conventional population of a σ*-antibond it was argued would not result in such stabilizations. Since many kinds of bonds have stabilization energies of similar magnitude, not least the weaker hydrogen bonds, agostic bonds, halogen bonds etc, let us for the sake of argument call it a bond here. Because four electrons might occupy the same space along the σ-symmetric C-C axis, they experience significant so-called static correlation∞ which results in partition into one electron pair occupying the central region (the endo-bond) and the other pair in the outer region (the exo-bond).  This separation decreases the Pauli electron repulsions along the entire C-C axis region.  An example of an exo-bond is found in [1.1.1] propellane, where the notional central C-C bond is thought to actually occupy the region outside the central C-C bond axis, but largely in this example because of angular strains. In this case however, the propellane bond is not competing with an endo-bond along the same axis. We might conclude therefore that the convention of characterising a bond using the separation between the two nuclei (the bond-length) is rather stressed when one has two different bonds along the axis of the nuclei, one of which is obviously “longer” than the other.

    Which brings us to representations; e.g. Chemdraw now allows drawing of quadruple bonds and so it can be drawn thus quite simply.

    The second form breaks the century-old convention that all bonds along a diatomic axis are drawn in the same manner, by isolating the exo-bond to make the point clear. Perhaps we should stick to the first, but be prepared to explain the underlying complexity of the quantum mechanical symmetries as we do to students with σ/π/δ/φ bonds, which are another mechanism for avoiding having bonds in exactly the same regions. I know the story has not yet ended; but is it time to at least speculate when the text-books will start to reflect/discuss the exo-bond?

  2. The second I dub the hyper-bond. This goes back to G. N. Lewis and his famous octet rule for main group elements, the expansion of which was subsequently described by the term hypervalent. That term has become rather confused with hypercoordinate, since hypervalent is often used to describe hypercoordinate species such as PCl5, SF6 or I.I7. But this does rather break the original definition, since few if indeed any of these hypercoordinate molecules have a significantly expanded octet shell. At the Aachen meeting, a molecule fitting the original definition was presented, appearing first in early form on this blog. Put simply, a wavefunction for CH3F2- can be calculated (ωB97XD/Def2-QZVPPD/SCRF=water, DOI: cb3n ) for which the two additional electrons populate a molecular orbital with significant contributions from the 3s/3p valence shell AOs (atomic orbitals) for both carbon and fluorine. The alternative would have been to populate the anti-bonding C-H or C-F orbitals composed of 2s/2p valence shell AOs. The former results in a total population of these higher valence shells of 1.55e and makes the C-F (Wiberg) bond order >1 (1.14) and the total Wiberg bond indices >4 for carbon (4.162) and >1 for F (1.275). The resulting HOMO (highest occupied molecular orbital) or NBO (they are very similar) looks as below. It takes the approximate form of a torus or cylinder wrapping the inner C-F bond, a second layer to the C-F bond if you wish. 

    Normal valence shell F-C σ-orbital defining the regular C-F bond.

    Higher valence shell F-C σ-orbital defining the C-F hyper-bond.

    Rather than the entire molecule being defined as hypervalent, only one (in this case localized) orbital is given the term and the other orbitals are conventional.

In both cases the molecules are either very reactive (C2) or with such a low barrier to fragmentation (into CH3– and F– for CH3F2-) that detection of the latter is unlikely. But these are interesting Gedanken experiments in quantum mechanics, which in turn catalyse the development of new techniques and in some cases might even lead to the design and isolation of new types of molecules.

†The known thermochemistry of the two reactions; HC≡CH → HC≡C + H•; HC≡C• → CC + H• is ~17 kcal/mol less endothermic for the second step, suggesting some factor is needed to account for the additional stabilization when CC is formed.

‡The singlet to triplet excitation energy for C2 is ~+30 kcal/mol, so the biradicaloid electrons are certainly spin-coupled.

∞Other “difficult” correlated molecules include Be2 and B2.

References

  1. R.S. Mulliken, "Note on Electronic States of Diatomic Carbon, and the Carbon-Carbon Bond", Physical Review, vol. 56, pp. 778-781, 1939. https://doi.org/10.1103/physrev.56.778

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One more WATOC 2017 Report.

August 31st, 2017

Conferences can be intense, and this one is no exception. After five days, saturation is in danger of setting in. But before it does, I include two more (very) brief things I have learnt.

  1. Sason Shaik introduced a theme he first investigated years ago, but for which no experiment had been devised for verification. He revived his theme when a journalist contacted him last year to report exactly such an observation, which I now recount. A Diels-Alder adduct was captured between a flat layer of gold atoms and the tip of a scanning-tunneling microscope. With the molecule exactly oriented, a strong external electric field (OEEF) was applied, in both senses of polarisation. This is exactly the model studied by Sason, who had argued thus. A Diels-Alder reaction can be modelled using VB theory as the avoided crossing of a covalent ground state with ionic excited states at the transition state. Depending on the polarisation of an applied external electric field and the orientation of the molecule, one of these ionic states can stabilized or destabilised by about 8 kcal/mol, thus either stabilising or destabilising the transition state itself by mixing with the covalent state.

    And so it was that the oriented molecule caught between a gold layer and an STM probe could be persuaded to undergo a retro-Diels-Alder far more easily than it would thermally. The technique can even be tuned to selecting between endo and exo isomers. Sason held out the prospect that the toolbox of the synthetic chemist, which already includes Δ, hν and ? (ultrasound) as reagents, might be extended using OEEF. He called this a smart reagent since it can be tuned to the reaction required (as of course can light). At the moment this technique can only be applied to one molecule at a time, but it might be just a matter of designing a suitable apparatus!

  2. Pavel Hobza talked about non-covalent interactions, an occasional theme on this blog. Amongst many interesting observations was that the DNA helix is not stabilised as such by the hydrogen bonding between the base pairs but by the π-π stacking between them. One of these examples caught my eye, the known weak “hydrogen bonded” weak complex between benzene and chloroform in the gas phase. The C-H hydrogen points directly to the ring centroid and the C-H vibrational wavenumber is blue shifted by 12 cm-1. At the time this (experimental) observation caused consternation, since all known hydrogen bonds (both strong and weak) were routinely characterised by the magnitude of their red shift (up to ~100 cm-1). In fact, as Pavel showed, this interaction is less electrostatic in nature and more like dispersion attraction. Accurate calculations including dispersion also predict a blue shift for this system. A question from the audience suggested that as many π-facial “hydrogen bonds” in the crystal state tend to point not to the ring centroid but to the ring edge, what would happen if the chloroform H were to slide across the surface of the ring until it reached the edge; would the CH shift invert to become red, implying a change from dispersion interaction to whatever is implied by a hydrogen bond?

Apologies to all those who gave fascinating talks which are unrecorded here. I hope some tiny and selective flavour nevertheless emerges of WATOC 17.

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(another) WATOC 2017 report.

August 29th, 2017

Another selection (based on my interests, I have to repeat) from WATOC 2017 in Munich.

  1. Odile Eisenstein gave a talk about predicted 13C chemical shifts in transition metal (and often transient) complexes, with the focus on metallacyclobutanes. These calculations include full spin-orbit/relativistic corrections, essential when the carbon is attached to an even slightly relativistic element. She noted that the 13C shifts of the carbons attached to the metal fall into two camps, those with δ ~+80 ppm and those with values around -8 ppm. These clusters are associated with quite different reactivities, and also seem to cluster according to the planarity or non-planarity of the 4-membered ring. There followed some very nice orbital explanations which I cannot reproduce here because my note taking was incomplete, including discussion of the anisotropy of the solid state spectra. A fascinating story, which I add to here in a minor aspect. Here is a plot of the geometries of the 52 metallacyclobutanes found in the Cambridge structure database. The 4-ring can be twisted by up to 60° around either of the C-C bonds in the ring, and rather less about the M-C bonds. There is a clear cluster (red spot) for entirely flat rings, and perhaps another at around 20° for bent ones, but of interest is that it does form something of a continuum. What is needed is to correlate these geometries with the observed 13C chemical shifts to see if the two sets of clusters match. I include this here because in part such a search can be done in “real-time” whilst the speaker is presenting, and can then be offered as part of the discussion afterwards. It did not happen here because I was chairing the meeting, and hence concentrating entirely on proceedings!

  2. Stefan Grimme introduced his tight binding DFT method, an ultra fast procedure for computing large molecules and in passing noted the arrival of his D4 procedure (almost everyone currently uses D3 methods for this, including many of the results reported on this blog) for correcting for dispersion energies in molecules based on computed charge dependencies using the TBDFT methods. Thus we see dispersion as a property which is based on the wavefunction of the molecule, but still fast enough to accurately correct dispersion energies. He followed this with his automated procedures based on the TBDFT methods for computing full spin-spin coupled 1H NMR spectra of organic molecules. The core of this method is to recognise conformational and rotational freedoms and to compute the NMR properties for all identified isomers. These parameters are then Boltzmann averaged prior to computation of the final spin-coupled simulated frequency domain spectrum (rather than inverting this procedure by computing spin-coupled spectra of all rotamers and conformations and then averaging the spectral envelopes). This should widely revolutionise the interpretation of 1H NMR spectra by synthetic chemists.
  3. Another automated tool for synthetic chemists was presented by Jan Jenson, and can be seen here. It used MOPAC PM3 semi-empirical theory to compute relative proton affinities for a series of regioisomers as a prelude to predicting the position of aromatic electrophilic substitutions in heteroaromatic molecules. Try it out by putting a SMILES string into the box provided (e.g. COC1=CC=CC=C1) waiting a bit and seeing what the prediction is (it should be p- for the preceding example). During Q&A, a question was asked about the canonical “purity” of the SMILES (the one used in this tool comes from the Chemdraw program, which might not be identical to a SMILES for the same molecule produced by a different program), and whether an InChI descriptor might be better (also produced by Chemdraw, but perhaps a bit more canonical). Also asked was whether the prediction for an electrophile rather larger than a proton might not give good predictions? This one perhaps could be tested by readers, who could report back here?
  4. Walter Thiel completes the semi-empirical theme when he reported the new ODM2 method, the D now including dispersion. This is a powerful program, which includes e.g. full CI (configuration interaction + gradients) capability and is especially good for excited states, for dynamic simulations, and for combining these into dynamic photochemical simulations. This was applied to the chromophore in the famous “nanocar” in studying the dynamics of the photochemical rotation of the motor of the car (the thermally induced rotation was not studied). At the time that the nanocar caught my attention, I wondered about how the four independent molecular motors synchronised their rotations to allow the car to drive in a straight line. No doubt the answer is known, and if anyone reading this knows, please tell! It is probably a dynamics problem on four rotors (Walter reported just on one!).

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