Henry Rzepa's blog

Here I investigate a recent report[1] of a new generation of polyesters with the intrinsic properties of high crystallinity and chemical recyclability. The latter point is key, since many current plastics cannot be easily recycled to a form which can be used to regenerate the original polymer with high yield. Here I show some aspects of this fascinating new type of polymer.

The starting monomer is 2-thiabicyclo[2.2.1]heptan-3-one, which is easily prepared on a 50g scale. When polymerised with the organocatalyst IMES (below) it produces a stereoregular threodisyndiotactic polymer of the structure shown above. Various other catalysts produced different stereochemistries.

The ¹³C NMR spectrum of the IMES-catalysed polymer showed just a single ¹³C carbonyl resonance, and the stereochemical assignment was based in part on DFT geometry optimisation calculations and then obtaining relative free energies of a model dimeric molecule, capped as a methyl ester rather than a benzyl ester. These showed that the (R,S,S,R) stereoisomer was lower than the next lowest by ~1.3 kcal/mol (Figure below). These calculations were done using a DFT procedure (BP86) that does not include dispersion corrections and so I could not but help wonder whether the conformational analysis was entirely reliable, especially if it is to be used to “tentatively” assign stereochemistry (the authors’ own description, Figure 3 below) to the pure stereopolymer B.

I thought I might make my own very quick investigation of the conformation of these quite flexible monomers. I proceeded as follows:

1. I drew the molecule as a tetramer as shown above, for the (R,S,S,R) stereoisomer and saved the coordinates as a molfile. This adds approximate three dimensionality based on the hashes and wedges. I used a tetramer to give it sufficient size to coil around on itself if it wanted to; a dimer is a little too small to do this.
2. This is then fed to a program which can refine such approximate structures using molecular mechanics (the MMFF94s force field, which intrinsically includes attractive dispersion terms). In this instance, I used Avogadro, producing a more accurate 3D model of the system.
3. This was then subjected to semi-systematic conformer searching using Avogadro. The lowest energy of 27 conformations found was then taken forward for optimisation using quantum mechanical procedures.
4. The first of these used PM7, a rapid semi-empirical procedure that includes the 3rd generation Grimme dispersion correction.
5. This was then subjected to B3LYP+GD3BJ/Def2-SVP final refinement (again a procedure that includes a modified GD3 dispersion term with BJ damping).^‡

The original dimer model reported in the supporting information for the article as stereoisomer 1 is shown below next to the tetramer optimised using the procedure described above.

Conformation of literature stereoisomer 1, (R,S,S,R). Click to show 3D rotatable mode

Conformation of 1 as obtained by the procedures above on the tetramer. Click to show 3D rotatable model.

Conformer 5.1 kcal/mol lower in free energy

You can explore both conformations yourself by clicking on the images above to get a 3D rotatable model. They do look rather different, in that the tetramer is wound back upon itself (a sort of hairpin looping), encouraged by the face of the phenyl group which accepts a 5-ring by dispersion attractions. The tentative assignment[1] that the (R,S,S,R) stereochemistry corresponds to that of the pure polymer B produced using the IMES catalyst must probably be just that, tentative. No doubt crystallography will verify this in due course.

We see here a possible glimpse of the future of plastics, whereby highly recyclable polymers can be produced that recover the original monomer with very little loss. All that is needed now is that the plastic is efficiently recycled and not just dumped into the oceans!

^‡ Data at DOI: 10.14469/hpc/7375

References

1. C. Shi, M.L. McGraw, Z. Li, L. Cavallo, L. Falivene, and E.Y. Chen, "High-performance pan-tactic polythioesters with intrinsic crystallinity and chemical recyclability", Science Advances, vol. 6, 2020. https://doi.org/10.1126/sciadv.abc0495

I occasionally notice that posts that first appeared here many years ago suddenly attract attention. Thus this post, entitled The strongest bond in the universe, from ten years back, has suddently become the most popular, going from an average of 0-2 hits per day to 92 in a single day on May 22nd (most views appear to originate from India). I can only presume that a university there has set some course work on this topic and Google has helped some of the students identify my post. Well, re-reading something you wrote ten years ago can be unsettling. Are the conclusions still sound? Would I establish my claim the same way now? After all, one picks up a little more experience in ten years. So here is my revisitation.

The hypothesis was that mono and then diprotonating dinitrogen strengthened the N-N bond, in the sequence N≡N → H-N≡N⁺ → H-N≡N-H²⁺ to the point that the latter was now a candidate for the strongest known bond between two (non-hydrogen) atoms. One of my original criteria was to calculate the N-N stretching wavenumber. To get this, I had to project out the coupling between the N-N stretching mode and the H-N modes in the latter two species. In the original discussion, Igor suggested another candidate O₂²⁺ in the comments. I speculated that the heavy atom diatomic force constant might be a better way of estimating how strong the bond was rather than the stretching wavenumber, but I never followed this up! So time to do so now.

The calculations are now at the CCSD(T)/Def2-TZVPP level (FAIR DOI: 10.14469/hpc/7214).

I did learn one new trick. To project out mode mixing between the hydrogen stretch and the heavy atom stretch, the hydrogen atom masses are now set at 10,000! This has the effect of suppressing any mode mixing, but it also results in exactly the same reduced mass for the NN stretch (14.0) for the three species N≡N, H-N≡N(+) and H-N≡N-H(2+), thus facilitating a like for like comparison. Ten years ago I had also tried the other direction, setting the mass of H to 0.001. Although this latter also eliminates the mode mixing, it does not result in the same reduced masses for the NN mode. So we will stick to the heavy hydrogen projection for comparisons.

The force constant increases almost linearly on mono and then diprotonation of dinitrogen, reaching 56.5 mDyne/Å. In comparison, both O₂²⁺ and NO¹⁺ are a little lower. Does monoprotonating NO¹⁺ strengthen its bond? Yes, but not quite surpassing HN≡NH²⁺. And the neutral HN≡C, which is isoelectronic with HN≡N⁺, also shows a weaker bond.

So my revisitation ten years on still shows that diprotonated nitrogen has the strongest bond (presumably in the universe), as now judged by the diatomic force constant. The hunt is still on for a species where the force constant between two non-hydrogen atoms is higher. Maybe I will return in another ten years to see the state of this challenge!

In 2001, Shaik and co-workers published the first of several famous review articles on the topic A Different Story of π-Delocalization. The Distortivity of π-Electrons and Its Chemical Manifestations[1]. The main premise was that the delocalized π-electronic component of benzene is unstable toward a localizing distortion and is at the same time stabilized by resonance relative to a localized reference structure.  Put more simply, the specific case of benzene has six-fold symmetry because of the twelve C-C σ-electrons and not the six π-electrons. In 2009, I commented here on this concept, via a calculation of the quintet state of benzene in which two of the six π-electrons are excited from bonding into anti-bonding π-orbitals, thus reducing the total formal π-bond orders around the ring from three to one. I focused on a particular vibrational normal mode, which is usefully referred to as the Kekulé mode, since it lengthens three bonds in benzene whilst shortening the other three. In this case the stretching wavenumber increased by ~207 cm-1 when the total π-bond order of benzene was reduced from three to one by spin excitation. In other words, each C-C bond gets longer when the π-electrons are excited, but the C-C bond itself gets stronger (in terms at least of the Kekulé mode).^† This behaviour is called a violation of Badger’s rule[2] for the relationship between the length of a bond and its stretching force constant. 

This blog has come about because I wanted to revisit my original calculations and complete them with a calculation for a heptet state of benzene in which three π-electrons are promoted from bonding into anti-bonding π-orbitals, thus resulting in a total π-bond order of zero. For completness, I here present the results not only for benzene but for some other small-annulene systems, both charged and neutral. These are all done at the coupled-cluster level of theory, both CCSD and CCSD(T), along with two basis set levels (see DOI: 10.14469/hpc/6624 for the whole collection of calculations).^‡

Before discussing the other systems, let your eye drop down the table below to the entries in red. These show the force constants for the singlet, quintet and heptet states of benzene vs the optimized C-C bond length for each (at the same level of theory). These confirm the earlier result in revealing that the quintet state (total ring π-bond order 1) has a longer bond but a stronger force constant for the Kekulé mode than the singlet state (total ring π-bond order 3). The heptet state now has a normal length C-C single bond (total ring π-bond order 0) but a Kekulé distorsion force constant higher than benzene itself! 

Things now start to get more complicated. Firstly, for benzene itself, reducing the remaining π-bond order from 1 to 0 on exciting from quintet to heptet substantially reduces the force constant. So one might conclude that reducing an annulene total π-bond order does not always result in an increase in force constant. Badger’s rule is not always violated and the distortivity of π-electrons may not be a linear phenomenon.

^aUnprojected, with possible Dushinsky coupling ^bProjected from Dushinksky coupling. In all cases, the excited states show -ve force constants for out of plane deformations, but the in-plane Kekule modes are all +ve except for the first entry.

I will now make some short comments about the other ring systems reported above.

1. Cyclobutadiene, dication. The Kekulé mode is very similar to benzene, but based clearly on just two π-electrons rather than six. There are two ways of forming a triplet state by exciting one of the two π-electrons to give a total π-bond order of zero. Both give a C-C distance a little longer than that typical of cyclobutanes (1.56Å). These triplet states however are not equilibrium species but transition states for the dissociation into two molecules of acetylene radical cation, a reaction driven no doubt by the large coulomb repulsions found for a di-cation.
2. Cyclobutadiene. The singlet ground state has Jahn-Teller effects (which by the way are absent from all the other excited states reported here), but the triplet state again has a Kekulé mode is very similar to benzene. Removing all the π-bond orders in the quintet reduces the Kekulé force constant. This is in contrast to benzene itself.
3. Cyclobutadiene, di-anion. Only the singlet state was calculable (the excited states did not converge), and now the Kekulé force constant is distinctly lower than benzene, probably again due to coulombic repulsions of the di-anion coupled with greater Pauli repulsions of the additional electrons. One other vibrational mode is worth showing here, the E_u mode (ν 1267 cm^-1) which shows interesting charge localisation into a carbon-centred anion and a delocalised allylic anion.
4. Cyclo-octatetraene Dication. Although isoelectronic with benzene, it shows very different behaviour. As the spin-multiplicity increases, so the Kekulé force constant decreases and the bond length increases, in accordance with Badger's rule. Again, another vibration (E_3u, ν 1544 cm^-1) shows charge localisation to give a 1,4-separated di-cation.
5. Cyclo-octatetraene. The triplet has a total ring π-bond order 3 (with two electrons in non-bonded orbitals) and a C-C bond length similar to benzene itself. The nonet state total ring π-bond order is reduced to 0, with a C-C length again identical to a single bond. As with the di-cation, the force constant is reduced as the bond length increases, in accordance with Badger's rule.
6. Cyclo-octatetraene di-anion is similar to the neutral system in following Badger's rule.

I do need to insert some caveats here. The original hypothesis[1] of distortive π-electrons was based on the singlet states (both ground and excited) and the results reported here are based on higher spin states, the assumption being that these are well-described by single reference states or configurations. It may well be that these higher spin states need more complex multi-reference determinants to describe them properly, in which case the coupled-cluster calculations reported here would be inappropriate. Thus for the larger rings, some of the CC calculations either failed to converge for large basis sets or gave some unphysical force constants (i.e. huge). This does tend to suggest that the internal MP expansion performed for coupled-cluster calculations is failing to converge, a well known propensity for systems where a multi-reference determinant is needed.

So one should not conclude too firmly that only benzene itself (in this series; there are many other examples to be found in [1]) exhibits Badger’s rule violations. Nonetheless, it would be valuable in the future to know whether the concept of distortivity of π-electrons can be applied to the small ring annulenes where the π-bond orders have been progressively reduced down to zero by specifying higher-spin π-states.

^†In 2014, I looked at some of the historical origins of this attribution to Kekulé, and you might also want to read the fascinating discussion by others on this topic.^‡I thank Sason Shaik for his comments on the above results!

References

1. S. Shaik, A. Shurki, D. Danovich, and P.C. Hiberty, "A Different Story of π-DelocalizationThe Distortivity of π-Electrons and Its Chemical Manifestations", Chemical Reviews, vol. 101, pp. 1501-1540, 2001. https://doi.org/10.1021/cr990363l
2. R.M. Badger, "A Relation Between Internuclear Distances and Bond Force Constants", The Journal of Chemical Physics, vol. 2, pp. 128-131, 1934. https://doi.org/10.1063/1.1749433

In a welcome move, one of the American chemical society journals has published an encouragement to submit what is called FAIR data to the journal.[1]. A reminder that FAIR data is data that can be Found (F), Accessed (A), Interoperated(I) and Re-used( R). I thought I might try to explore this new tool here.

You start at the ACS Research Data Center  with the tag line Submit your NMR Data. By this they mean the primary or “raw” NMR data as it emerges from a spectrometer. At this point I would note that primary data is not necessarily FAIR data yet. It is however a great deal more easily inter-operated and re-used than say the more conventional form of such data, which is a visual spectrum stored as a PDF file. If you did want to re-analyse the data, the primary data is the place to start, not the PDF spectrum!

The tool next asks to to drop your FID file into the upload area. Depending on the spectrometer type, this can take the form of a ZIP archive of various instrument files (typical of Bruker spectrometers) or just a single file (JDF, typical of Jeol spectrometers). The next request is for some “metadata” such as Title, Funder and Author(s), with an additional request to provide an ORCID for the latter. All these are easily provided. It was the next step where my exploration on this occasion had to stop, since the next button takes you to the Manuscript submission page, which can only be followed if you have a manuscript to complete! 

What would I expect to happen next? Well, this metadata has to be augmented with molecule metadata, such as for example an InChI of the molecule. This is what would turn our primary data in fully FAIR data. To complete the process, the data and its now completed metadata descriptors would need to be Registered, in order to facilitate its discovery and hence enable the F of FAIR. This is normally completed with the DataCite registration agency, and in exchange you get a DOI corresponding to the registered metadata and you can then infer a link of the type https://data.datacite.org/application/vnd.datacite.datacite+xml/…your-allocated…DOI which allows you to inspect the metadata and search for it (see eg DOI: 10.14469/hpc/5920 for examples of such searches). Currently I do not know if this happens with this ACS tool. I would certainly like to inspect the collected metadata before I could comment on whether the title of this post is accurate, ie the encouragement of FAIR data. It would also be interesting to see what (if any) procedures are used to generate an InChI for the molecule and its NMR data, and exactly how that is also included in the metadata.

I would also note one other crucial aspect of this process, how to enable the A of FAIR. Primary or raw NMR data is entirely opaque (the files themselves are often binary encoded files) and you do need a tool to transform this data into visual or spectral form. So you will need to acquire such a tool, most often in the form of software such as MestreNova or Topspin. This can be a complex process, and may well involve paying the vendors money. In this context, I would note the Mpublish tool,[2] which allows a single-free-to-use license to be generated which allows e.g. MestreNova to be freely used for that dataset only. Some form of suitable Access to a FAIR dataset is an essential (if often unmentioned) component of the process.

At this stage therefore, there are quite a few questions about this new ACS system which I cannot provide answers to. On these answers will depend whether the process can be truly described as the submission of FAIR data. If anyone reading this manages to complete the process above, do please describe the subsequent experiences. I fancy there will have to be a future follow up to this post! Meanwhile, if you do have a manuscript you are ready to submit, give it a go and perchance report your experiences here!

References

1. A.M. Hunter, E.M. Carreira, and S.J. Miller, "Encouraging Submission of FAIR Data at <i>The Journal of Organic Chemistry</i> and <i>Organic Letters</i>", Organic Letters, vol. 22, pp. 1231-1232, 2020. https://doi.org/10.1021/acs.orglett.0c00383
2. A. Barba, S. Dominguez, C. Cobas, D.P. Martinsen, C. Romain, H.S. Rzepa, and F. Seoane, "Workflows Allowing Creation of Journal Article Supporting Information and Findable, Accessible, Interoperable, and Reusable (FAIR)-Enabled Publication of Spectroscopic Data", ACS Omega, vol. 4, pp. 3280-3286, 2019. https://doi.org/10.1021/acsomega.8b03005

I noted in an earlier blog, a potential (if difficult) experimental test of the properties of the singlet state of dicarbon, C₂. Now, just a few days ago, a ChemRxiv article has been published suggesting another (probably much more realistic) test.[1] This looks at the so-called ⁷Σ open shell state of the molecule where three electrons from one σ and two π orbitals are excited into the corresponding σ^* and π^* unoccupied orbitals. The argument is presented that these states are not dissociative, showing a deep minimum and hence a latent quadruple bonding nature. They also note that the isoelectronic BN molecule IS dissociative.^† Thus to quote: “Hence, the proof of existence of a minimum in the ⁷Σ_u+ for C₂ and the absence of such a minimum in the equivalent case for BN is likely to corroborate our findings on quadruple bonding in these two cases.“

Although a PES (potential energy surface) is shown for ⁷Σ C₂, no vibrational wavenumber is reported. So in the spirit of a commentary on this pre-print, I have calculated these values (CCSD(T)/Def2-TZVPP) for the molecules noted in the article and a few other isoelectronic species. The results are collected at DOI: 10.14469/hpc/6599

The two singly occupied σ-orbitals are shown below and are in part responsible for the non-dissociative behaviour.

The results using this method (the article reports many more methods), reveal that C₂ does indeed exist in a minimum for the heptet state, whilst the isoelectronic BN is only very weakly bound, in effect dissociative. Another dissociative isoelectronic is BO¹⁺, whilst N₂²⁺ despite the coulombic repulsions of a double positive charge, still manages to be bound with a relatively short bond length. A further neutral diatomic BeO is also clearly non-dissociative.

Lets hope a spectroscopist somewhere tries to take a look at these heptet excited states of such molecules so that further experimental insight can be cast on this fascinating problem.

^‡The orbital occupancy of this species is different from the others. ^†As are the neutral ten valence electron N≡N (confirmed here) and HC≡CH.

References

1. I. Bhattacharjee, D. Ghosh, and A. Paul, "Resolving the Quadruple Bonding Conundrum in C2 Using Insights Derived from Excited State Potential Energy Surfaces: A Molecular Orbital Perspective", 2019. https://doi.org/10.26434/chemrxiv.11446224.v1