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

Tuesday, 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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π-Facial hydrogen bonds to alkenes (revisited): how close can an acidic hydrogen approach?

Saturday, April 15th, 2017

Back in the early 1990s, we first discovered the delights of searching crystal structures for unusual bonding features.[1] One of the first cases was a search for hydrogen bonds formed to the π-faces of alkenes and alkynes. In those days the CSD database of crystal structures was a lot smaller (<80,000 structures; it’s now ten times larger) and the search software less powerful. So here is an update. 

The search query (dataDOI:10.14469/hpc/2473) is shown below:

  1. A mid-point (centroid) of a C-C bond (of any type) is defined, but the carbons are each restricted to being 3-coordinate, with the substituents R being either C or H.
  2. The distance to a hydrogen (attached to group QA, where QA is any one of N,O,F,Cl, i.e. acidic H) is defined.
  3. The properties of the alkene are defined by the sines of the two angles subtended at the centroid. This defines how perpendicular the QA-H hydrogen bond is to the C-C bond.
  4. Four torsions R-C-centroid-H are defined by their sines. The mean of the absolute values of these will define how orthogonal the approach of the hydrogen to the π-π plane is.
  5. Further constraints in the search are no disorder, no errors, R < 0.05,  the H atom position is normalised and this position is defined as being <2.5Å from the C-C bond centroid, which is ~0.3Å < the sum of the van der Waals values for C and H.

The first search is limited to intermolecular contacts between the C-C bond and the H and reveals that for most of the 18 hits, the H approach is close to perpendicular to the centroid but the inclination to the π-π plane is more scattered. The most interesting (shortest H…centroid contact of ~2.22Å, orthogonal approach) can be inspected as KANYAA (dataDOI: 10.5517/CC8JRQ7). 
When the search is repeated for intramolecular contacts, rather shorter distances are obtained for 88 hits and with more variation in the angles of approach. The most interesting candidate (blue dots) is IGELAJ[2] (dataDOI: 10.5517/CC14PBW1 ) which has the very short intramolecular H approach of 1.90Å to the C-C centroid corresponding to ~2.04Å to the carbons,  a contraction of ~0.8Å from the van der Waals sum.

The authors remarked[2]  “that it possesses a better defined intramolecular hydrogen bond compared to the usual molecules for which it is noted“. They also note JOCQEX, which is present in the above plot, but for which there is  a non-orthogonal approach of the hydrogen bond to the π-π plane. The authors do not mention TIBCUD[3] (dataDOI: 10.5517/CCPL0FP), which has a similar close approach of 1.92Å to the C-C centroid, but at an angle inclined to the C-C axis.

IGELAJ, as an intramolecular H-bond, was amenable to calculation of its geometry and properties (inter-molecular interactions would ideally require the periodic lattice to be computed), with the observation[3] that “another test was to compare the energy calculation of IGELAJ to a non-hydrogen-bound version where the OH bond is rotated 180°” and “the results predict IGELAJ to be 7.30 kcal more stable than the non-hydrogen-bound version”. This value,  if correct,  is indeed typical of a very strong hydrogen bond!

Pedant (curious?) as I am, I wanted to be clear what kind of calculated energy was being reported. Was it the difference in total energies, or the energies corrected for ZPE (zero-point-energy) as ΔH or the free energies for which entropy is included as ΔG? The article[3] itself is unclear on this aspect and no energies are reported in the  supporting information. This is an illustration that “supporting information” in most current incarnations may often not provide crucial information; only a full deposition as the management of research (RDM) of FAIR data can provide. This process is illustrated for my own calculations of this system (ωB97XD/Def2-TZVPP, dataDOIs: 10.14469/hpc/2474, 10.14469/hpc/2475), which reveals that  ΔG298 4.8 kcal/mol and ν 3761 cm-1. In comparison when the OH bond is rotated 180° the wavenumber goes up 3956 cm-1, a difference of 195 cm-1 is calculated, which is indeed a large red-shift. But the “non-hydrogen-bound version where the OH bond is rotated 180°” is not a valid reference point for a non-hydrogen bonded isomer, since it manifests instead as a transition state for OH rotation with νi 166 cm-1, there being no minimum other than the π-facially hydrogen bonded one (dataDOI: 10.14469/hpc/2476). So, for the lack of a suitable reference system, we cannot conclude what the strength of this particular hydrogen bond is, nor make any conclusions about it being unusually strong.

So IGELAJ holds the current record for the shortest π-facial hydrogen bond to an alkene, but not necessarily the strongest! I wonder if this record might be broken with the aid of further computational design and prediction?

References

  1. H.S. Rzepa, M.H. Smith, and M.L. Webb, "A crystallographic AM1 and PM3 SCF-MO investigation of strong OH ⋯π-alkene and alkyne hydrogen bonding interactions", J. Chem. Soc., Perkin Trans. 2, pp. 703-707, 1994. https://doi.org/10.1039/p29940000703
  2. M.D. Struble, M.G. Holl, G. Coombs, M.A. Siegler, and T. Lectka, "Synthesis of a Tight Intramolecular OH···Olefin Interaction, Probed by IR,<sup>1</sup>H NMR, and Quantum Chemistry", The Journal of Organic Chemistry, vol. 80, pp. 4803-4807, 2015. https://doi.org/10.1021/acs.joc.5b00470
  3. B. Ndjakou Lenta, K.P. Devkota, B. Neumann, E. Tsamo, and N. Sewald, "4-(1,1-Dimethylprop-2-enyl)-1,3,5-trihydroxy-2-(3-methylbut-2-enyl)-9<i>H</i>-xanthen-9-one", Acta Crystallographica Section E Structure Reports Online, vol. 63, pp. o1629-o1631, 2007. https://doi.org/10.1107/s1600536807009907

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The π-π stacking of aromatic rings: what is their closest parallel approach?

Thursday, April 13th, 2017

Layer stacking in structures such as graphite is well-studied. The separation between the π-π planes is ~3.35Å, which is close to twice the estimated van der Waals (vdW) radius of carbon (1.7Å). But how much closer could such layers get, given that many other types of relatively weak interaction such as hydrogen bonding can contract the vdW distance sum by up to ~0.8Å or even more? This question was prompted by the separation calculated for the ion-pair cyclopropenium cyclopentadienide (~2.6-2.8Å).

The search query for the Cambridge structure database is shown below.


The query (dataDOI: 10.14469/hpc/2471) defines centroids for two benzenoid rings, both comprising only 3-coordinated carbons. The sine of an angle subtended at each centroid to the other and to one ring carbon attempts to track how parallel the two rings are (strictly speaking, 12 such angles should be included). If the sines of both angles are 1.00, then the two centroids overlap orthogonally. A search constrained to no disorder, no errors and R < 0.05 reveals 1107 hits at a centroid-centroid distance of < 3.5Å. The colour code (red) indicates the distances in the range 3.4-3.5Å, which matches that of graphite, while distances down to 3.2Å (yellow-green) are not uncommon. 

Here is another way of representing these results, in which the centroid-centroid distances (measured from the positions of 12 carbon atoms and hence statistically more reliable than any individual atom pair distance) are multiplied by either sin(ANGa) or sin(ANGb). The number of occurrences with distances < 3.2Å is less than 32 (out of 1107).

Taking a look at some of these outliers, PAZJEG has two entries, one with a short distance (dataDOI: 10.5517/ccsffzl) and one with a normal distance[1], which does tend to cast doubt on the former.

ZOMSEB[2], DataDOI: 10.5517/CCZS2MF) appears to have the planes of the molecules stacked ~2.5Å apart.

OXUDES02[cite10.1016/j.poly.2016.09.046[/cite], DataDOI: 10.5517/CCDC.CSD.CC1MBBFQ) has a separation of ~2.6Å.

Verifying these and other outliers would require expert inspection of the crystallographic data and its refinement. This might require access to the hkl  structure factors, data which are now being “strongly encouraged”‡ for deposition with the CSD, but which are not present for most structures deposited before ~2016. In extreme cases, the original diffraction images collected by the cameras would allow for a fully independent re-analysis, data which however is rarely if ever deposited.

So the separation of π-π stacked six-membered benzenoid rings is only infrequently less than ~3.2Å in measured crystal structures. There are hints it might reach as short as ~2.6Å, but  such examples with values significantly less than 3.2Å do require expert validation before they can be called real. 

‡See structuredepositioninformation/ “We strongly encourage data to be deposited either with imbedded structure factor data or with an associated FCF or HKL structure factor file.”

References

  1. J. Rogan, D. Poleti, and L. Karanović, "Synthesis, Structure, and Thermal Properties of Two New Inorganic‐organic Framework Compounds: Hexaaqua(<i>μ</i><sub>2</sub>‐1,2,4,5‐benzenetetracarboxylato)‐bis(<i>N</i>,<i>N′</i>‐1,10‐phenathroline)dicobalt(II) Dihydrate and Hexaaqua(<i>μ</i><sub>2</sub>‐1,2,4,5‐benzenetetracarboxylato)‐bis(<i>N</i>,<i>N′</i>‐2,2′‐dipyridylamine)dinickel(II) Tetrahydrate", Zeitschrift für anorganische und allgemeine Chemie, vol. 632, pp. 133-139, 2005. https://doi.org/10.1002/zaac.200500292
  2. P. Das, C.K. Jain, S.K. Dey, R. Saha, A.D. Chowdhury, S. Roychoudhury, S. Kumar, H.K. Majumder, and S. Das, "Synthesis, crystal structure, DNA interaction and in vitro anticancer activity of a Cu(<scp>ii</scp>) complex of purpurin: dual poison for human DNA topoisomerase I and II", RSC Adv., vol. 4, pp. 59344-59357, 2014. https://doi.org/10.1039/c4ra07127a

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Supporting information: chemical graveyard or invaluable resource for chemical structures.

Friday, March 31st, 2017

Nowadays, data supporting most publications relating to the synthesis of organic compounds is more likely than not to be found in associated “supporting information” rather than the (often page limited) article itself. For example, this article[1] has an SI which is paginated at 907; almost a mini-database in its own right! Here I ponder whether such dissemination of data is FAIR (Findable, accessible, interoperable and re-usable).[2]

I am going to use this article as my starting point.[3] One of the compounds discussed there is shown below; it is not explicitly discussed in the main body of the article. So how findable is it?

  1. A search of Scifinder (Chemical abstracts) using the structure above reveals one hit, the source being the expected one.[3]
  2. A search of Reaxys (used to be Beilstein) reveals no hits in their own database, but one hit is noted in …
  3. Pubchem, where it occurs as substance 163835830. The source is again cited correctly[3]. One of the properties reported is the InChI key: JSLVVAICXSKSEQ-UHFFFAOYSA-N. This is the same key generated from the structure drawing programs Chemdraw or ChemDoodle.
  4. Google on the other hand finds nothing for JSLVVAICXSKSEQ-UHFFFAOYSA-N.[4]
  5. I also tried Google Scholar but again with no luck.

So supporting information does appear to be indexed by both Chemical Abstracts and Pubchem; it is thankfully not a graveyard![5] The chemical databases do return valuable additional information about the molecule, such as e.g. its InChI key and much else besides. Given that presumably the open PubChem resource IS indexed by Google, it must be a policy somewhere that prevents e.g. JSLVVAICXSKSEQ-UHFFFAOYSA-N from being found.

I suppose the next question might be Supporting information: chemical graveyard or invaluable resource for chemical spectra? I confess here that this post was in fact inspired by a previous one on the topic of the provenance of NMR spectra. And perhaps also with some input from the concept of sonification of spectra, in which an instrumental spectrum is converted into a sound signature to allow blind people access to such information.‡ I wonder whether a sonified unique digital signature could be used to search for spectra, somewhat in the manner that InChI helped in tracking down (or not) the molecule above? I think it would be reasonable to say that e.g. NMR spectra as embedded in say a 907 page supporting information document are likely to be very much less FAIR[2]. The solution there of course is better provenance and better metadata, as I previously mulled.

‡I cannot help but wonder what a carbonyl group sounds like!

References

  1. J.M. Lopchuk, K. Fjelbye, Y. Kawamata, L.R. Malins, C. Pan, R. Gianatassio, J. Wang, L. Prieto, J. Bradow, T.A. Brandt, M.R. Collins, J. Elleraas, J. Ewanicki, W. Farrell, O.O. Fadeyi, G.M. Gallego, J.J. Mousseau, R. Oliver, N.W. Sach, J.K. Smith, J.E. Spangler, H. Zhu, J. Zhu, and P.S. Baran, "Strain-Release Heteroatom Functionalization: Development, Scope, and Stereospecificity", Journal of the American Chemical Society, vol. 139, pp. 3209-3226, 2017. https://doi.org/10.1021/jacs.6b13229
  2. M.D. Wilkinson, M. Dumontier, I.J. Aalbersberg, G. Appleton, M. Axton, A. Baak, N. Blomberg, J. Boiten, L.B. da Silva Santos, P.E. Bourne, J. Bouwman, A.J. Brookes, T. Clark, M. Crosas, I. Dillo, O. Dumon, S. Edmunds, C.T. Evelo, R. Finkers, A. Gonzalez-Beltran, A.J. Gray, P. Groth, C. Goble, J.S. Grethe, J. Heringa, P.A. ’t Hoen, R. Hooft, T. Kuhn, R. Kok, J. Kok, S.J. Lusher, M.E. Martone, A. Mons, A.L. Packer, B. Persson, P. Rocca-Serra, M. Roos, R. van Schaik, S. Sansone, E. Schultes, T. Sengstag, T. Slater, G. Strawn, M.A. Swertz, M. Thompson, J. van der Lei, E. van Mulligen, J. Velterop, A. Waagmeester, P. Wittenburg, K. Wolstencroft, J. Zhao, and B. Mons, "The FAIR Guiding Principles for scientific data management and stewardship", Scientific Data, vol. 3, 2016. https://doi.org/10.1038/sdata.2016.18
  3. G.M.S. Yip, Z. Chen, C.J. Edge, E.H. Smith, R. Dickinson, E. Hohenester, R.R. Townsend, K. Fuchs, W. Sieghart, A.S. Evers, and N.P. Franks, "A propofol binding site on mammalian GABAA receptors identified by photolabeling", Nature Chemical Biology, vol. 9, pp. 715-720, 2013. https://doi.org/10.1038/nchembio.1340
  4. S.J. Coles, N.E. Day, P. Murray-Rust, H.S. Rzepa, and Y. Zhang, "Enhancement of the chemical semantic web through the use of InChI identifiers", Organic & Biomolecular Chemistry, vol. 3, pp. 1832, 2005. https://doi.org/10.1039/b502828k
  5. M. Karthikeyan, and R. Vyas, "ChemEngine: harvesting 3D chemical structures of supplementary data from PDF files", Journal of Cheminformatics, vol. 8, 2016. https://doi.org/10.1186/s13321-016-0175-x

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George Olah and the norbornyl cation.

Friday, March 10th, 2017

George Olah passed away on March 8th. He was part of the generation of scientists in the post-war 1950s who had access to chemical instrumentation that truly revolutionised chemistry. In particular he showed how the then newly available NMR spectroscopy illuminated structures of cations in solvents such “Magic acid“. The obituaries will probably mention his famous “feud” with H. C. Brown over the structure of the norbornyl cation (X=CH2+), implicated in the mechanism of many a solvolysis reaction that characterised the golden period of physical organic chemistry just before and after WWII. 

The dispute between Olah and Brown was not played on a pitch using quite the same goal posts. Olah did much of his work in magic acid and Brown did his in aqueous solutions. I was involved in a tiny way when the discussion about the precise character of the norbornyl cation was reaching its peak in the mid 1970s. At the time, I was working with Michael Dewar, who was himself not shy in joining in the fun and sometimes very acrimonious disputes at conferences. We contributed by calculating the so-called core-electron carbon ESCA spectrum.[1] History records that we came down on the wrong side,‡ by suggesting that this form of spectroscopy supported Brown rather than Winstein/Olah on the basis of a 6:1 spectral deconvolution (classical) rather than 5:2 (non-classical). More recently of course the crystal structure of the parent cation itself has been shown to be non-classical[2] (there are other crystal structures which differ in respect to having one or more additional methyl groups[3]). For a 3D model of norbornyl cation, see DOI: 10.5517/CCZ21LN. This still leaves the issue (very slightly) open for the structure of the solvated cation when formed in water! 

When I started to teach a course in molecular modelling, I touched briefly on how modelling could contribute and whilst updating the notes in the 1990s, wondered why the boron analogue had never been so studied (X=BH2). Unlike the crystallographically difficult norbornyl ion-pair, the iso-electronic boron species would be neutral and not need a counter-ion. Perhaps it might be a more manageable molecule? Checking the Cambridge structural database, such a species has never been reported!† So here as my homage to Olah, I report its calculated structure (b2plypd3/Def2-TZVPP, DOI: 10.14469/hpc/2236).

The norbornyl cation has symmetrical C-C bridging distances of ~1.80±0.02Å and a basal C-C distance of ~1.39±0.02Å. The calculated values for the boron equivalent are 2.16Å and 1.36Å respectively, with all positive force constants. B-C bonds are normally 1.66-1.72Å, significantly longer than C-C bonds, which makes the longer B-C lengths in this example unsurprising. More interestingly, the species has one vibrational normal mode (ν 203 cm-1) which corresponds to the [1,2] shift of the BH2 group across the basal C-C. For a classical species, this vibrational motion would correspond to a transition state (an imaginary vibration) but for a non-classical species it is of course real. In this sense it is analogous to the so-called real Kekulé mode in non-classical benzene, which “equilibrates” the two classical Kekulé structures. The corresponding calculated vibration for the norbornyl cation itself is ν 194 cm-1 (DOI: 10.14469/hpc/2238).

Of course, the entire controversy over the structure of this species is littered with comparisons between not quite similar systems, differing in a methyl group more or less. So morphing a C+ to a B might be seen as quite a large change. But perhaps if it had been crystallised in say the 1960s, would the subsequent debates have taken a different turn?

‡ We were also wrong about the symmetry of the Diels-Alder cyclisation, which is nowadays accepted to be synchronous rather than asynchronous for simple  Diels-Alder reactions. But that is another story.

†GAXLIA is perhaps the closest analogue.[4],

References

  1. M.J.S. Dewar, R.C. Haddon, A. Komornicki, and H. Rzepa, "Ground states of molecules. 34. MINDO/3 calculations for nonclassical ions", Journal of the American Chemical Society, vol. 99, pp. 377-385, 1977. https://doi.org/10.1021/ja00444a012
  2. F. Scholz, D. Himmel, F.W. Heinemann, P.V.R. Schleyer, K. Meyer, and I. Krossing, "Crystal Structure Determination of the Nonclassical 2-Norbornyl Cation", Science, vol. 341, pp. 62-64, 2013. http://dx.doi.org/10.1126/science.1238849
  3. T. Laube, "Redetermination of the Crystal Structure of the 1,2,4,7‐<i>anti</i>‐tetramethylbicyclo[2.2.1]heptan‐2‐yl cation at 110 K", Helvetica Chimica Acta, vol. 77, pp. 943-956, 1994. https://doi.org/10.1002/hlca.19940770407
  4. P.J. Fagan, E.G. Burns, and J.C. Calabrese, "Synthesis of boroles and their use in low-temperature Diels-Alder reactions with unactivated alkenes", Journal of the American Chemical Society, vol. 110, pp. 2979-2981, 1988. https://doi.org/10.1021/ja00217a053

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Stable “unstable” molecules: a crystallographic survey of cyclobutadienes and cyclo-octatetraenes.

Sunday, March 5th, 2017

Cyclobutadiene is one of those small iconic molecules, the transience and instability of which was explained theoretically long before it was actually detected in 1965.[1] Given that instability, I was intrigued as to how many crystal structures might have been reported for this ring system, along with the rather more stable congener cyclo-octatetraene. Here is what I found.

The Conquest search query shown (with no disorder, no errors and R < 0.1 also specified). 

There are 23 instances (February 2017 database; see DOI: 10.14469/hpc/2231 for search query) of the supposedly unstable cyclobutadiene motif!

The three clusters deserve explanations. The orange cluster reveals a long C-C bond (rather longer than normal C-C bonds), accompanied by short C=C bonds, as indicated by the valence bond form shown below. Take particular note that the arrow connecting the two forms is NOT a resonance arrow but an equilibrium arrow. The “bond shifting” is not fast but slow, allowing long and short bonds to be measured in a crystal structure.

The rather larger blue cluster exhibits much more equal bonds. These arise from the presence of “push-pull” substituents on the ring which serve to delocalise the unfavourable cyclobutadiene ring and hence decrease the unfavourable anti-aromaticity. A typical example is shown below (EACBUT):

The small red cluster shows a long C=C bond and a short C-C bond! I have commented previously on apparently abnormally long C=C bonds, which in fact all turned out to be errors, and I suspect the same is true here. The bond orders in the indexing in the CSD data base have probably been mis-assigned, as per below for GANBII;

The Conquest search query is shown (with no disorder, no errors and R < 0.1 specified) for the 8-ring, which further specifies a torsion angle about a C-C bond to determine how planar the ring might be.

The “normal” cluster in the top left exhibits long C-C bonds and short C=C bonds. The colour code indicates how planar the ring is (red-blue spectrum = twisted ⇒ planar). The majority of examples are twisted about the C-C bond(s), but there are a few interesting examples that are not, as shown by the blue dots. There are only a few “bond-equalised” examples in the centre; perhaps “push-pull” induced equalisation is more difficult or perhaps few examples have been made?

The members of the red cluster in the bottom right all reveal short “C-C” bonds and long “C=C” bonds. Intriguingly they all also have low values of the torsion about one C-C bond (although not always about all four C-C bonds). A typical example (BAQVUK, DOI: 10.5517/CC4GWWB ) is shown below. These all need careful inspection and possibly reversal of the C-C and C=C indexing.

It was interesting to discover how many crystalline examples of this archetypal “unstable” cyclobutadiene motif have been made, and the means by which some of them at least have been stabilized. In the more abundant cyclo-octatetraene system, I learnt that one has to be cautious about blindly accepting the bond order designations in the database. Perhaps we might learn here that some of these have indeed been re-assigned in the next release of the database.

References

  1. L. Watts, J.D. Fitzpatrick, and R. Pettit, "Cyclobutadiene", Journal of the American Chemical Society, vol. 87, pp. 3253-3254, 1965. https://doi.org/10.1021/ja01092a049

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Stable "unstable" molecules: a crystallographic survey of cyclobutadienes and cyclo-octatetraenes.

Sunday, March 5th, 2017

Cyclobutadiene is one of those small iconic molecules, the transience and instability of which was explained theoretically long before it was actually detected in 1965.[1] Given that instability, I was intrigued as to how many crystal structures might have been reported for this ring system, along with the rather more stable congener cyclo-octatetraene. Here is what I found.

The Conquest search query shown (with no disorder, no errors and R < 0.1 also specified). 

There are 23 instances (February 2017 database; see DOI: 10.14469/hpc/2231 for search query) of the supposedly unstable cyclobutadiene motif!

The three clusters deserve explanations. The orange cluster reveals a long C-C bond (rather longer than normal C-C bonds), accompanied by short C=C bonds, as indicated by the valence bond form shown below. Take particular note that the arrow connecting the two forms is NOT a resonance arrow but an equilibrium arrow. The “bond shifting” is not fast but slow, allowing long and short bonds to be measured in a crystal structure.

The rather larger blue cluster exhibits much more equal bonds. These arise from the presence of “push-pull” substituents on the ring which serve to delocalise the unfavourable cyclobutadiene ring and hence decrease the unfavourable anti-aromaticity. A typical example is shown below (EACBUT):

The small red cluster shows a long C=C bond and a short C-C bond! I have commented previously on apparently abnormally long C=C bonds, which in fact all turned out to be errors, and I suspect the same is true here. The bond orders in the indexing in the CSD data base have probably been mis-assigned, as per below for GANBII;

The Conquest search query is shown (with no disorder, no errors and R < 0.1 specified) for the 8-ring, which further specifies a torsion angle about a C-C bond to determine how planar the ring might be.

The “normal” cluster in the top left exhibits long C-C bonds and short C=C bonds. The colour code indicates how planar the ring is (red-blue spectrum = twisted ⇒ planar). The majority of examples are twisted about the C-C bond(s), but there are a few interesting examples that are not, as shown by the blue dots. There are only a few “bond-equalised” examples in the centre; perhaps “push-pull” induced equalisation is more difficult or perhaps few examples have been made?

The members of the red cluster in the bottom right all reveal short “C-C” bonds and long “C=C” bonds. Intriguingly they all also have low values of the torsion about one C-C bond (although not always about all four C-C bonds). A typical example (BAQVUK, DOI: 10.5517/CC4GWWB ) is shown below. These all need careful inspection and possibly reversal of the C-C and C=C indexing.

It was interesting to discover how many crystalline examples of this archetypal “unstable” cyclobutadiene motif have been made, and the means by which some of them at least have been stabilized. In the more abundant cyclo-octatetraene system, I learnt that one has to be cautious about blindly accepting the bond order designations in the database. Perhaps we might learn here that some of these have indeed been re-assigned in the next release of the database.

References

  1. L. Watts, J.D. Fitzpatrick, and R. Pettit, "Cyclobutadiene", Journal of the American Chemical Society, vol. 87, pp. 3253-3254, 1965. https://doi.org/10.1021/ja01092a049

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More tetrahedral fun. Spherical aromaticity (and other oddities) in N4 and C4 systems?

Thursday, March 2nd, 2017

The thread thus far. The post about Na2He introduced the electride anionic counter-ion to Na+ as corresponding topologically to a rare feature known as a non-nuclear attractor. This prompted speculation about other systems with such a feature, and the focus shifted to a tetrahedral arrangement of four hydrogen atoms as a dication, sharing a total of two valence electrons. The story now continues here.

What emerged during comments about H42+ was that a density functional (DFT) derived wavefunction seemed to predict it to be a stable minimum, but that wavefunctions derived from coupled cluster or CASSCF methods predicted it to be a three-fold degenerate transition state instead. So I asked myself if perhaps other similar tetrahedral molecules less susceptible to such method ambiguity might be found. Here I record some of the species I investigated. 

  1. N4 in a tetrahedral allotropic arrangement of the element (ωB97XD/Def2-TZVPP DFT method: 10.14469/hpc/2217 and CCSD(T)/Def2-TZVPP 10.14469/hpc/2216). I found this intriguing, because each nitrogen has a lone pair of electrons and such an arrangement of eight electrons might be spherically aromatic according to the rule: 2(n+1)2, where n=1[1]. N4 itself is indeed a true minimum (rN-N  1.460Å) with all positive force constants at both the DFT (767, 1005 and 1443) and CCSD(T) (726, 940 and 1304 cm-1) levels, but with a free energy ~185 kcal/mol higher than dinitrogen. The electronic topology is uneventfully classical, with six line (bond) critical points along each N-N axis (magenta), four ring critical points (green) and one cage point (inner blue sphere); there is no non-nuclear attractor present.The NICS value at the centre of the tetrahedron (coincident with the cage critical point) is -73 ppm, which does suggest aromaticity.
  2. C4 in a tetrahedral allotropic arrangement of this element is also a minimum as closed shell singlet (rC-C 1.646Å) again with positive force constants (ωB97XD/Def2-TZVPP DFT, 10.14469/hpc/2224, 434, 715, 1052 cm-1) and the same electronic topology as N4.
    The magnetic shielding at the ring centre is -1685 ppm, a value clearly perturbed by core ring currents or other factors; the molecule does not map to the 2(n+1)2 spherical aromaticity rule, which only allows values of 2,8,18, 32… electrons. I tried applying the ELF procedure using the computed WFN file (either direct or symmetrised, using both TopMod and MultiWFN) but the results did not have Td symmetry.‡
  3. C42+ with two fewer electrons is also a minimum as a closed shell singlet (rC-C 1.521Å) tetrahedral species (ωB97XD/Def2-TZVPP: 10.14469/hpc/2218, 1132, 1136, 1448 cm-1; CCSD(T)/Def2-TZVPP 10.14469/hpc/2225 showing rather different normal mode energies of ~330, 592, 1126 cm-1 ) which can be thought as mapping to the spherical aromaticity formula 2(n+1)2, where n=0. The electronic topology is slightly different from C4 itself, with four ring points (green) very close to the cage point in the centre.The ELF function now behaves itself in terms of symmetry, and produces a result in fact very similar to the H42+ molecule which started this topic rolling. There is an ELF basin with 0.14e located in the centroid and six equivalent basins (2.25e) spanning each pair of carbon atoms, although these C-C bonds are hugely banana shaped! That central electron basin closely resembles the one found in H42+ itself. The magnetic shielding at the centre of 3349 ppm is not meaningful in deciding if the molecule is indeed “aromatic”.
  4. C41-  is again a tetrahedral minimum, this time as a quartet 4A1 state (ωB97XD/Def2-TZVPP: 10.14469/hpc/2219, 918, 1024, 1377 cm-1; CCSD(T)/Def2-TZVPP 10.14469/hpc/2237, 824, 895, 1303 cm-1). The electronic topology is the same as before.Open shell spherical aromaticity[2] is given by the 2N2 + 2N + 1 (with S = N + ½) rule. A quartet state has S=3/2, hence N=1 and the formula stipulates 5 delocalizable electrons for aromaticity, which this species has! The isotropic magnetic shielding is 695 ppm, which again is not immediately helpful.The ELF analysis ((above) shows just two types of basin, with four “lone pairs” at each carbon vertex (1.24e) and eight associated with the C-C “bent” bonds (1.95e). 

What did I learn?

  • Firstly, that the (very unstable) tetrahedral allotrope of nitrogen might be a spherical aromatic.
  • Secondly, that tetrahedral closed-shell singlet C4 has a very odd wavefunction; this needs further work.
  • Thirdly that tetrahedral C42+  closely resembles H42+  in having a basin of electrons at the very centre, but that unlike H42+ it does appear to be a stable minimum.
  • Finally, that the radical anion C4– might be perhaps the smallest possible example of an open shell spherical aromatic.

And perhaps also in trying to answer some simple questions, I have also raised several more puzzles. Onwards and occasionally upwards.

‡This wavefunction is clearly odd, and needs further analysis.

References

  1. A. Hirsch, Z. Chen, and H. Jiao, "Spherical Aromaticity inIh Symmetrical Fullerenes: The 2(N+1)2 Rule", Angewandte Chemie, vol. 39, pp. 3915-3917, 2000. https://doi.org/10.1002/1521-3773(20001103)39:21<3915::aid-anie3915>3.0.co;2-o
  2. J. Poater, and M. Solà, "Open-shell spherical aromaticity: the 2N2 + 2N + 1 (with S = N + ½) rule", Chemical Communications, vol. 47, pp. 11647, 2011. https://doi.org/10.1039/c1cc14958j

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The H4 (2+) dication and its bonding.

Wednesday, February 15th, 2017

This post arose from a comment attached to the post on Na2He and relating to peculiar and rare topological features of the electron density in molecules called non-nuclear attractors. This set me thinking about other molecules that might exhibit this and one of these is shown below.

The topology of the electron density is described by just four basic types, designed formally by the notation [3,-3], [3,-1], [3,1] and [3,3] and more colloquially by the terms nuclear attractor (NNA), line (or bond) critical point, a ring critical point and a cage critical point respectively. Mostly, the nuclear critical points coincide exactly with the actual nuclear positions, but more rarely these points are not found centered at a nucleus. It was such an NNA that was suggested as a comment on the post on Na2He. There I replied that another example of an NNA is to be found in H3+ and so its a short step to take a look at H42+ in a tetrahedral arrangement (DOI: 10.14469/hpc/2165). Since only two electrons are available for bonding, it is tempting to represent it as below, with dashed partial bonds connnecting the six edges of the tetrahedron and is associated with real normal vibrational modes; ν 416, 1490 and 1861 cm-1. A brief search on Scifinder, which appears to reference this species as hydrogen, ion (H42+), does not identify any publications associated with it (there are studies on H41+ however); if any reader here knows of any discussion please alert us!

Analysing the density however gives a different result. A NNA is located at the centre of the tetrahedron and a line (bond) critical point connects this to each of the four hydrogen nuclei. This result is similar to the obtained for H3+. It is rather odd that these non-nuclear attractors have not entered into the vocabulary used to describe the bonding in simple molecules, but this picture is certainly different from the more empirical dashed lines between the four nuclei that one is instinctively drawn to use (above).

The ELF analysis (performed using multiWFN) is more interesting. The nuclear basins associated with the hydrogens reveal each has 0.425e, but the central one (green below) has its own basin with 0.301e. 

The NICS value associated with the non-nuclear attractor is -27 ppm, which is indicative of strong spherical aromaticity.

All of which goes to show that even the simplest of molecular species may still have properties that are unexpected or certainly not well-known!

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Braiding a molecular knot with eight crossings.

Friday, January 20th, 2017

This is one of those posts of a molecule whose very structure is interesting enough to merit a picture and a 3D model. The study[1] reports a molecular knot with the remarkable number of eight crossings.

The DOI for the 3D model is 10.5517/CCDC.CSD.CC1M85Y0 (or click on the image above). Such topology intersects with work we did a few years back on high-order crossings in fully conjugated π-systems[2], which were then illustrated[3] with hypothetical charged higher order annulenes exhibiting linking numbers Lk of up to 6π. A fully π-conjugated system, also with a linking number in the π-framework of 6π but in the form of a trefoil braid was even suggested on this blog, with a common feature of a central templating atom (a cation rather than an anion). Another example of a previously reported pentadecanuclear manganese metallacycle[4] was also assigned a linking number of 6π.

The molecule above is not completely π-conjugated around the braid and so special properties related to aromaticity and associated ring currents resulting from the topology of the cyclic conjugation[5] are not expected to accrue in the eight-crossing molecular braid[1]. We might also look forward to examples of the characterisation of braids with an odd-number of crossings such as trefoils, pentafoils, heptafoils, etc, as associated with the name Möbius.

References

  1. J.J. Danon, A. Krüger, D.A. Leigh, J. Lemonnier, A.J. Stephens, I.J. Vitorica-Yrezabal, and S.L. Woltering, "Braiding a molecular knot with eight crossings", Science, vol. 355, pp. 159-162, 2017. https://doi.org/10.1126/science.aal1619
  2. S.M. Rappaport, and H.S. Rzepa, "Intrinsically Chiral Aromaticity. Rules Incorporating Linking Number, Twist, and Writhe for Higher-Twist Möbius Annulenes", Journal of the American Chemical Society, vol. 130, pp. 7613-7619, 2008. https://doi.org/10.1021/ja710438j
  3. C.S. Wannere, H.S. Rzepa, B.C. Rinderspacher, A. Paul, C.S.M. Allan, H.F. Schaefer, and P.V.R. Schleyer, "The Geometry and Electronic Topology of Higher-Order Charged Möbius Annulenes", The Journal of Physical Chemistry A, vol. 113, pp. 11619-11629, 2009. https://doi.org/10.1021/jp902176a
  4. H.S. Rzepa, "Linking Number Analysis of a Pentadecanuclear Metallamacrocycle: A Möbius-Craig System Revealed", Inorganic Chemistry, vol. 47, pp. 8932-8934, 2008. https://doi.org/10.1021/ic800987f
  5. P.L. Ayers, R.J. Boyd, P. Bultinck, M. Caffarel, R. Carbó-Dorca, M. Causá, J. Cioslowski, J. Contreras-Garcia, D.L. Cooper, P. Coppens, C. Gatti, S. Grabowsky, P. Lazzeretti, P. Macchi, . Martín Pendás, P.L. Popelier, K. Ruedenberg, H. Rzepa, A. Savin, A. Sax, W.E. Schwarz, S. Shahbazian, B. Silvi, M. Solà, and V. Tsirelson, "Six questions on topology in theoretical chemistry", Computational and Theoretical Chemistry, vol. 1053, pp. 2-16, 2015. https://doi.org/10.1016/j.comptc.2014.09.028

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