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(another) WATOC 2017 report.

Tuesday, 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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Chemistry rich diagrams: do crystal structures carry spin information? Iron-di-imine complexes.

Sunday, June 18th, 2017

The iron complex shown below forms the basis for many catalysts.[1] With iron, the catalytic behaviour very much depends on the spin-state of the molecule, which for the below can be either high (hextet) or medium (quartet) spin, with a possibility also of a low spin (doublet) state. Here I explore whether structural information in crystal structures can reflect such spin states.

We studied this a few years back and the talk I gave on the topic included some of our first statistical explorations of the CSD (Cambridge structure database). Here I update those searches, using the search query (DOI: 10.14469/hpc/2675) shown below. The di-imine ligand contains only 3-coordinate atoms, whilst the iron is 5-coordinate. The angles subtended at the Fe and group X=NM (any non-metal atom) are as defined below.

The resulting scatterplot is shown below and contains a rich variety of phenomena.

  1. In the bond length region of 1.85-1.95Å one sees three clusters, one arranged on the diagonal indicating both N-Fe lengths are the same and two off the diagonal which indicates one length is ~0.1Å longer than the other.
    • To explain this, one needs to know that 5-coordinate Fe has a trigonal bipyramidal shape in which one X=NM group subtends an (anti-periplanar)  angle of ~180° at Fe with one of the ring nitrogens and the other two X=NM groups each subtend an angle of <120° with the other ring nitrogen. The result is that if the group X has the appropriate (electron withdrawing) properties, the two N-Fe bond lengths are no longer equal. If group X is more passive, the two N-Fe bond lengths may remain more equal.
  2. A second cluster occurs at ~2.00-2.1Å, mostly along the diagonal but with hints of smaller off-diagonal clusters.
  3. A third feature occurs at ~2.1-2.3Å, where now the off-diagonal clusters contain more examples than are on the diagonal itself.

Clearly, there is more going on here than can be explained simply by the orientation of X=NM with respect to the Fe-N bond axis. That something is the spin-multiplicity of the molecule. With the Fe complex shown above, this can be one of doublet (one unpaired electron), quartet (three unpaired electrons) or hextet (five unpaired electrons). To gain insight into how this affects the bond lengths, some calculations are needed, using X=Cl, R=H. Here they are done at the TPSSH/Def2-TZVPP level. In fact it is well-known[2] that the energy separations of low/medium/high spin Fe complexes are highly sensitive to the functional, but TPSSH seems to be amongst the best.‡ This shows that the energy ordering of the three states using this particular method is hextet (0.0, DOI: 10.14469/hpc/2676) < quartet (10.5, DOI: 10.14469/hpc/2677) < doublet (13.2 kcal/mol, DOI: 10.14469/hpc/2678), with the bond lengths shown below (for X=Cl).

We might make tentative hypotheses based on these values:

  1. The off-diagonal bottom left clusters (1 in list above) might arise from doublet states.
  2. The off-diagonal top right clusters (3 in list above) might arise from sextet states.
  3. The cluster (2 in list above) might be quartet states for which X is not sufficiently electronegative to induce bond length discriminations.
  4. It is worth noting that the energy span between the three states for the above molecule is only ~13 kcal/mol, which is small enough to be altered by substituents.

Testing these hypotheses requires knowledge of the spin state of all the entries in any cluster. This information is unfortunately not carried by the CSD, which has relatively little information over and above structural data. Each entry would have to be individually inspected. Indeed the spin state of many of these complexes may not even be known. Nevertheless, it would be great to repeat the graphs shown above as a function of known spin state so that the (again I repeat tentative) hypotheses might be confirmed or refuted.

‡This article evaluates a whole host of functionals against e.g. the spin-state energy separations of the Fe2+ ion. As it happens, TPSSH was not one that was evaluated, but in fact it gives more or less the best match to experiment. Thus Esinglet-Equintet obs = 85.6 kcal/mol, calc 92.4; Etriplet-Equintet obs 56.1, calc 59.5 kcal/mol. A hypothesis therefore is that the TPSSH functional is a reasonable one to go exploring such high-spin species.

References

  1. M.P. Shaver, L.E.N. Allan, H.S. Rzepa, and V.C. Gibson, "Correlation of Metal Spin State with Catalytic Reactivity: Polymerizations Mediated by α‐Diimine–Iron Complexes", Angewandte Chemie International Edition, vol. 45, pp. 1241-1244, 2006. https://doi.org/10.1002/anie.200502985
  2. P. Verma, Z. Varga, J.E.M.N. Klein, C.J. Cramer, L. Que, and D.G. Truhlar, "Assessment of electronic structure methods for the determination of the ground spin states of Fe(<scp>ii</scp>), Fe(<scp>iii</scp>) and Fe(<scp>iv</scp>) complexes", Physical Chemistry Chemical Physics, vol. 19, pp. 13049-13069, 2017. https://doi.org/10.1039/c7cp01263b

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Tautomeric polymorphism.

Thursday, June 1st, 2017

Conformational polymorphism occurs when a compound crystallises in two polymorphs differing only in the relative orientations of flexible groups (e.g. Ritonavir). At the Beilstein conference, Ian Bruno mentioned another type;  tautomeric polymorphism, where a compound can crystallise in two forms differing in the position of acidic protons. Here I explore three such examples.

The term occurs in the title of this article,[1] for a compound known as Omeprazole.

When the bottom structure (the 6-methoxy) is used to search the CSD, two separate series are found. The first of these is UDAVIF (DOI:  10.5517/ccp82qq,  6-Methoxy-2-((4-methoxy-3,5-dimethyl-2-pyridinyl)methylsulfinyl)-1H-benzimidazole). There is no information regarding the absolute configuration of the chiral S-centre. Although the downloaded coordinates show it as R it is probably a racemic mixture. A note added to the structure declares disorder: “Omeprazole exists as solid solutions of the two tautomers. The structure is mixed 5-methoxy/6-methoxy with occupancies 0.078:0.922“, which indicates 7.8% is present as in the upper structure above. 

The second hit is VAYXOI (DOI: 10.5517/ccp82pp, rac-6-Methoxy-2-(((4-methoxy-3,5-dimethyl-2-pyridinyl)methyl)sulfinyl)-1H-benzimidazole) which now contains no disorder; the contaminating 5-methoxy tautomer is no longer present. Perhaps not quite a true tautomeric polymorph, since the 5-methoxy tautomer is never observed in pure form.

This does occur with a second example. DEBFAR[2] represents the keto form on the right which crystallises from methanol, whilst YUYDOL as the enol form on the left crystallises from n-hexane. 

Calculations shed some light on this behaviour. DEBFAR has a computed (DOI: 10.14469/hpc/2591)  dipole moment of 11D, whereas YUYDOL (DOI: 10.14469/hpc/2590) is 2.5D. In chloroform solutions (~half way between the two solvent polarities), the keto form is ~6.1 kcal/mol lower in ΔG than the enol. The crystal packing for the two forms is very different and the differences in this packing must clearly amount to >6.1 kcal/mol to over-ride the lesser stability of DEBFAR in solution.


The final example [3] is illustrated using scheme 2 from that article, one entitled tautomeric species of 4-hydroxynicotinic acid:

The original diagram has two unfortunate bond errors which are NOT reproduced above (and which perhaps are a good topic for discussion in tutorials with students), along with an unusual interpretation of the term tautomerism. The blue arrows above are mine and I suggest the isomerism between the connected species is resonance isomerism, and not tautomerism. So three possible different true tautomers then. Five crystal structures are reported which I list below.

  1. 10.5517/cctswjz (KUXPUP, 4-oxo-1,4-dihydropyridine-3-carboxylic acid, no H2O),  10.5517/ccdc.csd.cc1kfyxv (KUXPUP01 no H2O) and 10.5517/ccdc.csd.cc1kfyzx (KUXPUP02 no H2O)
  2. 10.5517/ccx59s4 (AVEMUK, 4-Oxo-1,4-dihydropyridine-3-carboxylic acid hemihydrate) and  10.5517/ccdc.csd.cc1kfz21 (AVEMUK01)
  3. 10.5517/ccdc.csd.cc1kfz54 (AKIHIN, 4-hydroxypyridin-1-ium-3-carboxylate monohydrate) 
  4. 10.5517/ccdc.csd.cc1kfz10 (AKIHAF, 4-hydroxypyridin-1-ium-3-carboxylate)

KUXPUP and AVEMUK differ only in the presence of one solvent water molecule and both represent tautomer 2 above. AKIHIN and AKIHAF similarly represent tautomer 3 above; both are represented as 3a in the CSD and not as 3b. There are no examples of tautomer 1 in the crystal structure database; it may only exist in the gas phase. So the equilibrium 2 ⇌ 3 is another genuine example of tautomeric polymorphism, with the keto form favoured by more polar solvents, as was noted for the previous example.

With this last article,[3] comprehensive calculations at a good level were reported, including modelling the periodic cell using the Crystal program and including corrections such as BSSE (basis set superposition error) and dispersion terms. I was hopeful that this might lead me to something as simple as the computed dipole moments of the (isolated) species (as I reported above for the previous system), but these were not mentioned in the text of the article. Unfortunately, the supporting information also had no details of any such calculations, which left me frustrated again at how difficult it can be in (it has to be said) the vast majority of articles which report calculations to get details of such calculations. 

Tautomeric polymorphism remains a very rare phenomenon. SciFinder for example only has 19 references citing it (2 of which are to conference talks). Perhaps the most intriguing[4] claims that 2-thiobarbituric acid has the richest collection of tautomeric polymorphs with five. Since no calculations are reported there, I might try these out and report back here.

Postscript:  Here is some analysis of 2-thiobarbituric.

  1. THBARB (DOI 10.5517/cctbxcd, 10.5517/cctbxfg  and 10.5517/cctbxgh) are three polymorphs of  the keto tautomer, the isolated molecule having a small calculated dipole moment (DOI: 10.14469/hpc/2632).
  2. PABNAJ (DOI: 10.5517/cctbxbc) is a polymorph in the enol form, with a much larger calculated dipole moment (DOI: 10.14469/hpc/2633)
  3. PABNIR (DOI: 10.5517/cctbxdf) is a mixed polymorph with one enol paired with one keto form. 

The relative free-energies of the isolated molecules are 0.0 (keto) and 9.0 (enol). The keto-enol pair is 0.4 kcal/mol more stable than the isolated components. This again shows the effect that crystal packing can have on the relative energies and also shows that a  simple inspection of the dipole moment may cast light on the polymorphism.

 

References

  1. P.M. Bhatt, and G.R. Desiraju, "Tautomeric polymorphism in omeprazole", Chemical Communications, pp. 2057, 2007. https://doi.org/10.1039/b700506g
  2. Y. Akama, M. Shiro, T. Ueda, and M. Kajitani, "Keto and Enol Tautomers of 4-Benzoyl-3-methyl-1-phenyl-5(2H)-pyrazolone", Acta Crystallographica Section C Crystal Structure Communications, vol. 51, pp. 1310-1314, 1995. https://doi.org/10.1107/s0108270194007389
  3. S. Long, M. Zhang, P. Zhou, F. Yu, S. Parkin, and T. Li, "Tautomeric Polymorphism of 4-Hydroxynicotinic Acid", Crystal Growth & Design, vol. 16, pp. 2573-2580, 2016. https://doi.org/10.1021/acs.cgd.5b01639
  4. M. Chierotti, L. Ferrero, N. Garino, R. Gobetto, L. Pellegrino, D. Braga, F. Grepioni, and L. Maini, "The Richest Collection of Tautomeric Polymorphs: The Case of 2‐Thiobarbituric Acid", Chemistry – A European Journal, vol. 16, pp. 4347-4358, 2010. https://doi.org/10.1002/chem.200902485

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How does carbon dioxide coordinate to a metal?

Saturday, May 6th, 2017

Mention carbon dioxide (CO2) to most chemists and its properties as a metal ligand are not the first aspect that springs to mind. Here thought I might take a look at how it might act as such.

There are up to five binding modes with one metal that one might envisage:

  1. Bonded interaction with the metal via just one oxygen atom,
  2. Bonded interaction via just the central carbon atom,
  3. Bonded interaction via the π-face of one C=O double bond,
  4. A weaker non-bonded interaction via carbon, or
  5. via oxygen.

Search queries of the Cambridge structure database (CSD) for these five modes are illustrated below (dataDOI: 10.14469/hpc/2524), with the constraints being applied to how many bonds (of unspecified type) each atom carries, along with no disorder and no errors. Thus query 1 is constrained by 1-coordination on one oxygen, and two on the carbon and other oxygen. 

  1. This query yields four hits: 10.5517/ccvcdq9, 10.5517/cc12nq6n, 10.5517/cc12nq5m, 10.5517/cc12nq4l. The angle subtended at the central carbon of the CO2 ranges from 172-176°, a very modest bending of the linear CO2. There are no examples where the metal is bonded to both oxygens.
  2. The next category involves the metal binding just to the central carbon. Two examples are known, differentiated from O-coordination by a more acute angle at the central carbon of 121-132°.
  3. The π-coordinated type requires a slightly more complex search query, shown below. The π-complex is defined as adding one coordination to each of one oxygen and the carbon. 

    This reveals 16 examples:

    The sine of the angle subtended at the centroid of one C-O bond shows that for most of the examples, the metal is close to perpendicular to this bond. The angle subtended at the central carbon ranges from 128-138, rather larger than the examples where the metal is bound just to the carbon. I have picked these two for illustration. The first (dataDOI: 10.5517/cc86r17) contains both CO2 and CO coordinated to the metal.This one (dataDOI: 10.1021/ic101652e) contains a short metal-centroid distance of 1.78Å (as also does 10.5517/ccz34kr). 

    There are two examples where BOTH π-CO bonds are coordinated to a metal; 10.5517/ccqlv7c and 10.5517/ccqlv8d (Ni-centroid distance 1.9Å) but these are intriguing because the two π-complexes are co-planar and not orthogonal.

  4. The final two cases are defined in the CSD database by having not so much bonds between metal and either C or O, as close intermolecular contacts typical of e.g. hydrogen bonds. This one (dataDOI: 10.5517/cc12nq9r) is to Fe, with a metal-C distance of 2.87Å which is significantly shorter than the anticipated sum of the van der Waals radii of the two atoms. The next (dataDOI: 10.5517/cc12npn2) has a close approach of Co to O of 2.23Å. The angles subtended at the carbon range from 174-180°. There are no convincing examples of close non-bonded approaches of the metal to both oxygen atoms simultaneously.

It is striking that the searches (as defined above) reveal relatively few examples. This might simply be a result of how the compounds are indexed in the CSD, reflected in the coordination constraints applied in the searches. Nevertheless, we see three quite different types of ligand-metal coordination in which bonds can be said to form and a more diffuse spectrum of weaker interactions to carbon dioxide. As a metal ligand, it is certainly interesting! Several deserve their wavefunctions looked at and I might report back on this aspect.

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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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The conformation of carboxylic acids revealed.

Tuesday, April 11th, 2017

Following my conformational exploration of enols, here is one about a much more common molecule, a carboxylic acid.

The components of the search are shown as four queries below, which will be combined in various Boolean senses (DOI: 10.14469/hpc/2462).

  1. Query one defines the carboxylic acid, with 3-coordinate carbon specified at the carbonyl along with 1-coordinate for the carbonyl oxygen. Then the HO-C=O torsion (o° for the syn conformation shown on the left above and 180° for the anti-conformation shown on the right) and the length of the O-C bond as variables.
  2. Query two defines a contact as ≤ the sum of van der Waals radii between QA (=N,O,F,Cl) and the hydrogen of the carboxylic acid (pink).
  3. Query three defines a contact as ≤ the sum of van der Waals radii between QA-H (QA=N,O,F,Cl) and the oxygen of the acid (pink).
  4. Query four defines a temperature of <100K for the data collection temperature.

The first search uses just Query 1, with additional constraints of no errors, no disorder and R < 0.05.

This can then be focused by combining Query 1 + Query 4, which shows a clear preference for the syn conformation.

Next, Query 1 with NOT query 2, which restricts the search to carboxylic acids that do not have contacts to the hydrogen of the OH group. This excludes carboxylic acid dimers, as shown above. The predominant hot-spot now corresponds to the anti conformation.

Again this is narrowed using Query 4, which removes almost all the syn examples.

Now using Query 3 (as shown above), which restricts the search to examples where the oxygen of the HO group is itself not in contact with an acidic hydrogen. This allows carboxylic acid dimers. This now reveals the syn preference again.

At <100K reinforces this effect.

Finally, Query 1 and NOT query 2 (no dimers) and NOT query 3, where a smaller preference for anti is seen.

So it seems that an interesting difference emerges between enols and carboxylic acids in that when no hydrogen bonding to the HO group is allowed, an anti preference emerges. The electronic origins of this effect will be probed in a future post.

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Cyclopropenium cyclopentadienide: a strangely neutral ion-pair?

Sunday, April 9th, 2017

Both the cyclopropenium cation and the cyclopentadienide anion are well-known 4n+2-type aromatic ions, but could the two together form an ion-pair?

A search of the Cambridge structure database reveals 52 instances of the cyclopropenium cation with a variety of counter-anions, 77 cyclopentadienide anions with a variety of counter-cations and one (SOWMOG, private communication to CSD) where the two sub-structures are common. The pyridinium-cyclopropenium fragment is actually a di-cation stabilized with dimethylamino substituents, with these charges balanced by two cyclopentadienide anions stabilized with ester substituents. The stacking distance between the ion-pairs is ~3.5-3.6Å, a bit larger than normal π-π stacking distances of 3.2-3.3Å

So could a “pure” cyclopropenium cyclopentadienide ion-pair exist, and if so what would its π-π stacking distance be? A ωB97XD/Def2-TZVPPD/SCRF=water calculation (DOI: 10.14469/hpc/2442) provides one answer to this question; 2.57Å!‡ It is a true minimum in the potential energy surface (all +ve force constants) with a calculated dipole moment of only 7.57D. This species is “only” 27.1 kcal/mol higher in ΔG than the neutral hydrocarbon (DOI: 10.14469/hpc/2443), a difference which is as low as it is because of the gain in aromatic stabilization of two rings upon ion-pair formation.

A few posts back, I was considering candidates for the most polar neutral compound synthesized and I suggested a candidate with a dipole moment of ~22D, based as it happens on cyclopropenium and cyclopentadienide rings directly connected by a bond. So when this bond is removed and the two rings are allowed to stack one above the other, we now have an interesting inversion of the original challenge: what is the least-polar ionic organic compound (ionic in the sense of being an unconnected ion-pair)?

Here are some more properties of this intriguing “neutral” ion-pair.

  1. It has a number of low-frequency modes with correspond to the two rings moving with respect to each other (ν 216 cm-1)
  2. The molecular electrostatic potential illustrates the sense of polarization, with negative region (orange) residing on the 5-membered ring:
  3. The most stable π-type molecular orbital (below) reminds of the π-complex formed in the benzidine rearrangement and that in fact modelling this ion-pair may require a multi-reference (CASSCF) wavefunction, with the single-determinantal one used here only being a first approximation.
  4. A QTAIM analysis of the electron density topology shows only weak “bond” connectors between the two rings, with ρ(r) being typical of weak interactions such as hydrogen bonds.
  5. An ELF (electron localisation function) analysis also holds no surprises, with all the electron density basins (purple) confined to the two rings, just as expected of an ion-pair.
  6. I will leave one further question to a future discussion; what happens to the aromaticity and ring currents of the two individual rings as they combine to form this ion-pair? Might this property be connected to the very close separation between the two rings?

So we have a remarkably “neutral” ionic hydrocarbon to match the “ionic” neutral organic molecules previously discussed. This ion-pair may yet prove to have interesting properties, even if is unlikely to be synthesized without the addition of stabilising substituents.

‡ For example, the stacking distance in graphite is 3.35Å.

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The conformation of enols: revealed and explained.

Thursday, April 6th, 2017

Enols are simple compounds with an OH group as a substituent on a C=C double bond and with a very distinct conformational preference for the OH group. Here I take a look at this preference as revealed by crystal structures, with the theoretical explanation.

First, a search of the Cambridge structure database (CDS), using the search query shown below (DOI: 10.14469/hpc/2429)


The first search (no errors, no disorder, R < 0.05) is unconstrained in the sense that the HO group is free to hydrogen bond itself. The syn conformer has the torsion of 0° and it has a distinct preponderance over the anti isomer (180°). There is the first hint that the most probable C=C distance for the syn isomer may be longer than that for the anti, but this is not yet entirely convincing.
To try to make it so, a constrained search is now performed, in which only structures where the HO group has no contact (hydrogen bonding) interaction are included. This is achieved using a “Boolean” search;

The number of hits approximately halves, but the proportion of syn examples increases considerably. There is an interesting double “hot-spot” distribution, which amplifies the lengthening of the C=C bond compared to the anti orientation.

The next constraint added is that the data collection must be <100K (to reduce thermal noise) which reduces the hits considerably but now shows the lengthening of the C=C bond for the syn isomer very clearly.

A final plot is of the C=C length vs the C-O length (no temperature, but HO interaction constraint). If there were no correlation, the distribution would be ~circular. In fact it clearly shows that as the C=C bond lengthens, the C-O bond contracts.

Now for some calculations (ωB97XD/Def2-TZVPP, DOI: 10.14469/hpc/2429) which reveal the following:

  1. The free energy of the syn isomer is 1.2 kcal/mol lower than that of the syn. The effect is small, and hence easily masked by other interactions such as hydrogen bonding to the OH group. Hence the reason why removing such interactions from the search above increased the syn population compared to anti.
  2. The syn C=C bond length (1.325Å) is longer than the anti (1.322Å). 
  3. The syn isomer has one unique σO-Lp/σ*C-C NBO orbital interaction (below) with a value of E(2) 7.7 kcal/mol, which is absent in the anti form. As it happens, a πO/π*C=C interaction is present in both forms but is also stronger in the syn isomer (E(2)= 46.8 vs 44.2 kcal/mol).
    unoccupied NBO, σ*C-C
    Occupied NBO, σO-Lp
  4. The overlap of the filled σO-Lp with the empty σ*C-C orbital is shown below (blue overlaps with purple, red overlaps with orange).

    To view the overlap in rotatable 3D, click on any of the colour diagrams above.‡

It is nice to see how experiment (crystal structures) and theory (the calculation of geometries and orbital interactions) can quickly and simply be reconciled. Both these searches and the calculations can be done in just one day of “laboratory time” and I think it would make for an interesting undergraduate chemistry lab experiment.

‡ This visualisation uses Java. Increasingly this browser plugin is becoming more onerous to activate (because of increased security) and some browsers do not support it at all. The macOS Safari browser is one that still does, but you do have to allow it via the security permissions.

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What is the (calculated) structure of a norbornyl cation anion-pair in water?

Saturday, April 1st, 2017

In a comment appended to an earlier post, I mused about the magnitude of the force constant relating to the interconversion between a classical and a non-classical structure for the norbornyl cation. Most calculations indicate the force constant for an “isolated” symmetrical cation is +ve, which means it is a true minimum and not a transition state for a [1,2] shift. The latter would have been required if the species equilibrated between two classical carbocations. I then pondered what might happen to both the magnitude and the sign of this force constant if various layers of solvation and eventually a counter-ion were to be applied to the molecule, so that a bridge of sorts between the different states of solid crystals, superacid and aqueous solutions might be built.

I augmented the model in stages. The results are summarised in the table below.

  • Firstly, adding a self-consistent-reaction-field (SCRF) continuum model for water.
  • Then adding to that four explicit water molecules symmetrically arranged around the four C-H groups mostly likely to be solvated via hydrogen bonds.
  • The final model added a chloride anion to complete the ion pair and a further three water molecules to act as its solvation sphere. A search of the Cambridge structure database for any instances of a molecule with a designated C+ and a nucleophilic halide– with zero coordination number (a free halide anion) reveals no hits; such ion-pairs are clearly very unstable towards covalent bond formation, existing if at all only as transient species or when the counter-ion is non-nucleophilic such as R4B–.
Calculated geometries, Def2-TZVPP/SCRF=water

Model

Apical C-C

distance,Å

Basal C-C

distance,Å

ν [1,2]

cm-1

 DataDOI
Vacuum, cation
B3LYP+D3BJ		 1.888 1.388 +140 10.14469/hpc/2410
Vacuum, cation
ωB97XD		 1.830 1.388 +235 10.14469/hpc/2409
Vacuum, cation
B2PLYPD3		 1.872 1.390 +194 10.14469/hpc/2238
SCRF, cation
ωB97XD		 1.819 1.387 +236 10.14469/hpc/2413
SCRF, cation
B2PLYPD3		 1.858 1.388 +202 10.14469/hpc/2243
SCRF+4H2O, cation
B2PLYPD3		 1.838 1.390 +254 10.14469/hpc/2246
SCRF+7H2O+Cl– ion pair
B3LYP+D3BJ		 1.593, 2.485 1.510 – 10.14469/hpc/2408
SCRF+7H2O+Cl– ion pair
ωB97XD		 1.795, 1.817 1.385 +249 10.14469/hpc/2411

As the solvation and environment of the cationic model improves, the apical distance shortens significantly. But the crunch comes when a chloride counter-anion is added to desymmetrise this environment. Using the veritable B3LYP functional, but with an added dispersion term (D3BJ) and starting from a partially optimised ion-pair geometry, this geometry optimisation (shown animated below) rapidly quenches the ion-pair to form a covalent norbornyl chloride. It is noteworthy that the magnitude of the [1,2] vibration force constant (140 cm-1) is rather smaller using B3LYP than the other methods explored. 

The next method tried was ωB97XD, which contains a built-in dispersion term (D2) and also reveals a larger force constant for the gas phase [1,2] shift (≡235 cm-1). Starting from the same initial geometry as the B3LYP calculation, optimisation of the ion-pair proceeds remarkably slowly‡ (even using the recalcfc=5 keyword to recompute the force constant matrix/search direction every five cycles to improve behaviour), suggesting that the potential energy surface is very flat indeed. The final geometry retains the ion-pair character (dipole moment 23D) but reveals distinct asymmetry in the resulting bridged structure, for which the [1,2] shift is ν 249 cm-1.

It is clear that the structure of the norbornyl ion-pair is balanced on a knife-edge. Perturbations such as change of density functional (e.g. B3LYP+D3BJ) can topple it over that edge. Weaker asymmetry can also be induced by the presence of the contact-anion and water molecules. I have selected just one solvation model, which includes seven water molecules and an explicit anion. Clearly a more statistical and dynamical approach to the number of waters and their orientation around the norbornyl ring system would sample a much larger set of models. It may be that some of them do again topple the symmetric bridge structure off its delicate perch whilst others retain it. Perhaps this is why the results from the enormous range of solvolysis mechanisms are so difficult to always reconcile. A crystal structure may also be a relatively large perturbation to the solution structure of this species!

The title of one of the last articles published (posthumously) with Paul Schleyer as a co-author[1] is “Norbornyl Cation Isomers Still Fascinate“. True indeed.

‡This renders refinement using the B2PLYPD3 double-hybrid method[2] an exceptionally slow process, since computing the force constant matrix using this method is very computationally intensive at the selected triple-ζ level.

References

  1. P.V.R. Schleyer, V.V. Mainz, and E.T. Strom, "Norbornyl Cation Isomers Still Fascinate", ACS Symposium Series, pp. 139-168, 2015. https://doi.org/10.1021/bk-2015-1209.ch007
  2. L. Goerigk, and S. Grimme, "Efficient and Accurate Double-Hybrid-Meta-GGA Density Functionals—Evaluation with the Extended GMTKN30 Database for General Main Group Thermochemistry, Kinetics, and Noncovalent Interactions", Journal of Chemical Theory and Computation, vol. 7, pp. 291-309, 2010. https://doi.org/10.1021/ct100466k

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