Natural abundance kinetic isotope effects: mechanism of the Baeyer-Villiger reaction.

June 10th, 2015

I have blogged before about the mechanism of this classical oxidation reaction. Here I further explore computed models, and whether they match the observed kinetic isotope effects (KIE) obtained using the natural-abundance method described in the previous post.

BV

There is much previous study of this rearrangement, and the issue can be reduced to deciding whether TS1 or TS2 is rate-limiting. The conventional text-book wisdom is that the carbon migration step TS2 is the “rds” and it was therefore quite a surprise when Singleton and Szymanski[1] obtained KIE which seemed to clearly point instead to TS1 as being rate limiting, inferred from a large 13C effect (~1.05) at the carbonyl carbon (blue star) and none at the α-carbon (red star). This result (for this specific reaction and conditions, which is dichloromethane as solvent) is now routinely quoted[2] when the mechanism is discussed. This latter article reports[2] calculated energetics for TS1 and TS2 (see Table 1 in this article) and after exploring various models, the conclusion is that TS1 and TS2 are essentially isoenergic. However, no isotope effects are computed for their models, and so we do not know if TS1 or TS2 agrees better with the reported values.[2] Since I had managed to get pretty good agreement with experimental KIEs using the ωB97XD/Def2-TZVPP/SCRF=xylenes model for the Diels-Alder reaction, I thought I would try the same method to see how it performs for the Baeyer-Villiger.

It is in fact non-trivial to set up a consistent model. Using arrow pushing, one can on paper draw three variations for TS1, the formation of the peroxyhemiacetal tetrahedral intermediate (TI) and also often called the Criegee intermediate.

BV2

  1. TS1a is the “text-book” variation, involving the production of a zwitterionic intermediate which immediately undergoes a proton transfer (PT). The arrows tend not to be used for this last step, since the direct transfer would involve a 4-membered ring and a highly non-linear geometry at the transferring proton which is understood to be “unfavourable”. Such zwitterions involve a large degree of charge separation and hence a large dipole moment. In a non-protic solvent such as dichloromethane, one is very loath to use such species in a mechanism, and it’s not modelled here either.
  2. Using just cyclohexanone and peracid, it is in fact difficult to avoid ionic species. TS1b is an attempt which shows the proton transfer is done first on the peracid to create a so-called carbonyl ylid, and this then reacts with the ketone
  3. If however a proton transfer agent is introduced as TS1c, one can use this species (shown in red above) to transfer the proton as part of a concerted mechanism; this was in fact the expedient used in the earlier theoretical study[2] and this route tends to avoid much if not all of the charge separation. The acid comes from the product of the reaction, and hence the kinetics may in fact have an induction period when this acid builds up. The initial proton transfer reagent may also be traces of water present in reagents or solvent. Singleton and Szymanski in fact include no supporting information in their article and so we do not know what the concentrations used were (assumed for the present discussion as 1M) whether everything was rigorously dried, or indeed what the kinetic order in [peracid] turned out to be.

The same problem is faced with TS2; how to transfer a proton? Because we want to compare the relative energies of TS1 and TS2, we also have to atom-balance the mechanism, and so the additional acid component introduced into TS1c is also retained in two alternative mechanisms for TS2 (and for TS1b).

BV3

  1. TS2a uses just the components of the tetrahedral intermediate (TI), but again in a fashion that requires no charge separation during the reaction. The additional acid component (red) plays a passive role, hydrogen bonding to the TI.
  2. TS2b now incorporates the additional acid by expanding the ring (green) in an active role.

IRCs using the 6-311G(d,p) basis) for TS1[3] and TS2[4] are interesting in revealing relative synchronicity of the proton transfers for TS1 but asynchronicity for TS2 involving a hidden intermediate.
BV1a

BV2a

The energy, energy gradient and dipole moment magnitudes for this second step are particularly fascinating. The dipole moment starts off quite small (3.1D) at the TI, and is still so at the TS, but almost immediately afterwards, it shoots up to ~12D as the hidden intermediate develops (IRC ~4) Two successive proton transfers (IRC ~6, 7) then reduce the value down again.
BV2E
BV2G
BV2D

A table of results can now be constructed for these various models, evaluating two different basis sets for the calculation.

system ΔΔG298 (1M)
ωB97XD/6-311G(d,p)/SCRF=DCM, kcal/mol		 Dipolemoment,D ΔG298 (1M)
ωB97XD/Def2-TZVPP/SCRF=DCM
Reactants +1.4a – -3.3a[5],[6],[7]
Complexed state 0.0[8] 5.0 0.0[9]
TS1a n/a n/a n/a
TS1b 32.9[10] 8.6 32.2[11]
TS1c 14.9[12] 3.0 16.1[13]
TI -1.7[14] 3.1 -0.3[15]
TS2a 22.2[16] 9.3 25.0[17]
TS2b 20.2[12] 5.4 22.7[18]
Product -69.8[19] 5.3 [20]

aThis value is corrected to a standard state of 1M for a termolecular reaction by 3.78 kcal/mol from the computed free energies at 1 atm as described previously.[21]

  1. Firstly, one must note that the resting state for the reactants depends on the concentration. At 1M at the higher basis set, its the separated reactants, but at the lower it is the hydrogen bonded complex between them. Increasing the concentration would favour the latter.
  2. TS1c is significantly lower in free energy than TS2b, a result somewhat at variance with the earlier report.[2] The functional used in the present calculation, the basis set, the dispersion model and the solvation model are all improvements on the original work.
  3. Likewise, the energy of TI, the Criegee intermediate emerges as similar to the reactants. Coupled with the magnitude of the barrier for TS1c this does tend to point to a relatively rapid pre-equilibrium and that TS2b determines the rate of reaction.

Kinetic isotope effects for our models

Having constructed models, we can now subject them to testing against the measured kinetic isotope effects.[1]

bv4

  1. The measured values are shown above. The first set (a) are what are described as intermolecular isotope effects and result from measuring changes in the isotopic abundance obtained by recovering unreacted starting material after a large proportion of the reaction has gone to completion. This was interpreted as indicating TS1 was rate limiting. Using instead the uncomplexed cyclohexanone has only a small effect (C1: 1.023 complexed, 1.021 uncomplexed).
  2. The values in parentheses were obtained using the TS1c model above and are relative to the complexed reactant involving hydrogen bonds between the cyclohexanone, the peracid and the acid catalyst. The agreement can only be described as partial.
    •  The predicted 13C isotope effect at C1 is about half of the measured value. The previous calibration of the method being used had resulted in agreement within experimental error for the Diels Alder reaction, and so this large disagreement is unexpected.
    • The 2H KIE at C2 is within experimental error.
    • The  2H KIE at C3 is badly out. Here, it is the experimental result that seems wrong, since there is no reason to expect any KIE at this position especially since the 13C at the same position is 1.00 for both measured and calculated values.
  3. So we might infer an inconclusive result. I can only speculate on the computed model here, and invoke in effect the variation principle. If the model is wrong, we would expect a more correct model to have a lower rather than higher energy relative to reactants. The free energy of activation however is already low, corresponding to a very fast room temperature reaction; too fast indeed to easily recover any unreacted starting material if that were to be rate limiting!
  4. Set (b) corresponds to what is described as an intramolecular KIE as defined by TS2, since it is measured from isotopic ratio changes in the product rather than reactant as the reaction progresses.
    • The value in (…) is relative to the complexed reactants and the value in […] is relative to TI.
    • The predicted 13C isotope effect at C2m (the migrating carbon) agrees within experimental error with the measured value if the TI is used as the reference. This nicely shows how isotope effects for what may not be a rate limiting step can be measured by this technique.
    • The predicted 13C isotope effect at C1 (which is not reported in the original article) relative to TI is significant, and it would be nice to confirm the computed model by a measurement at this position.
    • The other KIE also agree reasonably with experiment when TI is specified as the reactant for this step.

So is there support from the calculations for the formation of the semi-peroxyacetal being rate limiting, as claimed by Singleton and Szymanski[1]? There is no doubt that the KIE obtained from measuring the product is different from measuring the reactant, but the lack of agreement for two of the measured values for TS1 is a concern. Perhaps one might conclude that this is an experiment well worth repeating. Of the two computed models, TS1 and TS2, the variation principle would again lead us to suspecting that the one with higher energy can only be decreased by improvement, whereas improvement of the one with the lower energy cannot also increase its relative energy. So if a new model for the carbon migration step can be found, its activation free energy must be lower than that already identified. But the excellent agreement between TS2b shown in (b) suggests that this model is already pretty good! Lowering its energy by >7kcal/mol to make TS1 rate limiting would probably require quite a different model.

What I think is more certain is the value of subjecting the measured KIE to computed models, in the knowledge that if the model is indeed realistic a good agreement should be expected. And it is a shame that the natural abundance KIE method cannot be applied to oxygen isotope effects, which would surely settle the issue.‡ And I should end by reminding that there is evidence that the mechanism may be quite sensitive to variation of solvent, ketone, peracid, pH, etc, and so these conclusions only apply to this specific reaction in  dichloromethane.

‡ For TI > TS2, the 18O KIE is predicted as 1.048 (peroxy oxygen) and 1.032 (acyl oxygen). For Reactant > TS1, the values are respectively 0.998 and 1.003.

References

  1. D.A. Singleton, and M.J. Szymanski, "Simultaneous Determination of Intermolecular and Intramolecular <sup>13</sup>C and <sup>2</sup>H Kinetic Isotope Effects at Natural Abundance", Journal of the American Chemical Society, vol. 121, pp. 9455-9456, 1999. https://doi.org/10.1021/ja992016z
  2. J.R. Alvarez-Idaboy, and L. Reyes, "Reinvestigating the Role of Multiple Hydrogen Transfers in Baeyer−Villiger Reactions", The Journal of Organic Chemistry, vol. 72, pp. 6580-6583, 2007. https://doi.org/10.1021/jo070956t
  3. H.S. Rzepa, "C20H20Cl2O6", 2015. https://doi.org/10.14469/ch/191318
  4. H.S. Rzepa, "C20H20Cl2O6", 2015. https://doi.org/10.14469/ch/191317
  5. H.S. Rzepa, "C 7 H 5 Cl 1 O 2", 2015. https://doi.org/10.14469/ch/191322
  6. H.S. Rzepa, "C 7 H 5 Cl 1 O 3", 2015. https://doi.org/10.14469/ch/191323
  7. H.S. Rzepa, "C 6 H 10 O 1", 2015. https://doi.org/10.14469/ch/191324
  8. H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191307
  9. H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191315
  10. H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191313
  11. H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191325
  12. H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191306
  13. H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191312
  14. H.S. Rzepa, "C20H20Cl2O6", 2015. https://doi.org/10.14469/ch/191311
  15. H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191319
  16. H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191314
  17. H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191321
  18. H.S. Rzepa, and H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191320
  19. H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191310
  20. H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191327
  21. J.R. Alvarez-Idaboy, L. Reyes, and J. Cruz, "A New Specific Mechanism for the Acid Catalysis of the Addition Step in the Baeyer−Villiger Rearrangement", Organic Letters, vol. 8, pp. 1763-1765, 2006. https://doi.org/10.1021/ol060261z

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Natural abundance kinetic isotope effects: expt. vs theory.

June 3rd, 2015

My PhD thesis involved determining kinetic isotope effects (KIE) for aromatic electrophilic substitution reactions in an effort to learn more about the nature of the transition states involved.[1] I learnt relatively little, mostly because a transition state geometry is defined by 3N-6 variables (N = number of atoms) and its force constants by even more and you get only one or two measured KIE per reaction; a rather under-defined problem in terms of data! So I decided to spend a PostDoc learning how to invert the problem by computing the anticipated isotope effects using quantum mechanics and then comparing the predictions with measured KIE.[2] Although such computation allows access to ALL possible isotope effects, the problem is still under-defined because of the lack of measured KIE to compare the predictions with. In 1995 Dan Singleton and Allen Thomas reported an elegant strategy to this very problem by proposing a remarkably simple method for obtaining KIE using natural isotopic abundances.[3] It allows isotope effects to be measured for all the positions in one of the reactant molecules by running the reaction close to completion and then recovering unreacted reactant and measuring the changes in its isotope abundances using NMR. The method has since been widely applied[4],[5] and improved.[6] Here I explore how measured and calculated KIE can be reconciled.

The original example uses the Diels-Alder cycloaddition as an example, with the 2-methylbutadiene component being subjected to the isotopic abundance. Although comparison with calculation on related systems was done at the time[7] the computational methods in use then did not allow effects such as solvation to be included. I thought it might be worth re-investigating this specific reaction using more modern methodology (ωB97XD/Def2-TZVPP/SCRF=xylenes), giving an opportunity for testing one key assumption made by Singleton and Allen, viz the use of an internal isotope reference for a site where the KIE is assumed to be exactly 1.000 (the 2-methyl group in this instance). This assumption made me recollect my post on how methyl groups might not be entirely passive by rotating (methyl “flags”) in the Diels-Alder reaction between cis-butene and 1,4-dimethylbutadiene. I had concluded that post by remarking that Rotating methyl groups should be looked at more often as harbingers of interesting effects, which in this context may mean that such rotations may not be entirely isotope agnostic.

DA

To start, I note that the endo (closed shell, i.e. non-biradical; the wavefunction is STABLE to open shell solutions) transition state obtained for this reaction[8],[9] has a computed dipole moment of 6.1D, just verging into the region where solvation starts to make an impact. Perhaps the most important conclusion drawn from Singleton and Allen’s original article[2] was that the presence of an apparently innocuous 2-methyl substituent is sufficient to render the reaction asynchronous, which means that one C-C bond forms faster than the other. They drew this conclusion from observing that the inverse deuterium isotope effect was larger at C1 than C4, the difference being well outside of their estimated errors. The calculations indicate that the two bonds have predicted lengths of 2.197 (to C1) and 2.294Å (to C4) at the transition state. This means that an asynchronicity as small as Δ0.1Å can be picked up in measured isotope effects!

The calculated activation free energy is 19.2 kcal/mol (0.044M), which is entirely reasonable for a reaction occurring slowly at room temperature. The barrier for the exo isomer is 21.0 kcal/mol, 1.8 kcal/mol higher in free energy.† The measured isotope effects are shown below with the predicted values in brackets. The colour code is green=within the estimated experimental error, red=outside the error.

DA1

The following observations can be made:

  1. The internal isotope reference assumed as 1.000 is reasonable for carbon, but the “rotating methyl groups” resulting from hyper conjugation between the C-H groups and the π system do have a small effect resulting in a predicted KIE of 0.996 rather than the assumed 1.000. This will impact upon all the other measured values to some extent.
  2. All the predicted‡ 13C isotope effects agree with experiment within the error estimated for the latter. The calculation also has its errors, of which the most obvious is that harmonic frequencies are used rather than the more correct anharmonic values.
  3. The 2H isotope effects show more deviation. This might be a combination of the assumption that the internal Me reference has no isotope effect coupled with the use of harmonic frequencies for the calculation.
  4. Although the 2H values differ somewhat beyond the experimental error, the E/Z effects are well reproduced by calculation. The inverse isotope effect for the (Z) configuration is significantly larger in magnitude than for the (E) form, as was indeed noted by Singleton and Thomas.
  5. So too is the asymmetry induced by the methyl group. The inverse isotope effects are greater for the more completely formed bond (to C1) than for the lagging bond (to C4). They are indeed a very sensitive measure of reaction synchronicity.

The pretty good agreement between calculation and experiment provides considerable reassurance that the calculated properties of transition states can indeed be subjected to reality checks using experiment. Indeed, it takes little more than a day to compute a complete set of KIEs, far less than it takes to measure them. One could easily argue that such a computation should accompany measured KIE whenever possible.

‡This gives me an opportunity to extol the virtues of effective RDM (research data management). The two DOIs for the data include files containing the full coordinates and force constant matrices for both reactant and TS. Using these, one can obtain frequencies for any isotopic substitution you might wish to make in <1 second each, and hence isotope effects not computed here. One option might be to e.g. invert the reactant from the 2-methylbutadiene to the maleic anhydride and hence compute the isotope effects expected on this species (not reported in the original article) or to monitor instead the product.[10]

†The KIE have only subtle small differences to the endo isomer; too small to assign the stereochemistry with certainty.

References

  1. B.C. Challis, and H.S. Rzepa, "The mechanism of diazo-coupling to indoles and the effect of steric hindrance on the rate-limiting step", Journal of the Chemical Society, Perkin Transactions 2, pp. 1209, 1975. https://doi.org/10.1039/p29750001209
  2. M.J.S. Dewar, S. Olivella, and H.S. Rzepa, "Ground states of molecules. 49. MINDO/3 study of the retro-Diels-Alder reaction of cyclohexene", Journal of the American Chemical Society, vol. 100, pp. 5650-5659, 1978. https://doi.org/10.1021/ja00486a013
  3. D.A. Singleton, and A.A. Thomas, "High-Precision Simultaneous Determination of Multiple Small Kinetic Isotope Effects at Natural Abundance", Journal of the American Chemical Society, vol. 117, pp. 9357-9358, 1995. https://doi.org/10.1021/ja00141a030
  4. https://doi.org/
  5. Y. Wu, R.P. Singh, and L. Deng, "Asymmetric Olefin Isomerization of Butenolides via Proton Transfer Catalysis by an Organic Molecule", Journal of the American Chemical Society, vol. 133, pp. 12458-12461, 2011. https://doi.org/10.1021/ja205674x
  6. J. Chan, A.R. Lewis, M. Gilbert, M. Karwaski, and A.J. Bennet, "A direct NMR method for the measurement of competitive kinetic isotope effects", Nature Chemical Biology, vol. 6, pp. 405-407, 2010. https://doi.org/10.1038/nchembio.352
  7. J.W. Storer, L. Raimondi, and K.N. Houk, "Theoretical Secondary Kinetic Isotope Effects and the Interpretation of Transition State Geometries. 2. The Diels-Alder Reaction Transition State Geometry", Journal of the American Chemical Society, vol. 116, pp. 9675-9683, 1994. https://doi.org/10.1021/ja00100a037
  8. H.S. Rzepa, "C 9 H 10 O 3", 2015. https://doi.org/10.14469/ch/191299
  9. H.S. Rzepa, "C 9 H 10 O 3", 2015. https://doi.org/10.14469/ch/191301
  10. D.E. Frantz, D.A. Singleton, and J.P. Snyder, "<sup>13</sup>C Kinetic Isotope Effects for the Addition of Lithium Dibutylcuprate to Cyclohexenone. Reductive Elimination Is Rate-Determining", Journal of the American Chemical Society, vol. 119, pp. 3383-3384, 1997. https://doi.org/10.1021/ja9636348

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Discovering chemical concepts from crystal structure statistics: The Jahn-Teller effect

May 30th, 2015

I am on a mission to persuade my colleagues that the statistical analysis of crystal structures is a useful teaching tool.  One colleague asked for a demonstration and suggested exploring the classical Jahn-Teller effect (thanks Milo!). This is a geometrical distortion associated with certain molecular electronic configurations, of which the best example is illustrated by octahedral copper complexes which have a d9 electronic configuration. The eg level shown below is occupied by three electrons and which can therefore distort in one of two ways to eliminate the eg degeneracy by placing the odd electron into either a x2-y2 or a z2 orbital. Here I explore how this effect can be teased out of crystal structures.

JT

The search is set up with Cu specified as precisely 6-coordinate, and X=oxygen. The six X-Cu distances are defined as DIST1-DIST6. The R-factor is specified as < 0.05 (no disorder, no errors). The problem now is how to plot what is in effect a six-dimensional set of data, from which we are exploring whether four of the distances are different from the other two, and whether those four are the longer or the shorter. This requires analysis beyond the capability (as far as I know) of the Conquest program, and so here I will show sets of plots showing just the relationship between any two distances at a time. Of the 15 possible combinations of two distances, only four are shown below.

Some obvious patterns can already be spotted in the 400 or so compounds which satisfy the search criteria.

  • The largest clustering occurs at ~1.95Å, with two clusters each of fewer hits at ~2.5Å. The Wikipedia page notes that for Cu(OH2)6 the Jahn-Teller distortion favours four short bonds at ~1.95Å and two long ones at ~2.38Å, which agrees approximately with the positions and sizes of the centroids of these clusters.†
  • Plots 1 and 2 show very little along the diagonals, where the two plotted distances have the same value. This probably means that one of the distances relates to an equatorial ligand and the other to an axial ligand.
  • Plots 3 and 4 show a strong diagonal trend, and so these distances both relate to either axial or equatorial, but not one of each.
  • All four plots show a hot spot at ~1.95Å, which hints that the Jahn-Teller distortion is four short bonds/two long.
  • Plot 4 also shows a green spot at ~2.5Å which is a tantalising suggestion of examples of four long bonds/two short.‡
  1. CuO-12
  2. CuO-34
  3. CuO-56
  4. CuO-13

Clearly this analysis can be followed up by a visual inspection of individual molecules in each cluster (as well as the outliers which appear to follow no pattern!), together with a more bespoke analysis of the six distances. Unfortunately, the spin state of the complexes cannot be quickly checked (are they all doublets?) since the database does not record these.  But the basic search described above takes only a few minutes to do, and it is surprising at how quickly the Jahn-Teller effect can be statistically tested with real experimental data obtained for ~400 molecules. Of course, here I have only explored X=O but this can easily be extended to X=N or X=Cl, to other metals or to alternative coordination numbers such as e.g. 4 where the Jahn-Teller effect can also in principle operate.

‡ One genuine example of this type, also called compressed octahedral coordination, was reported for the species CuFAsF6 and CsCuAlF6[1]

† The measured geometry of Cu(H2O)6 may in fact manifest with six equal Cu-O bond lengths due to the dynamic Jahn-Teller effect, because the kinetic barrier separating one Jahn-Teller distorted form and another (equivalent) isomer is small and hence averaged atom positions are measured which mask the effect. Thus the Jahn-Teller effects shown in the plots above may be under-estimated because of this dynamic masking. Reducing the temperature of the sample at which data was collected would reduce this dynamic effect. Indeed, Cu(D2O)6 collected at 93K shows a very clear Jahn-Teller distortion[2] with four long bonds ranging from 1.97-1.99Å and two long bonds 2.37-2.39Å.[3] Another example measured at 89K with dimethyl formamide replacing water and coordinated via oxygen[4] shows four short (1.97-1.98Å) and two long (2.315Å) bonds. This latter example is also noteworthy because this analysis is as yet unpublished in a journal, but the data itself has a DOI via which it can be acquired. A nice example of modern research data management!

References

  1. Z. Mazej, I. Arčon, P. Benkič, A. Kodre, and A. Tressaud, "Compressed Octahedral Coordination in Chain Compounds Containing Divalent Copper: Structure and Magnetic Properties of CuFAsF<sub>6</sub> and CsCuAlF<sub>6</sub>", Chemistry – A European Journal, vol. 10, pp. 5052-5058, 2004. https://doi.org/10.1002/chem.200400397
  2. W. Zhang, L. Chen, R. Xiong, T. Nakamura, and S.D. Huang, "New Ferroelectrics Based on Divalent Metal Ion Alum", Journal of the American Chemical Society, vol. 131, pp. 12544-12545, 2009. https://doi.org/10.1021/ja905399x
  3. Zhang, Wen., Chen, Li-Zhuang., Xiong, Ren-Gen., Nakamura, T.., and Huang, S.D.., "CCDC 755150: Experimental Crystal Structure Determination", 2010. https://doi.org/10.5517/cctbspl
  4. M.M. Olmstead, D.S. Marlin, and P.K. Mascharak, "CCDC 1053817: Experimental Crystal Structure Determination", 2015. https://doi.org/10.5517/cc14cl36

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R-X≡X-R: G. N. Lewis’ 100 year old idea.

May 22nd, 2015

As I have noted elsewhere, Gilbert N. Lewis wrote a famous paper entitled “the atom and the molecule“, the centenary of which is coming up.[1] In a short and rarely commented upon remark, he speculates about the shared electron pair structure of acetylene,  R-X≡X-R (R=H, X=C). It could, he suggests, take up three forms. H-C:::C-H and two more which I show as he drew them. The first of these would now be called a bis-carbene and the second a biradical.

In 1916, it was too early for Lewis to speculate what the geometries of such species might be, and in particular the C…C (or generalising, X…X) distance, and the two angles, one for each X. Well, we do not need to speculate, we can perform a search of the crystal structure database. Here it is (R < 0.05, no errors, no disorder):

Lewis-CC4

A little more explanation of this 4-dimensional plot is needed:

  1. The two angles are plotted as X and Y.
  2. The X…X distance is plotted as colour, with red representing the longest distances and blue the shortest
  3. The size of each “bin” is represented by the radius of the circle; small circles represent few examples, larger circles represent more examples in each “bin” defined by a regular range of angles.

There are one or two off-diagonal  “outliers”, each of which probably deserves individual inspection. But dealing just with the obvious clusters, the overwhelmingly largest is for both angles of ~180°, and these are the triple bonds we know and love. As far as I know, Lewis was the first to propose a triple bond between two atoms, but if anyone reading this blog knows of an antecedent, do let me know. The next cluster is for angles of ~109° and these are clearly bis-carbenes. These all occur when X ≠ C. There are two small clusters worthy of note; one ~130° and one ~90°. The latter are mostly Pb-Pb and Sn-Sn, where the bonding is unhybridised pure p.

One of the limitations of searching for crystal structures is that the spin state of each molecule is never given. The biradical structure given by Lewis could well have a triplet ground state, and perhaps that might have very characteristic angles (~130° ?). It would be great to identify a genuine example of this biradical form!

As usual, the search itself took around 10 minutes, and it provides much interesting food for thought; not bad for a 100-year-old idea!

 

References

  1. G.N. Lewis, "THE ATOM AND THE MOLECULE.", Journal of the American Chemical Society, vol. 38, pp. 762-785, 1916. https://doi.org/10.1021/ja02261a002

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R-X≡X-R: G. N. Lewis' 100 year old idea.

May 22nd, 2015

As I have noted elsewhere, Gilbert N. Lewis wrote a famous paper entitled “the atom and the molecule“, the centenary of which is coming up.[1] In a short and rarely commented upon remark, he speculates about the shared electron pair structure of acetylene,  R-X≡X-R (R=H, X=C). It could, he suggests, take up three forms. H-C:::C-H and two more which I show as he drew them. The first of these would now be called a bis-carbene and the second a biradical.

In 1916, it was too early for Lewis to speculate what the geometries of such species might be, and in particular the C…C (or generalising, X…X) distance, and the two angles, one for each X. Well, we do not need to speculate, we can perform a search of the crystal structure database. Here it is (R < 0.05, no errors, no disorder):

Lewis-CC4

A little more explanation of this 4-dimensional plot is needed:

  1. The two angles are plotted as X and Y.
  2. The X…X distance is plotted as colour, with red representing the longest distances and blue the shortest
  3. The size of each “bin” is represented by the radius of the circle; small circles represent few examples, larger circles represent more examples in each “bin” defined by a regular range of angles.

There are one or two off-diagonal  “outliers”, each of which probably deserves individual inspection. But dealing just with the obvious clusters, the overwhelmingly largest is for both angles of ~180°, and these are the triple bonds we know and love. As far as I know, Lewis was the first to propose a triple bond between two atoms, but if anyone reading this blog knows of an antecedent, do let me know. The next cluster is for angles of ~109° and these are clearly bis-carbenes. These all occur when X ≠ C. There are two small clusters worthy of note; one ~130° and one ~90°. The latter are mostly Pb-Pb and Sn-Sn, where the bonding is unhybridised pure p.

One of the limitations of searching for crystal structures is that the spin state of each molecule is never given. The biradical structure given by Lewis could well have a triplet ground state, and perhaps that might have very characteristic angles (~130° ?). It would be great to identify a genuine example of this biradical form!

As usual, the search itself took around 10 minutes, and it provides much interesting food for thought; not bad for a 100-year-old idea!

 

References

  1. G.N. Lewis, "THE ATOM AND THE MOLECULE.", Journal of the American Chemical Society, vol. 38, pp. 762-785, 1916. https://doi.org/10.1021/ja02261a002

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Posted in Chemical IT, Historical, Interesting chemistry | 1 Comment »

Impact factors, journals and blogs: a modern distortion.

May 21st, 2015

A lunchtime conversation with a colleague had us both bemoaning the distorting influence on chemistry of bibliometrics, h-indices and journal impact factors, all very much a modern phenomenon of scientific publishing. Young academics on a promotion fast-track for example are apparently advised not to publish in a well-known journal devoted to organic chemistry because of its apparently “low” impact factor. Chris suggested that the real reason the impact factor was “low” is that this particular journal concentrates on full articles, which for a subject area such as organic chemistry can take years to assemble and hence years for others to assimilate and report their own results, and only then creating a citation for the first article. So this slow but steady evolution of citations in a long time frame apparently shows such a journal up as having less (short-term) impact than the fast-publishing notes-type variety where the impact is immediate but possibly less long-lived. That would be no reason of itself not to publish there of course!

Most would describe a blog as an ultimate medium for short-term publishing (shortened only by e.g.  Twitter). I began to wonder what the statistics for this particular blog would show. So I looked at the time lines for the five most read posts, ranked below in terms of total hits. The oldest (and second most popular) is exactly six years old and so represents a reasonably long evolutionary time frame. The graphs below show the daily hits (red bars are annual). The immediate impact of each lasts less than a week, but the long-term analysis shows each accumulated their totals not by such immediate impact but by long-term accretion. For most, the first derivatives are still on the increase. This might all come as a surprise to those who tend to regard scientific blogs as having only short-term impact. But it would also be true to say that chemistry operates not on a time scale of days or years but of centuries, and so it will take a little while longer to assess impacts on that scale.
post-5114
post-439post-7779post-9606post-10937

What of course is not measured by simply integrating total views over time is what purpose if any each viewing serves. This is as true of journal articles as it is of blogs. And a viewing is not quite the same as a citation (although the latter does not always imply a viewing!). But it is tempting to conclude that we have all become far too fixated on short-term impacts and the bibliometrics that provide this information.

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The Bürgi–Dunitz angle revisited: a mystery?

May 12th, 2015

The Bürgi–Dunitz angle is one of those memes that most students of organic chemistry remember. It hypothesizes the geometry of attack of a nucleophile on a trigonal unsaturated (sp2) carbon in a molecule such as ketone, aldehyde, ester, and amide carbonyl. Its value obviously depends on the exact system, but is generally taken to be in the range 105-107°. A very good test of this approach is to search the crystal structure database (this was how it was originally established[1]).

search-BDThe search is defined as follows

  1. R can be either H or C
  2. The carbon is constrained to 3-coordinate
  3. The carbonyl oxygen is constrained to 1-coordinate
  4. QA can be any of N, O, S, Cl, F.
  5. QB can be any of H (aldehyde), C (ketone), N (amide), O (ester) or S (thioester).
  6. The distance QA…C is constrained to any intermolecular non-bonded contact ≤ the sum of the van der Waals radii of the two atoms involved and the angle QA…C=O is the Bürgi–Dunitz angle.
  7. I have also added a torsion constraint to specify that Nu has got to be ± 20° from orthogonality to the plane of the carbonyl to allow it to attack the π* orbital.
  8. The crystallographic R factor must be < 0.05, no disorder, no crystallographic errors and the temperature is either any or < 120K.

With no temperature specified, 6994 hits are obtained as below. So the most probable angle (red spot) is ~90°.

BD

One important change to the search is to decrease the temperature to 120K, since structures will have less vibrational noise. The number of hits decreases to 1279, but the most probable angle if anything reduces slightly.

BD-120K

So we have something of a mystery; this crystallographic data shows an angle of approach about 15° less than the oft quoted value. Here are some thoughts:

  1. This search is the average for all types of carbonyl, whereas the original suggestion was constrained to four types of nucleophiles and simple ketones.
  2. This search extends the interacting distance of the nucleophile and the carbon out to 3.5Å which is significantly longer than the normally considered length of ~2.85Å. The hotspots occur at about 3.15Å and not 2.85Å.
  3. There is obviously considerably more data available in 2015 than in 1974, and in particular at low temperature.
  4. The Bürgi–Dunitz angle is in fact one of two defining the trajectory, the other being the Flippin–Lodge angle which defines the displacement towards R or QB. The search above gives no direct information about this angle, but the torsion is related since it is constrained to bisect the C=O to within ± 20° and hence bisect the groups R and QB.
  5. An angle of ≤ 90° does not match to the normal explanation, which is that the nucleophile attacks the π* orbital, each lobe of which “leans out” from the centre at about 105° rather than leaning in at ≤ 90°.
  6. Decreasing the torsion range to  ± 5° at 120K gives 592 hits with a hot spot at 95°
  7. Also constraining the distance QA…C to be 0.3Å less than the van der Waals sum at 120K gives 59 hits with a hot spot at 95° and 2.9Å.

Well, to get to the bottom of this will require reducing the scope of both QA and QB, to find which if any of discrete values for these two variables can indeed give an angle of 105-107°. This would make for quite a good student group project; I expect a group of 8 students could sort this out quite quickly!

References

  1. H. B:urgi, J. Dunitz, J. Lehn, and G. Wipff, "Stereochemistry of reaction paths at carbonyl centres", Tetrahedron, vol. 30, pp. 1563-1572, 1974. https://doi.org/10.1016/s0040-4020(01)90678-7

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Posted in Chemical IT, crystal_structure_mining | 3 Comments »

The status of blogging as scientific communication.

May 10th, 2015

Blogging in chemistry remains something of a niche activity, albeit with a variety of different styles. The most common is commentary or opinion on the scientific literature or conferencing, serving to highlight what their author considers interesting or important developments. There are even metajournals that aggregate such commentaries. The question therefore occasionally arises; should blogs aspire to any form of permanence, or are they simply creatures of their time.

In this blog, as you might have noticed, I take a slightly different tack. One focus is on exploring, perchance in more detail than might be found in the standard text-book, some of the dogmas of chemistry.  It happens that occasionally when writing a conventional scientific article, I find myself wishing to cite such sources. This of itself raises interesting issues (such as should one cite what might be considered material that has not been peer-reviewed in the conventional manner) but the most important would be whether one should cite evanescent sources. So this brings me to the topic of this post; can a post be archived in a sense that achieves a greater perceived permanence? Nowadays, permanence tends to be associated with a digital object identifier, or DOI. So one can boil this question down to: can one assign a DOI to a blog post?

Well, if you came to this post via the main page, you may indeed have spotted that some do have a DOI. This is an experiment I have been running with an organisation known as The Winnower, who provide a WordPress extension to archive any individual post and assign it a (CrossRef) DOI. The archived version also includes metadata that points back to the original post.

This archival is not yet perfect. In its current state it does not (yet) capture:

  1. Comments on any post (which could be considered a form of open peer review)
  2. Enhancements such as the links to Jmol/JSmol that I associate with some of the posts
  3. The ORCID identifier, which adds a layer of additional provenance.
  4. We of course do not yet know what the lifetime expectancy archiving organisations will achieve (could it be 100 years for example?).

It does capture the citation list when there is one, and since I include citations to my data sources (for the computations performed in support of many of my posts) the archive is I think accordingly rendered more valuable.

What brought this post on? Well, the Journal of Chemical Education has put out a call for articles on chemical information for a special issue. I decided to contribute by aggregating some of my teaching related posts; indeed individually could perhaps have only appeared here as opposed to a more traditional means of dissemination such as the JCE journal itself. And I wanted to cite them using the DOI rather than simply the URL of the post. It’s an experiment, and one which I do not yet know if anyone else will try. That in some ways is the point of a blog; it is an interesting experimental vehicle!

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Posted in Chemical IT | 5 Comments »

Allotropic halogens.

April 26th, 2015

Allotropes are differing structural forms of the elements. The best known example is that of carbon, which comes as diamond and graphite, along with the relatively recently discovered fullerenes and now graphenes. Here I ponder whether any of the halogens can have allotropes.

Firstly, I am not aware of much discussion on the topic. But ClF3 is certainly well-known, and so it is trivial to suggest BrBr3, i.e. Br4 as an example of a halogen allotrope. Scifinder for example gives no literature hits on such a substance (either real or as a calculation; it is not always easy nowadays to tell which). So, is it stable? A B3LYP+D3/6-311++G(2d,2p) calculation reveals a free energy barrier of 17.2 kcal/mol preventing Br4 from dissociating to 2Br2.[1] The reaction however is rather exoenergic, and so to stand any chance of observing Br4, one would probably have to create it at a low temperature. But say -78° would probably be low enough to give it a long lifetime; perhaps even 0°.

Br4c
Br4

So how to make it? This is pure speculation, but the red colour of bromine originates from (weak, symmetry forbidden) transitions, with energies calculated (for the 2Br2 complex) as 504, 492nm. Geometry optimisation of the first singlet excited state of 2Br2 produces the structure below, not that different from Br4.
2Br2-excited

 

At least from these relatively simple calculations, it does seem as if an allotrope of bromine might be detectable spectroscopically, if not actually isolated as a pure substance.

References

  1. H.S. Rzepa, "Br4", 2015. https://doi.org/10.14469/ch/191228

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Posted in reaction mechanism | 11 Comments »

ORCID identifiers galore!

April 21st, 2015

Egon has reminded us that adoption of ORCID (Open researcher and collaborator ID) is gaining apace. It is a mechanism to disambiguate (a Wikipedia term!) contributions in the researcher community and to also remove much of the anonymity (where that is undesirable) that often lurks in social media sites.

This blog is now ORCID-enabled (my ORCID should appear at the top of this post for example, where you should be able to find it as , although the signature thumbnail orcid_24x24 is obscured by my gravatar, an older system for providing information about someone‡). We also add ORCIDs to all data depositions[1].

You will not yet find them in many journal articles, which was the whole original point of their introduction. They can however already be used to log into e.g. manuscript submission sites, for example the Journal of Chemoinformatics and I gather many other journal submission systems will probably start using it in 2015. From there it is short step to incorporating them into journal articles routinely.

To counter the slightly awkward association with “being reduced to a mere number”,† we need to start seeing genuine benefits from its pervasive use. From my point of view, there will be one immediate application. At my university we run a system called Symplectic, which in effect tracks all aspects of one’s research activities, including sourcing online publications. Each time Symplectic thinks it has found e.g. one of my articles, it sends me an email asking me to verify its discovery. I then have to spend 5 minutes or so acknowledging it was written by me, and then adding further links to e.g. instrumental resources used for that research. One of those resources is the high performance computing unit here. But since that resource already incorporates ORCID via e.g. [1], there is no reason why Symplectic need ever bother me with such questions in the future; it could automatically harvest all the information defined by my ORCID.

As with many steps forward, there are often steps back, following the law of unforeseen consequences. Perhaps “identity theft” is one; how easy could it be to use someone else’s ORCID for example? I think however that ORCID is here to stay, and we should explore both the good and the potentially bad aspects of its increasing deployment.

‡Gravatar offer a list of verified services similar in concept to ORCID. But ORCID itself is not on that list; http://en.gravatar.com/profiles/edit/#verified-services
†In the dystopian novel We by Yevgeny Zamyatin, there is no way of referring to people save by their given numbers. Wikipedia tells us We is considered  as having influenced the later novel 1984 by George Orwell.

References

  1. H.S. Rzepa, "C 6 H 6 Br 2", 2015. https://doi.org/10.14469/ch/191199

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Posted in Chemical IT | 3 Comments »

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