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Molecule orbitals as indicators of reactivity: bromoallene.

Thursday, September 1st, 2016

Bromoallene is a pretty simple molecule, with two non-equivalent double bonds. How might it react with an electrophile, say dimethyldioxirane (DMDO) to form an epoxide?[1] Here I explore the difference between two different and very simple approaches to predicting its reactivity. bromoallene

Both approaches rely on the properties of the reactant and use two types of molecule orbitals derived from its electronic wavefunction. The first of these is very well-known as the molecular orbital (MO), which has the property that it tends to delocalise over all the contributing atoms (the “molecule”). MOs are often used in this context; the highest energy occupied MO is thought of as being associated with the most nucleophilic (electron donating) regions of the molecule and so such a HOMO would be expected to predict the region of nucleophilic attack. The second is known as the natural bond orbital (NBO), which is evaluated in a manner that tends to localise it on bonds (the functional groups or reaction centres) and atom centres. What do these respective orbitals reveal for bromoallene? 

The MOs
HOMO, -0.3380 HOMO-1, -0.3692 au
Click for 3D

Click for 3D
Click for 3D

Click for 3D
The NBOs
HONBO, -0.3769 HONBO-2, -0.3898
Click for 3D

Click for 3D
Click for 3D

Click for 3D

The table above shows the energies (in Hartrees) of the four relevant orbitals. The less negative (less stable) the orbital, the more nucleophilic it is. The (heavily) delocalized HOMO is located on the C=C bond bond carrying the C-Br bond, Δ1,2 alkene, but it also has a large component on the Br. The more stable HOMO-1 is located on the C=C bond located away from the Br, the Δ2,3 alkene and also with a (different type of) component on the Br.

In contrast, the HONBO is located on the Δ2,3 alkene and it is the HONBO-2 that is on the Δ1,2 alkene. Both these orbitals have very little “leakage” onto other atoms, they are almost completely localised.

Well, now we have a problem since these two analyses lead to diametrically opposing predictions! So what does experiment say? A recent article[1] addresses this issue by isolating the initially formed epoxide from reaction with DMDO and characterising it using crystallography. But here comes the catch; such isolation only proved possible if the allene was also substituted with large sterically bulky groups such as t-butyl or adamantyl. And the isolated product was the Δ1,2 epoxide. So does that mean that the MO method was correct and the NBO method wrong? Well, not necessarily. Those large groups play an additional role via steric effects. To factor in such effects one has to look at the transition state model for the reaction rather than depending purely on the reactant properties. And the steric effects in this case appear to win out over the electronic ones.[1]

The Klopman[2]-Salem[3] equation (shown in very simplified, and original, form below for just the covalent term) casts some light on what is going on. This term is a double summation over occupied/unoccupied (donor-acceptor) orbital interactions, involving the coefficients of the orbitals (the overlap integrals in effect) in the numerator and the energy difference between the occupied/unoccupied orbital pair as denominator.

KS1

Performing such a double summation is rarely attempted; instead the equation is reduced to just one single term involving the donor of highest energy and the acceptor of lowest energy, ensuring the energy difference is a minimum and hence the term itself is (potentially) the largest in the summation. There is still the issue of the orbital coefficients, and here we get to the crux of the difference between the use of MOs and NBOs. You can see by inspection that the two π-MOs for bromoallene have different coefficients on the two atoms of interest, the two carbons of the double bond. One really has to evaluate the size of this term in the summation by using quantitative values for the respective coefficients and to very probably include the further terms in the summation for any other orbitals which also have significantly non-zero coefficients on these two atoms. But with the NBOs, the localisation procedure used to derive them has reduced the coefficients to just the carbon atoms and effectively no other atoms; all the other terms in the double summation in effect do drop out entirely. So with NBOs, the only number that matters is the energy difference between the occupied/empty orbitals (the denominator). But since the acceptor (the electrophile, DMDO in this case) is the same for both regiochemistries, things reduce even further to just comparing the donor energies for the two alternatives (Table above). The higher/less stable of these will have the greater contribution in the Klopman-Salem equation.

This little molecule teaches the important lesson that electronic and steric effects both play a role in directing reactions, and in this system they may well oppose each other. Simple interpretations based on reactant orbitals may give only a partial and even potentially misleading answer.

References

  1. D. Christopher Braddock, A. Mahtey, H.S. Rzepa, and A.J.P. White, "Stable bromoallene oxides", Chemical Communications, vol. 52, pp. 11219-11222, 2016. https://doi.org/10.1039/c6cc06395k
  2. G. Klopman, "Chemical reactivity and the concept of charge- and frontier-controlled reactions", Journal of the American Chemical Society, vol. 90, pp. 223-234, 1968. https://doi.org/10.1021/ja01004a002
  3. L. Salem, "Intermolecular orbital theory of the interaction between conjugated systems. I. General theory", Journal of the American Chemical Society, vol. 90, pp. 543-552, 1968. https://doi.org/10.1021/ja01005a001

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A periodic table for anomeric centres, this time with quantified interactions.

Monday, August 8th, 2016

The previous post contained an exploration of the anomeric effect as it occurs at an atom centre X for which the effect is manifest in crystal structures. Here I quantify the effect, by selecting the test molecule MeO-X-OMe, where X is of two types:

  1. A two-coordinate atom across the series B-O and Al-S, and carrying the appropriate molecular charge such that X carries two lone pairs of electrons (thus the charge is 0 for O, but -3 for B).
  2. A four-coordinate atom across the series B-O and Al-S, with X-H bonds replacing the lone pairs on this centre in the previous example, and again with appropriate molecule charges (e.g. +2 for  SH2).

The donor in the anomeric interaction always originates on the oxygen of the MeO group attached to X. The acceptor is always the X-O σ* empty orbital. The results (table below, ωB97XD/Def2-TZVPP calculation, NBO E(2) in kcal/mol) confirm that as X gets more electronegative, the X-O σ* empty orbital becomes a better acceptor, and so the NBO E(2) interaction energy which quantifies the anomeric interaction gets larger. Eventually (with X=OH2) the donation of electrons into the X-O σ* empty orbital becomes so effective that the X-O bond (in this case O-O) dissociates fully and the NBO perturbation cannot be computed. Also for reference, a “normal” anomeric interaction (such as is found in e.g. sugars) is around 18 kcal/mol. Anything larger than this could be considered especially strong, and anything less than ~10 kcal/mol would be regarded as weak. 

X[1]*
BH2 CH2 NH2 OH2
12.5 17.7 18.5 dissociates
AlH2 SiH2 PH2 SH2
6.9 12.9 21.9 31.3
B C N O
8.3 11.7 12.9 14.2
Al Si P S
4.8 6.6 11.2 18.2

For the entry X=S, the E(2) term is actually larger than for the oxygen. I should note that the Me group itself is not passive in this process. The C-H bonds can also act as significant electron donors, but here I am not going to analyse this additional complexity.

This table reveals that there is nothing special about carbon as an anomeric centre, and here also the normal intimate association with the term anomeric and heterocyclohexanes such as found in sugars.

* Here I introduce a refinement to my normal process of citing the data produced for any specific calculation. Rather than including 16 individual citations for each cell in the table, I have gathered all these calculations into a collection and cite here only the DOI of that collection. When resolved, the individual members of that collection can then be inspected for the actual data.

References

  1. H. Rzepa, "Anomeric interactions at atom centres", 2016. https://doi.org/10.14469/hpc/1221

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A periodic table for anomeric centres.

Saturday, August 6th, 2016

In the last few posts, I have explored the anomeric effect as it occurs at an atom centre X. Here I try to summarise the atoms for which the effect is manifest in crystal structures.

The effect is defined by X bearing two substituents, one of which Z is a centre bearing a “lone pair” of electrons (or two electrons in a π-bond), and another Y in which the X-Y bond has a low-lying acceptor or σ* empty orbital into which the lone pair can be donated. This donation will only occur if the Z-lone pair and the X-Y bond vectors align antiperiplanar. Here is the summary so far.

X Blog entry
B 16601
C 14508,8898
N this one
O 16646
Si 16601
P 16601
S this one

As required of a good periodic table, it has gaps that need completing, in this case X=N and X=S. Firstly N, for which the small molecule below is known (FUHFAP).

FUHFAP

A ωB97XD/Def2-TZVPP calculation[1] yields an electron density distribution, which can be collected into monosynaptic basins using the ELF technique. There are two oxygen lone pairs (17 and 20) that are close to antiperiplanar to the adjacent N-O bond, having E(2) interaction energies obtained using the NBO method of 15.1 and 15.8 kcal/mol, typical of the anomeric range. The basin labelled 13 on X=N1 below is also perfectly aligned antiperiplanar with the adjacent O3-C2 bond, but its E(2) interaction energy is only 7.3 kcal/mol. Thus a strong anomeric interaction on the anomeric atom itself does not seem to occur. The same effect was noted for X=O in the previous post; the explanation remains unidentified.

FUHFAP

With the X=S gap, we have lots of opportunity with polysulfide compounds, a good example of which is the C2-symmetric and helical S8 dianion TEGWAF[2]

TEGWAF

Each of the 8 sulfur atoms exhibits antiperiplanar orientation of an S lone pair with an adjacent S-S acceptor σ* orbital;
1:2-3=23.7 kcal/mol;
2:3-4=18.5;
3:4-8=11.7, 3:2-1=7.4;
4:8-7=11.4, 4:3-2=9.2.

This just surveys the central main group elements, and it is possible that this little mini-periodic table may yet grow.

References

  1. H.S. Rzepa, "C 2 H 7 N 1 O 2", 2016. https://doi.org/10.14469/ch/195294
  2. Rybak, W.K.., Cymbaluk, A.., Skonieczny, J.., and Siczek, M.., "CCDC 880780: Experimental Crystal Structure Determination", 2012. https://doi.org/10.5517/ccykj88

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Managing (open) NMR data: a working example using Mpublish.

Monday, August 1st, 2016

In March, I posted from the ACS meeting in San Diego on the topic of Research data: Managing spectroscopy-NMR, and noted a talk by MestreLab Research on how a tool called Mpublish in the forthcoming release of their NMR analysis software Mestrenova could help. With that release now out, the opportunity arose to test the system.

I will start by reminding that NMR data associated with a published article is (or should be) openly free: one should not need a subscription to the journal to access it (although one might in order to find it). Now, NMR data as it emerges from a spectrometer is highly sophisticated, comprising a collection of (sometimes) binary proprietary files containing the measured free induction decays (FID). Turning this raw data into an interpretable NMR spectrum, the visual form of the data that so appeals to human beings, is non trivial. This requires what may be highly sophisticated software and that in turn means that it may be a commercial product. Of course there are also examples of non-commercial open software packages that are best-of-breed; indeed in its early life-cycle MestreNova was known as MESTREC before becoming a commercial product. Could one achieve the benefits of both open and fully functional NMR data with no loss from the original instrument coupled with the ability to apply top-quality software for its analysis in an open manner? This is a demonstration of how Mpublish achieves this.

  1. Invoke the URL data.datacite.org/chemical/x-mnpub/10.14469/hpc/1087 from a browser
  2. This action queries the metadata deposited with DataCite for the doi 10.14469/hpc/1087 and retrieves the first instance of any file associated with that dataset that has the format type chemical/x-mnpub. You can directly view this metadata by invoking just data.datacite.org/10.14469/hpc/1087 where you can find both mnpub and mnova formats listed. A command such as data.datacite.org/chemical/x-mnpub/10.14469/hpc/1087 allows the file retrieval to be incorporated into automated workflows based just on the doi and the media type desired. Note my parenthetical comment above about finding data; here you only need its doi to retrieve it!
  3. The URL above downloads a small text file with the suffix .mnpub which contains in essence two components:

    • A URL pointing directly to an .mnova file at the repository for which the doi has been issued
    • A signature key derived used to verify that the public key of the publisher (the data repository in this instance) was counter-signed by Mestrelab.
  4. If you now download the application program and install it (but for the purpose of this demonstration, ignore any requests to try to license the program. Use it unlicensed) and open the .mnpub file using it, you should get the below.The application program has checked the signature key, and if valid, proceeds to download a full data file (a .mnova file in this case), and to analyze and display it within the program. The data is fully active; it can be manipulated and analysed. Notice in the picture below, the red arrow points to the state of the license, in this case not present.
    mn
  5. It is also possible to apply this procedure to the raw data as it emerges from the (Bruker) spectrometer, and compressed into a .zip archive. The MestreNova software will automatically process the contents by applying various default parameters, although the result may not correspond exactly to that present in e.g. the equivalent .mnova file (which may have had specific parameters applied).

It is my hope that anyone who records NMR data and processes it using software such as MestreNova will now consider using the mechanism above to accompany their submitted articles, rather than just automatically pasting a static image of the spectrum into a PDF file as "supporting information". This is part of what is meant by "managed research data" (RDM).

One cannot help but note that many types of scientific instrument nowadays come with bespoke software for analysing the data they produce. Very often this software is unavailable to anyone who has not purchased the instrument itself. To make the data available to others, the processed data and its visual interpretation often have to be reduced, with much consequent information loss, to a lowest common denominator format such as Acrobat/PDF. Here we see a mechanism for avoiding any such information loss whilst enabling, for that dataset only, the full potential for (re)analysing the data. It will be interesting to see if other examples of this model or its equivalent emerge in the near future.

 
 
 

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Anomeric effects at carbon involving lone pairs originating from one or two nitrogens.

Friday, July 8th, 2016

The previous post looked at anomeric effects set up on centres such as B, Si or P, and involving two oxygen groups attached to these atoms. Here I vary the attached groups to include either one or two nitrogen atoms.[1]

.aminol-sq

The plot below shows aminols, C(NHR)(OR”). A torsion along either the C-O or C-N bond of ~60° implies that (at two coordinate oxygen or three coordinated nitrogen) there may be a lone pair with a torsion of 180°, which would set up an antiperiplanar alignment between that lone pair and the adjacent C-O or C-N bond (the anomeric effect). The clear hotspot is at angles of ~80°, which does raise the issue of why it deviates from 60°. Only a location of the lone pair centroid (using eg the ELF quantum mechanical technique) would cast light on that. There is a less distinct region for which the C-N torsion is 60° and the C-O torsion 180°, and an even less distinct region for the reverse (C-O torsion is 60° and the C-N torsion 180°). This tends to imply that a nitrogen lone pair is a better donor into a C-O bond than the reverse. Electronegativity suggests this should indeed be so, with the N lone pair less bound by the N nucleus and hence easier to release into a C-Oσ* orbital which is a better acceptor than then equivalent C-Nσ* orbital. aminol This plot is where both heteroatoms are nitrogen (geminal diamines). There are about twice as many examples, resulting in more distinct clustering. The anomeric hotspot is now around 70°  and there are equally populated clusters where only one torsion is ~70°. There is another cluster for which both torsions are 180° (no stereoelectronic alignment of lone pairs) and three small clusters where the torsions are either 180° or 0°. There is finally an intriguing cluster for which both torsions at ~120° (again no stereoelectronics). diamine

Searches like this seem to be good at creating more questions than they answer. Clearly, the origins of the various hotspots need to be investigated, ideally using quantum mechanics to quantify the stereoelectronic interactions involved. So this sort of (ten minute) exercise is very good at raising research project investigations.

References

  1. H. Rzepa, "Anomeric effects at carbon, involving lone pairs originating from one or two nitrogens", 2016. https://doi.org/10.14469/hpc/936

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The formation of tetrahedral intermediates.

Friday, June 12th, 2015

In the preceding post, I discussed the reaction between mCPBA (meta-chloroperbenzoic acid) and cyclohexanone, resulting in Baeyer-Villiger oxidation via a tetrahedral intermediate (TI). Dan Singleton, in whose group the original KIE (kinetic isotope measurements) were made, has kindly pointed out on this blog that his was a mixed-phase reaction, and that mechanistic comparison with homogenous solutions may not be justified. An intriguing aspect of the (solution) mechanism would be whether the TI forms quickly and/or reversibly and what the position of any equilibrium between it and the starting ketone is. This reminded me of work we did some years ago,[1] and here I discuss that.

It involved the addition of phenyl hydroxylamine, PhNHOH to acetyl cyanide at 215K. Because the CN group is poor at leaving, the tetrahedral intermediates do not collapse and instead accumulate in seconds to the point of becoming detectable by NMR (both N-C and O-C isomers). The position of the equilibrium clearly favours the TI rather than the starting materials. In another context, both the rate of reaction and the equilibrium can be driven towards the TI by the application of pressure.[2] Hydroxylamines are known to be super nucleophiles, enhanced by the so-called α-effect from buttressing of adjacent lone pairs on the N and O. This reminds that a peracid also should exhibit a related α-effect; it should be a better nucleophile than a normal carboxylic acid. So I decided to take the TI formed from cyclohexanone and mcPBA and look at the NBO orbitals, which should tell us about the anomeric effects present in this TI, and in particular if they might be larger than normal (which could be equated with greater stability for the TI). Here are the relevant NBO energies.[3]

TI-NBO

  1. The conventional anomeric effect in O-C-O manifests as a E(2) perturbation energy of ~16-18 kcal/mol between one oxygen lone pair and the antibonding C-O orbital. There are two combinations, and these are normally similar in energy.
  2. For the system above, the O1-C2-O6 interaction is 25.6 kcal/mol, much larger than normal, but partially counterbalanced by:
  3. O6-C1-O2 =13.0 kcal/mol which is a little lower than normal. This is overall an unusually strong anomeric effect for the O-C-O motif!
  4. The energetic asymmetry is matched by the two computed bond lengths, 1.381Å for the larger interaction and 1.455Å for the smaller. The pseudo-α-effect has desymmetrized the anomeric effect, but nevertheless strengthened it overall.
NBO 103

NBO 103 for O1(Lp)

NBO 97

NBO 97 for O6(Lp)

NBO 123

NBO 123 for C2-O6 antibonding σ*orbital

One concludes that the asymmetric anomeric effect makes the TI resemble the reactants. The transition state leading to the TI must be even earlier. In this context, I note that the (mixed phase) 13C effect reported for the carbonyl by Singleton and Szymanski[4] was quite a large one for carbon (1.045-1.051), a magnitude which argues against a very early transition state under these conditions. But the calculated value for a homogenous solution state model of ~1.023 is certainly more in accord with an early transition state.

Finally, a search of the CSD reveals 12 molecules containing either a O-O-C-O-O or a O-C-O-O sub unit This one[5] shows a bis HO-C-O-O-C-OH structure at room temperature; these species need not be unstable! There are none however with Ac-O-O-C-O. And of course the potent antimalarial artemisinin contains a O-O-C-O-C-O-Ac unit, for which stereoelectronic effects may also be important.

References

  1. A.M. Lobo, M.M. Marques, S. Prabhakar, and H.S. Rzepa, "Tetrahedral intermediates formed by nitrogen and oxygen attack of aromatic hydroxylamines on acetyl cyanide", The Journal of Organic Chemistry, vol. 52, pp. 2925-2927, 1987. https://doi.org/10.1021/jo00389a050
  2. N.S. Isaacs, H.S. Rzepa, R.N. Sheppard, A.M. Lobo, S. Prabhakar, and A.E. Merbach, "Volumes of reaction for the formation of some analogues of tetrahedral intermediates", Journal of the Chemical Society, Perkin Transactions 2, pp. 1477, 1987. https://doi.org/10.1039/p29870001477
  3. H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191327
  4. 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
  5. A. Kobayashi, Y. Ikeda, K. Kubota, and Y. Ohashi, "Syntheses and crystalline structures of several aldehyde peroxides as new flavor compounds", Journal of Agricultural and Food Chemistry, vol. 41, pp. 1297-1299, 1993. https://doi.org/10.1021/jf00032a025

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

Wednesday, 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.

Wednesday, 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

Saturday, 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.

Friday, 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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