Posts Tagged ‘dielectric’

The dipole moments of highly polar molecules: glycine zwitterion.

Saturday, December 24th, 2016

The previous posts produced discussion about the dipole moments of highly polar molecules. Here to produce some reference points for further discussion I look at the dipole moment of glycine, the classic zwitterion (an internal ion-pair).

Dielectric relaxation studies of glycine–water mixtures yield values that range from 15.7D[1] to 11.9D[2] although these have to be derived using various approximations and assumptions for up to 4 independent Debye processes. Before proceeding to calculations, I looked at the properties of ionized amino acids in the solid state, using the following search query for the Cambridge structure database (CSD). 

The distance measures hydrogen bonds to the carboxylate oxygens and the torsion their orientation. The O…H hydrogen bond distances vary between 1.7-1.85Å, which are short. The orientation of the hydrogen bond can be to the in-plane oxygen “σ-lone pair” (torsion 0 or 180°) and also an out-of-plane ~π form (torsion ~60-90°).

In aqueous solution, it is normally assumed that glycine sustains five such strong H-bonds (three to the H3N+ group and two[3] to the carboxylate anion), forming a polarised “salt bridge” across the ion-pair. Two model types were subjected to calculation using ωB97XD/Def2-TZVPP/SCRF=water. Aqueous glycine without any added explicit water molecules yields a dipole moment of 12.9D (DOI: 10.14469/hpc/2000), which is within the range noted above.‡

The solvated form is shown below, in one specific conformation of the three studied (ωB97XD/Def2-TZVPP/SCRF=water). The calculated O…H hydrogen bond lengths fall into the range revealed from crystal structures. The calculated dipole moments range from 12.6 (DOI: 10.14469/hpc/2007), 15.3 (DOI: 10.14469/hpc/2006) and 14.9D (DOI: 10.14469/hpc/2005), which is a modest increase over the model with no explicit water molecules. The actual dipole is of course a Boltzmann average over these and other as yet unexplored conformations, as well as other values for the number of water molecules.

Given the difficulties in interpreting the dipole moment of a complex Debye system such as hydrated glycine, the agreement between the limited range of solvated models and the measured values seems reasonable, and provides at least some measure of “calibration” for the polar molecules commented on previously.

‡Optimized with the solvent field on. If a vacuum model is used, the proton transfers from the N to the O.

References

  1. M.W. Aaron, and E.H. Grant, "Dielectric relaxation of glycine in water", Transactions of the Faraday Society, vol. 59, pp. 85, 1963. https://doi.org/10.1039/tf9635900085
  2. T. Sato, R. Buchner, . Fernandez, A. Chiba, and W. Kunz, "Dielectric relaxation spectroscopy of aqueous amino acid solutions: dynamics and interactions in aqueous glycine", Journal of Molecular Liquids, vol. 117, pp. 93-98, 2005. https://doi.org/10.1016/j.molliq.2004.08.001
  3. T. Shikata, "Dielectric Relaxation Behavior of Glycine Betaine in Aqueous Solution", The Journal of Physical Chemistry A, vol. 106, pp. 7664-7670, 2002. https://doi.org/10.1021/jp020957j

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Autoionization of hydrogen fluoride.

Sunday, April 24th, 2016

The autoionization of water involves two molecules transfering a proton to give hydronium hydroxide, a process for which the free energy of reaction is well known. Here I ask what might happen with the next element along in the periodic table, F.

I have been unable to find much about the autoionization of HF in the literature; the pH of neat HF appears unreported (unlike that of H2O, which of course is 7). Even the dielectric constant of liquid HF[1],[2] seems to vary widely, the largest reported being ~84. It is suggested that liquid HF is much less ordered than e.g. water, and this suggests that a single static model is unlikely to be entirely realistic. Nonetheless, I thought it might be informative to take the model I previously constructed for water and try applying it to HF. Here is part of the geometry optimisation cycle[3] from the original edited water model. I used ωB97XD/Def2-TZVPPD/SCRF=water for the model. Why continuum water as the solvation treatment? Well, standard parameters for liquid HF are not available (perhaps given the variation in dielectric) and since the upper bound might be similar to water, I decided to use that to see what I got. Clearly however an approximation.

The low energy final geometry corresponds to 10 HF molecules and lies about 16 kcal/mol lower (in total energy) than the cyclic structure containing H2F+.F– species connected by two (HF)3 bridges and two further non-bridge HF molecules hydrogen bonding to the H2F+ and the F–. In fact the ionic structure turns out to be a transition state for proton shifting along the chain to create (HF)10, with a free energy barrier of 9.2 kcal/mol above the neutral form.[4] This difference between ionic and non-ionic forms is considerably less than that for water as previously indicated. Note also how much shorter the hydrogen bonding H…F distances are in the HF cluster.

So unlike water, where the hydronium hydroxide is a clear minimum in the potential with a small but distinct barrier (~3.5 kcal/mol[5]) to proton transfer, with HF at the same level of theory the barrier is zero. Perhaps the difference might be because whereas hydronium hydroxide can support three stabilizing (H2O)3 bridges, only two (HF)3 bridges are possible with H2F+.F–. It might also be higher levels of theory (or better/larger models of the HF cluster) could well give a barrier for the process, but this does tend to suggest that the dynamics of HF liquid may suggest quite different lifetimes for autoionized forms of HF compared to water. Liquid HF is clearly just as complicated a liquid as is H2O, certainly much less is known about it.

References

  1. R.H. Cole, "Dielectric constant and association in liquid HF", The Journal of Chemical Physics, vol. 59, pp. 1545-1546, 1973. https://doi.org/10.1063/1.1680219
  2. P.H. Fries, and J. Richardi, "The solution of the Wertheim association theory for molecular liquids: Application to hydrogen fluoride", The Journal of Chemical Physics, vol. 113, pp. 9169-9179, 2000. https://doi.org/10.1063/1.1319172
  3. H.S. Rzepa, "H 10 F 10", 2016. https://doi.org/10.14469/ch/192032
  4. H.S. Rzepa, "H 10 F 10", 2016. https://doi.org/10.14469/ch/192034
  5. H.S. Rzepa, "H22O11", 2016. https://doi.org/10.14469/ch/192022

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Deuteronium deuteroxide. The why of pD 7.435.

Friday, April 22nd, 2016

Earlier, I constructed a possible model of hydronium hydroxide, or H3O+.OH– One way of assessing the quality of the model is to calculate the free energy difference between it and two normal water molecules and compare the result to the measured difference. Here I apply a further test of the model using isotopes.

Pure water has pH 7, which means equal concentrations for both [H3O+] and  [OH–] of 10-7M. Converting this to a free energy one gets ΔG298 19.088 kcal/mol. Now the pD of pure deuterium oxide is reported as 7.435, equivalent to ΔG298 20.274, an isotope effect on the free energy of ΔΔG298 =1.186 kcal/mol. How does the theoretical model (ωB97XD/Def2-TZVPPD/SCRF=water‡) previously reported[1],[2] do? The value obtained is 1.215,[3] an apparent error of only 0.029 kcal/mol. I am quite pleased with the close correspondence; at least the model is capable of reporting good isotope effects on the ionisation equilibrium of pure water!

Finally, with some confidence assured, one might apply this to tritonium tritoxide. Tritiated water is so radioactive it would boil in an instant, probably well before its pT could be measured. ΔΔG298 is calculated as 1.798 kcal/mol. Will this estimate ever be challenged by experiment?

‡ It is assumed no isotope effect acts on the dielectric constant of water and hence the continuum model used here to model it. In fact the isotope effect on this property is modest; ε298 = 77.94, compared with 78.36 for normal water.[4]

References

  1. H.S. Rzepa, "H 22 O 11", 2016. https://doi.org/10.14469/ch/191999
  2. H.S. Rzepa, "H 22 O 11", 2016. https://doi.org/10.14469/ch/191998
  3. H. Rzepa, "Deuteronium deuteroxide; free energy differences.", 2016. https://doi.org/10.14469/hpc/407
  4. C. Malmberg, "Dielectric constant of deuterium oxide", Journal of Research of the National Bureau of Standards, vol. 60, pp. 609, 1958. https://doi.org/10.6028/jres.060.060

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The roles of water in the hydrolysis of an acetal.

Wednesday, November 18th, 2015

In the previous post, I pondered how a substituent (X below) might act to slow down the hydrolysis of an acetal. Here I extend that by probing the role of water molecules in the mechanism of acetal hydrolysis.

acetal1

Water molecules can participate in three ways:

  1. One water acts as a nucleophile to replace one of the oxygen atoms of the acetal
  2. n waters in total participate in a proton transfer relay, in which a proton from the acid used to protonate one oxygen in the acetal is counterbalanced by another removed by a cooperating water.
  3. m waters serve as a stabilizer via hydrogen bonding. 
  4. Water can also be modelled as a continuum dielectric solvent.

My previous model included just one explicit water molecule (n=1) participating in 1 and 2 above (but not via 3) + the continuum model 4; the objective then being to study variation in X. I noted that the resulting barriers to reaction were too high for a facile thermal reaction; the model had to be incomplete. Here the objective is to probe the consequences of various deployments of up to four water molecules in this mechanism (X=R=H) to see if the model can be improved.

n m ΔE, kcal/mol ΔG‡ DataDOI
1 0 38.4 38.2 [1]
2 0 36.5 34.1 [2],[3],[3]
3 0 32.1 30.4 [4],[5][6]
4 0 28.1 29.9 [7],[8],[5]
3 1 29.8 29.5 [9],[8],[10]
2 2 30.5 31.3 [11],[8],[12]
1 3 26.9 29.7 [13],[8],[14]

The energies shown above generally show that water molecules are almost as happy when participating in a (cyclic) proton relay as when (passively) solvating the acid. This is probably in part at least because a cyclic proton transfer relay cross-polarises adjacent waters, increasing their own hydrogen bond strengths. Nevertheless, with four water molecules, the possible arrangements in the table above are all in fact quite similar in energy, suggesting that the actual system is a complex dynamic one involving many states of similar energy. A proper molecular-dynamics based sampling of these and other states is probably needed to construct the most realistic model. The extended four-water model results in a lowering of the predicted barrier by ~9-10 kcal/mol to become a more reasonable value for a thermal reaction, perhaps appropriate for catalysis by a relatively weak acid such as acetic. The improvement in part may be because the linear requirement for an Sn2 displacement is more easily accommodated by the larger rings created by using more water molecules.

Click for 3D

Click for 3D

An intrinsic reaction coordinate (IRC) is also instructive, shown as the gradient normal along the IRC. The features are as follows:

  1. IRC ~8, the water molecules are reorganising themselves ready for the proton relay
  2. IRC 2, a dip in the gradient norm reveal a hidden intermediate corresponding to the first proton transfer to the oxygen of the acetal.
  3. IRC 0 is of course the transition state
  4. IRC -2 corresponds to a dip for the second proton transfer
  5. IRC -3 to -4 the third and fourth proton transfers occur, showing that they are sequential rather than synchronous.

3+0G

3+0a

This examples shows how modelling using transition state theory can yield reasonably realistic answers, but also that the next step in computational modelling, reaction dynamics, is probably needed to properly explore the statistical aspects of mechanism.

References

  1. H.S. Rzepa, "C 6 H 14 O 5", 2015. https://doi.org/10.14469/ch/191581
  2. H.S. Rzepa, and H.S. Rzepa, "C 6 H 16 O 6", 2015. https://doi.org/10.14469/ch/191599
  3. H.S. Rzepa, "C6H16O6", 2015. https://doi.org/10.14469/ch/191600
  4. H.S. Rzepa, "C 6 H 18 O 7", 2015. https://doi.org/10.14469/ch/191601
  5. https://doi.org/
  6. H.S. Rzepa, "C 6 H 20 O 8", 2015. https://doi.org/10.14469/ch/191606
  7. H.S. Rzepa, and H.S. Rzepa, "C 6 H 20 O 8", 2015. https://doi.org/10.14469/ch/191607
  8. H.S. Rzepa, "C 6 H 20 O 8", 2015. https://doi.org/10.14469/ch/191604
  9. H.S. Rzepa, "C6H20O8", 2015. https://doi.org/10.14469/ch/191610
  10. H.S. Rzepa, "C 6 H 20 O 8", 2015. https://doi.org/10.14469/ch/191603
  11. H.S. Rzepa, "C6H20O8", 2015. https://doi.org/10.14469/ch/191605
  12. H.S. Rzepa, "C 6 H 20 O 8", 2015. https://doi.org/10.14469/ch/191609
  13. H.S. Rzepa, "C6H20O8", 2015. https://doi.org/10.14469/ch/191621

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A computed mechanistic pathway for the formation of an amide from an acid and an amine in non-polar solution.

Wednesday, November 12th, 2014

In London, one has the pleasures of attending occasional one day meetings at the Burlington House, home of the Royal Society of Chemistry. On November 5th this year, there was an excellent meeting on the topic of Challenges in Catalysis, and you can see the speakers and (some of) their slides here. One talk on the topic of Direct amide formation – the issues, the art, the industrial application by Dave Jackson caught my interest. He asked whether an amide could be formed directly from a carboxylic acid and an amine without the intervention of an explicit catalyst. The answer involved noting that the carboxylic acid was itself a catalyst in the process, and a full mechanistic exploration of this aspect can be found in an article published in collaboration with Andy Whiting’s group at Durham.[1] My after-thoughts in the pub centered around the recollection that I had written some blog posts about the reaction between hydroxylamine and propanone. Might there be any similarity between the two mechanisms?

amide

That mechanism can be represented as above, which (as per the hydroxylamine mechanism) comprises three transition states and two intermediates. The original study[1] reported just the one TS1. Editing out the starting coordinates from the PDF-based supporting information (the process is not always easy) enabled an IRC (intrinsic reaction coordinate) for TS1 to be easily computed.[2]

origa

origa
This reveals that TS1 is not the complete story, there is still much of the reaction left to complete. The energy profile is charted (using the ωB97XD/6-311G(d,p/SCRF=p-xylene method) according to the scheme above as reactants ⇒ TS1 ⇒ Intermediate 1 ⇒ TS2 ⇒ Tetrahedral intermediate ⇒ TS3 ⇒ products. Computed properties for this more detailed pathway are transcluded here from the digital repository[3] and appear at the end of this post.

  1. TS1 yields what might be called a zwitterionic intermediate. However, this has a relatively small dipole moment (5.7D). Thus, against accepted wisdom, such apparently ionic intermediates CAN be involved in reactions occurring in non-polar solvents!
  2. TS2 is rather unexpected, involving synchronous proton transfer coupled to anomerically related C-OH bond rotation. This rotation changes the anomeric interactions with the adjacent substituents; in my experience I have never before seen a reaction mode quite like this one!
  3. TS3 collapses the tetrahedral intermediate by synchronous proton transfer and C-O bond cleavage, and is (in this model) the rate determining step.  The free energy barrier corresponds to a half-life at 298K of about half an hour.
  4. The product is calculated as exoenergic with respect to reactants,; the reaction does drive to form an amide (and any catalysis of course will not influence that final outcome, only its kinetics).

If you read the original article[1] you will realise the above only scratches the surface of the many fascinating properties of this apparently very simple reaction. Thus, not addressed above is why amides are only formed in certain solvents (xylene for example) but not others. The solvent may have a specific role to play which is not modelled simply by its continuum dielectric or its boiling point. There is much else that could be said.

References

  1. H. Charville, D.A. Jackson, G. Hodges, A. Whiting, and M.R. Wilson, "The Uncatalyzed Direct Amide Formation Reaction – Mechanism Studies and the Key Role of Carboxylic Acid H‐Bonding", European Journal of Organic Chemistry, vol. 2011, pp. 5981-5990, 2011. https://doi.org/10.1002/ejoc.201100714
  2. H.S. Rzepa, "C21H21NO4", 2014. https://doi.org/10.14469/ch/74636
  3. H.S. Rzepa, "A computed mechanistic pathway for the formation of an amide from an acid and an amine in non-polar solution.", 2014. https://doi.org/10.6084/m9.figshare.1235300

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The mechanism of the Birch reduction. Part 2: a transition state model.

Monday, December 3rd, 2012

I promised that the follow-up to on the topic of Birch reduction would focus on the proton transfer reaction between the radical anion of anisole and a proton source, as part of analysing whether the mechanistic pathway proceeds O or M.

To add some context, Hammond’s postulate [1] states that “the structure of a transition state resembles that of the species nearest to it in free energy.” If the structure of the transition state for proton transfer above resembles that of the radical anion precursor we would call this an early transition state and it would be a reasonable approximation to infer properties of the reaction from the properties of that radical anion. The previous post explored those properties via the computed molecular electrostatic potential (MEP) and the highest energy NBO (natural bond orbitals, which are used here instead of molecular orbitals). Unfortunately, they did not agree with each other. Remember that Hammond’s postulate dates from 1955, an era when it was not practical to compute the structure of a transition state directly using quantum mechanics (certainly not so for such a complex reaction as that shown above). Indeed, one might argue that such a structure has only become computable in a practical sense very recently! As I showed previously, the radical ion-pair resulting from a 1-electron transfer from sodium to anisole has a dipole moment of ~11.6D, and the reaction is conducted in a solvent of medium polarity. This combination means that one really is obliged to take into account the dielectric of the solvent, and indeed any strong explicit hydrogen bonds that might be present. The codes for doing this have really only recently become robust enough to tackle such an endeavour[2], which might explain why such calculations are not yet abundant, or ubiquitously cited in the text books.

Proton transfer for M mechanism. Click for 3D.

The proton transfer via one M mechanism is shown above. The proton source is ammonia, which is known from experiment to lead to sluggish reactions (the more acidic t-butanol is often added to speed up the reaction), but we can see that the transition state is very late, νi 423.8 cm-1. The N…H bond is largely broken, and the C-H bond is mostly formed. The dipole moment is 7.7D, also different from that of the reactant. Perhaps, knowing this, it is not too surprising that inferences based on Hammond’s postulate as applied to the reactant are not reliable. The value of ΔG†298computed from this model is 22.8 kcal/mol, which is on the high-ish side for a reaction to occur readily at room temperatures or below.[3] This nevertheless nicely conforms what we already know, that a more acidic proton donor is needed to achieve a fast reaction.

Proton transfer for O mechanism. Click for 3D.

The proton transfer via one O mechanism is similar, but a tad less “late”. This already raises doubts about application of Hammond’s postulate to this system; one cannot really compare two reactions in which each reactant differs in its resemblance to its transition state. The dipole moment of this alternative transition state is also 7.7D, but the transition imaginary mode is much higher at νi 869 cm-1. The free energy barrier is 21.0, some 1.8 kcal/mol lower than the barrier for the M mechanism. This corresponds to a rate about 21 times faster for O over M (at 298K).

To conclude, we characterise two (of the four) isomeric transition states for protonation of the radical anion intermediate in the Birch reduction of anisole. These two transition states are actually different in several subtle regards, differences which would not have manifested if only the properties of the reactant had been considered. The final word must be that the text books are likely correct on this one, although a little more work is still needed to tidy up loose ends.  

References

  1. G.S. Hammond, "A Correlation of Reaction Rates", Journal of the American Chemical Society, vol. 77, pp. 334-338, 1955. https://doi.org/10.1021/ja01607a027
  2. J. Kong, P.V.R. Schleyer, and H.S. Rzepa, "Successful Computational Modeling of Isobornyl Chloride Ion-Pair Mechanisms", The Journal of Organic Chemistry, vol. 75, pp. 5164-5169, 2010. https://doi.org/10.1021/jo100920e
  3. H.E. Zimmerman, and P.A. Wang, "Regioselectivity of the Birch reduction", Journal of the American Chemical Society, vol. 112, pp. 1280-1281, 1990. https://doi.org/10.1021/ja00159a078

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The mechanism of the Birch reduction. Part 1: reduction of anisole.

Saturday, December 1st, 2012

The Birch reduction is a classic method for partially reducing e.g. aryl ethers using electrons (from sodium dissolved in ammonia) as the reductant rather than e.g. dihydrogen. As happens occasionally in chemistry, a long debate broke out over the two alternative mechanisms labelled O (for ortho protonation of the initial radical anion intermediate) or M (for meta protonation). Text books seem to have settled down of late in favour of O. Here I take a look at the issue myself.

Readers of my blog will note that I promote the use of models which are as reasonably complete as one can make them. In this case, if the intermediate is an anion, then I argue that the model should include the positive counter-ion. This is very often simply not included, on the grounds that it “probably does not influence things”. Well, not on this blog! My model is methoxybenzene, a sodium atom solvated by 3NH3 (the reaction itself is done in liquid ammonia with some added t-butanol) and continuum solvent (not ammonia itself, but acetonitrile which has a similar dielectric to liquid ammonia with some added butanol). 

The start point is a solvated sodium atom (loosely) coordinated to anisole (methoxybenzene). The calculation (ωB97XD/6-311+G(d,p)/SCRF=acetonitrile) on this neutral system shows the spin density arising from the single unpaired electron is mostly (0.851) on the sodium, although a little spin density has crept onto the anisole. The dipole moment (12.0D) shows that solvation cannot just be ignored. 

Start point, with select spin densities. Click for 3D

The next stage involves an electron transfer from the sodium to the anisole ring, and indeed the spin densities transfer from the Na to the two ortho- and two meta-positions on the ring (the residual value on Na is -0.02). This suggests that the valence bond representations in the diagram above are incomplete (they imply spin density on only two rather than four carbon atoms). The geometry of the anisole ring now shows bond alternation, with two long bonds (1.45 – 1.46Å) and four short bonds (1.39-1.41Å). This could be viewed as the result of a pseudo-Jahn-Teller distortion resulting from placing an electron into one of the degenerate LUMO molecular orbitals of the benzene-like set. The free energy ΔG298 of this charge-transferred product is 11.1 kcal/mol exothermic compared to the reactant and it has a dipole moment of 11.6D, similar to the precursor despite being an ion pair!

The contact ion-pair resulting from electron transfer. Click for 3D.

I start the analysis of how this species will protonate by inspecting the four highest energy NBOs (natural bond orbitals). Their energies are -0.144, -0.152, -0.167 and -0.167 au. The first of these with the highest energy might be expected to be the most basic. It corresponds to M in the above scheme (below). The next however is O and the last two are the remaining O/M positions.

Highest energy (-0.144) NBO orbital on M. Click for 3D.


Next highest energy (-0.152)  NBO on O. Click for 3D.

Another measure of basicity is the molecular electrostatic potential (a measure of how attractive any point in space is towards a proton). It is shown below (as a green surface) only as the -ve potential (that part that is attractive to a proton). On the face bearing the proton donors (the ammonia groups attached to the Na) there is a clear preference for O (marked with a magenta arrow, but not the same O as predicted by the NBO), but with a slightly smaller basin corresponding to M (again, not the M from the NBO analysis and marked with an orange arrow).

Molecular electrostatic potential (-ve phase). Click for 3D

Viewed from the other side of the anisole ring (and rendered at a higher threshold), the electrostatic potential seems to favour O, but only very slightly over M. There really is not much in it.

Molecular electrostatic potential (-ve phase, other face). Click for 3D.

All these properties are measures of the radical-anion-ion-pair. It is clear these different measures do not agree with one another! What we really need is the transition state for the proton transfer. I will go off and hunt for these. If I find them, I will report back here. And beyond the transition state are the dynamic trajectories for the protonation, which ultimately may be the only way of finally resolving this conundrum. 

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Dynamic effects in nucleophilic substitution at trigonal carbon.

Monday, July 16th, 2012

Singleton and co-workers have produced some wonderful work showing how dynamic effects and not just transition states can control the outcome of reactions. Steve Bachrach’s blog contains many examples, including this recent one.

This shows that tolyl thiolate (X=Na) reacts with the dichlorobutenone to give two substitution products in a 81:19 ratio. Singleton and Bogle argue[1] that this arises from a single transition state, and that the two products arise from a statistical distribution of dynamic trajectories bifurcating out of a transition state favouring 2 over 3. Steve puts it very elegantly “I think most organic chemists hold dear to their hearts the notion that selectivity is due to crossing over different transition states“. When I read this, Occam’s razor came to mind: could a simpler (in this case a more conventional) answer in fact be better? 

My thoughts in fact followed a point I have been making here recently, the principle that modelling a complete system is probably better than a partial one. Now, if you look at Figure 1 of the Singleton/Bogle article, captioned “Qualitative energy surface for the reaction of 1 with sodium p-tolyl thiolate” I was struck by something missing; the sodium (X=Na), and possibly also explicit solvent (ethanol). I wanted to see if these missing components may influence the mechanism.

The red arrows follow the proposed mechanism (a), whereas the blue arrows represent a more conventional 1,4-nucleophilic addition to form an intermediate enol anion, this then eliminating to the final product. Singleton & co. explored the potential energy surface using the following computational model: B3LYP/6-31+G(d,p)/PCM(ethanol) for the anionic system (defined by setting an overall charge of -1 during the calculation), finding the potential energy surface corresponded to path (a). They then went on to explore the dynamics of the system emerging out of this single TS, showing that in fact both products would be formed in more or less exactly the ratio observed. 

I thought two things could be considered missing from this model; X+ (the counterion) and explicit solvent (continuum solvent was invoked using the PCM model). On the latter point, I have thought for a little while that there are two types of solvent; those which act via their dielectric field, and those that act via hydrogen bonds. Ethanol does both, and so in this case (I argue) it should be explicitly included (actually, in the first instance it can be approximated using water instead of ethanol). The missing counter-ion is a greater challenge. In what follows I am going to approximate it too, using H+ (Na+ itself I reserve for a future post). The objective is to find out what (if anything) changes when this more complete model is built. It is shown below as the first transition state encountered. Its features include:

First transition state TS1. Click for 3D

  1. Two explicit solvent (water) molecules.
  2. A H+ (I will discuss Na+ in another post), attached to one of the water molecules as a hydronium ion.
  3. The hydronium ion bridges to the carbonyl group (this is the final optimised position; the second water molecule serves only to H-bond to the hydronium ion). 
  4. This overall system is neutral, charge=0 (I like to say it might be found in a bottle or flask; pure anions of course cannot be bottled). 
  5. The model used was B3LYP/6-31+G(d,p)/CPCM(ethanol); I find the CPCM method to be better for calculating intrinsic reaction coordinates (IRC).
  6. Using this transition state to initiate an IRC shows that the presence of this solvent bridge allows X (=H+) to smoothly transfer from sulfur to oxygen as part of a concerted process. This avoids excessive build up of charge separation.
  7. This now forms an intermediate (we are clearly following path (b) and not path (a) now). This is because the enolate anion is stabilised by protonation and a hydrogen bond from the proton to the solvent water, and so this becomes an explicit intermediate in the potential energy surface.

    Intermediate in reaction. Click for 3D

This intermediate now collapses along path (b) to the final product, via the transition state shown below. Again, an IRC shows a solvent bridge allows X to be concertedly transferred, this time from the oxygen to form hydronium chloride and 2 (I have not yet found the equivalent pathway to 3, but given the hydrogen bonds involved it is bound to be different).

Second transition state TS2. Click for 3D 

ΔG† (kcal/mol) along this sequence is 1 (0.0), TS1 (28.2), Int (8.0), TS2 (12.6); the intermediate existing only in a shallow well of 4.6 kcal/mol. The activation barrier is on the high side (the reaction occurs easily at room temperature), and it might be expected that (in part) this might be due to using X=H+ rather than X=Na+ for the model. Watch this space!

What might we conclude from this? That the presence of additional molecules (H3O+ and H2O) can result in structures which can depend on other features of the molecule, in this case the carbonyl group, one that plays little role in mechanism (a). In path (b), the carbonyl group is far from passive, receiving and then releasing X during the course of the reaction. This must mean that the transition state for forming product 2 may indeed be a separate one from the transition state for forming product 3, since the relationship of these two to the carbonyl is different. To re-quote Steve again “I think most organic chemists hold dear to their hearts the notion that selectivity is due to crossing over different transition states”.

Perhaps the explanation might indeed be due to different transition states rather than different dynamics? Clearly, more research needs to be done; I for one do not regard the case as closed on this example just yet.

References

  1. X.S. Bogle, and D.A. Singleton, "Dynamic Origin of the Stereoselectivity of a Nucleophilic Substitution Reaction", Organic Letters, vol. 14, pp. 2528-2531, 2012. https://doi.org/10.1021/ol300817a

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Why are α-helices in proteins mostly right handed?

Saturday, April 9th, 2011

Understanding why and how proteins fold continues to be a grand challenge in science. I have described how Wrinch in 1936 made a bold proposal for the mechanism, which however flew in the face of much of then known chemistry. Linus Pauling took most of the credit (and a Nobel prize) when in a famous paper in 1951 he suggested a mechanism that involved (inter alia) the formation of what he termed α-helices. Jack Dunitz in 2001 wrote a must-read article on the topic of “Pauling’s Left-handed α-helix” (it is now known to be right handed).  I thought I would revisit this famous example with a calculation of my own and here I have used the ωB97XD/6-311G(d,p) DFT procedure to calculate some of the energy components of a small helix comprising (ala)6 in both left and right handed form.

Firstly, it is important to note that Pauling was apparently not aware of the absolute handedness of amino acids (which are (S) in CIP terminology). This had in fact only been established a few months before Pauling’s publication by Bijvoet, and news of this might not have reached Pauling. So Pauling guessed (or perhaps, he had already built his models, and did not have time to reconstruct them) and his famous α-helix diagram turned out to be the enantiomer of the real McCoy. As with DNA itself, the helix bears a diastereomeric relationship to the chirality of the amino acids; both have to be inverted to get the proper enantiomer (which is what Pauling did). The secret that Pauling had discovered was hydrogen bonding, and particular, weak N-H…O=C interactions (Wrinch had thought it was strong covalent N-C-OH bonding instead). Of course, there are other effects at work, which include van der Waals or dispersion interactions, electrostatic effects resulting from the large dipoles in peptides (not least due to the zwitterionic character), the planarity of the peptide bond itself, the potential for other types of hydrogen bond (e.g. C-H…O) and entropic effects. I have split some of these down for left and right handed forms of DNA in another post.

It turns out calculating most of these effects on an even-handed basis is not that easy. Only the recent advent of dispersion-corrected DFT procedures, together with solvation algorithms that allow for accurate geometry optimisation and subsequent evaluation of free energies allows such a calculation to be performed. Hitherto, it has been mostly molecular mechanics that has been used (which itself relies on many parameters from quantum mechanics, such as atom charges, and explicitly identifying interactions for hydrogen bonding). By returning to a quantum-mechanical model, some of these assumptions inherent in the mechanics method need not be made.

We showed in 1991 that an effective solvation treatment required for the zwitterionic form of amino acids in aqueous solutions would ideally comprise not only a self-consistent-reaction-field, but also explicit water molecules as solvent. Here only the former solvation term is included, but expanding the model to include water is certainly possible. Both the zwitterionic and the neutral forms of (ala)6 are included below, so that the effect of a large dipole on the structure and relative helical stability can be estimated. One notes that (even in a dielectric cavity corresponding to water), the extended zwitterions are high energy species.  In a protein, they of course would be stabilized by the immediate environment of the ions. The right-handed helix clearly comes out as more stable (by about 1 kcal/mol per residue, see also DOI: 10.1021/ja960665u),  but this is not really due to either dispersion effects or entropy and must therefore arise largely from the hydrogen-bond like interactions. Ionizing the termini to form a zwitterion increases the propensity for a right handed helix slightly.

Relative thermodynamic energies (kcal mol-1) of (ala)6 α-helices
System Total energy Dispersion ΔΔH298 Δ(T.ΔS298) ΔΔG298
Left, neutral 0.0
 0.0 0.0 0.0 0.0
Right, neutral -4.0
 +0.2 -4.0 0.9 -4.9
Left, zwitterion 0.0 0.0 0.0 0.0 0.0
Right, zwitterion -7.1 0.1 -6.3 1.7 -8.0

Shown below are the calculated structures. The chains have (inter alia) unusual bifurcated hydrogen-bonding interactions, between one carbonyl group and two N-H groups (show as atom with halo). These are not quite the models that Linus Pauling built!

Left handed. Click for 3D

Right handed. Click for 3D

Left handed zwitterion. Click for 3D

Right handed zwitterion. Click for 3D

For a more objective analysis of the interactions within the system, a QTAIM analysis is shown below.

Left helix. Bond critical points in green. Click for 3D.

Right helix. Click for 3D

Whilst the overall conclusion is that theory agrees well with the experimental observation that peptide sequences tend to coil into right rather than left handed helices,  the reasons they do so is a little more subtle than simple model building alone can reveal.  As the AIM shows, a plethora of unusual and weaker interactions occur within these helices, a full analysis of which must await presentation elsewhere.

An NCI analysis reveals strong hydrogen bonds as blue-shaded surfaces.

NCI surface. Click for 3D.

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Do electrons prefer to move in packs of 4, 6 or 8 during proton exchange in a calixarene?

Friday, January 7th, 2011

This story starts with a calixarene, a molecule (suitably adorned with substituents) frequently used as a host to entrap a guest and perchance make the guest do something interesting. Such a calixarene was at the heart of a recent story where an attempt was made to induce it to capture cyclobutadiene in its cavity.

The basic skeleton of a calixarene

At the base of the calixarene are four hydroxyl groups, arranged in either a left or right handed manner. The molecule, in other words is chiral (C4 symmetry to be precise). As a chiral molecule, it might trap left and right-handed guests in a slightly different manner (forming two possible diastereomeric host-guest complexes).  As it happens, the guest in the cyclobutadiene story was just such a chiral molecule. But an essential question to ask is what the barrier to enantiomerization of such a calixarene might be?  One can envisage several ways of accomplishing such a conversion.

Enantiomerization pathways for a chiral calixarene

All four hydrogens can be moved in a single step, one might move two at a time in two steps, or one might move one at a time in four steps. These processes would involve respectively 8, 6 or 4 electrons in each step. There is a fundamental difference between the first pathway and the last two;  the latter involve  ionic intermediates (zwitterions) whereas the first is neutral. As such one might imagine the process would depend on the ability of the solvent to stabilize any such zwitterion.

Let us start with a gas phase model (ωB97XD/6-311G(d,p)), and a transition state with one negative force constant is indeed found with  C4v symmetry. The free energy barrier ΔG† for the process is 14.0 kcal/mol, which means the reaction will occur rapidly, even at lower temperatures of  ~200K. A pack size of 8 seems preferred for this model. This is hardly a surprise since the formation of ionic intermediates would not be expected. One might however speculate thus. In the schematic above, n=1 and one might be tempted to ask if higher values of n (lets say  n=2, a pack size of 10, or n=3, a pack size of 12, etc ) might exhibit similar behaviour. Is there any limit to the ring/pack size for this type of proton exchange?

Transition state for enantiomerization of a calixarene in the gas phase. Click for 3D.

What about in solution? Well, let us apply the mildest of solvents, benzene as a so-called continuum field. This has a very low dielectric (2.3) and you might imagine it would have hardly any effect. Well click on the below. The C4v geometry now has three computed negative force constants; the two additional ones are shown below (they are degenerate with a wavenumber of 101i cm-1).

C4v symmetric geometry for calixarene in benzene solvent, with three negative force constants. Click for animation of E mode.

C4v geometry for calixarene in benzene. Click for animation of second E mode.

Each of these additional two negative force constants shows a displacement heading towards the zwitterion shown in the scheme below. As one increases the polarity of the solvent, so the force constant becomes more negative. Thus for dichloromethane, it is now 322i cm-1 and with water it is 376i cm-1

So now the question is what happens when either of the two additional negative force constants is followed downhill? Will it form a true zwitterion (which would have Cs symmetry), in which case it would be (two) 6 electron processes to enantiomerize the calixarene instead of one 8 electron one.

True transition state for proton exchange in solution phase calixarene

In fact this geometry of Cs symmetry, which does resemble the zwitterion shown in the scheme above, is NOT a minimum but a true transition state itself (the free energy barrier hardly changed from the value for the gas phase). So the answer seems to be that a calixarene enantiomerizes via transition state not of C4v but of Cs symmetry, and which resembles a zwitterion but is not actually one. The 8-packof electrons was tempted to take a short rest-break on their way to shifting the four protons, but in the end did it in a single journey! So we have an unusual zwitterionic but nevertheless concerted transition state for the process.

Still unresolved is whether such cyclic transfer of four protons between four oxygen atoms continues to be concerted for larger rings, or whether the system is finally tempted to break up the transfer by resting with one or more discrete intermediates along the way. I finally note that in the calixarene reported which catalysed the thoughts above, the four oxygens are capped with a guanidinium cation sitting just above them, and this too may have an interesting effect on the proton transfer process.

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