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Free energy relationships and their linearity: a test example.

Sunday, January 13th, 2019

Linear free energy relationships (LFER) are associated with the dawn of physical organic chemistry in the late 1930s and its objectives in understanding chemical reactivity as measured by reaction rates and equilibria.

The Hammett equation is the best known of the LFERs, albeit derived “intuitively”. It is normally applied to the kinetics of aromatic electrophilic substitution reactions and is expressed as;

log KR/K0 = σRρ (for equilibria) and extended to log kR/k0 = σRρ for rates.

The equilibrium constants are normally derived from the ionisation of substituted benzoic acids, with K0 being that for benzoic acid itself and KR that of a substituted benzoic acid, with σR being known as the substituent constant and ρ the reaction constant. The concept involved obtaining the substituent constants by measuring the ionisation equilibria. The value of σR is then assumed to be transferable to the rates of reaction, where the values can be used to obtain reaction constants for a given reaction. The latter would then be assumed to give insight into the electronic nature of the transition state for that reaction.

The term log kR/k0 (the ratio of rates of reaction) can be related to ΔΔG = -RT ln kR/k0 and this latter quantity can be readily obtained from quantum calculations, where ΔΔG is the difference in computed reaction activation free energies for two substituents (of which one might be R=H). The most interesting such Hammett plots are the ones where a discontinuity becomes apparent. The plot comprises two separate linear relationships, but with different slopes. This is normally taken to indicate a change of mechanism, on the assumption that the two mechanisms will have different responses to substituents. 

A test of this is available via the calculated activations energies for acid catalyzed cyclocondensation to give furanochromanes[1] which is a two-step reaction involving two transition states TS1 and TS2, either of which could be rate determining. A change from one to the other would constitute a change in mechanism. In this example, TS1 involves creation of a carbocationic centre which can be stabilized by the substituent on the Ar group; TS2 involves the quenching of the carbocation by a nucleophilic oxygen and hence might be expected to respond differently to the substituents on Ar. As it happens, the reaction coordinate for TS2 is not entirely trivial, since it also includes an accompanying proton transfer which might perturb the mechanism.

Fortunately for this reaction we have available full FAIR data (DOI: 10.14469/hpc/3943), which includes not only the computed free energies for both sets of transition states but also the entropy-free enthalpies for comparison. This allows the table below to be generated. For each substituent, the highest energy point is in bold, indicating the rate limiting step. The span of substituents corresponds to a range of rate constants of almost 1010, which in fact is rarely if ever achievable experimentally.

Highest free energy overall route for HCl catalysed mechanism,

trans stereochemistry
Sub ΔH‡/ΔG‡ Reactant ΔH‡/ΔG‡, TS1 ΔH‡/ΔG‡, TS2 RDS
p-NH2 0.2/6.36 0.0/0.0 0.15/4.0 0.2/6.4 TS2/TS2
p-OMe 2.7/8.48 0.0/0.0 2.7/8.45 2.1/8.48 TS1/TS2
p-Me 5.5/10.00 0.0/0.0 5.5/9.9 3.9/10.00 TS1/TS2
p-Cl 7.7/12.28 0.0/0.0 7.7/12.28 5.9/11.84 TS1/TS1
p-H 7.6/13.01 0.0/0.0 7.6/13.01 5.5/11.51 TS1/TS1
p-CN 10.6/18.02 0.0/0.0 10.6 /17.61 10.5/18.02 TS1/TS2
p-NO2 12.4/19.85 0.0/0.0 12.4/18.24 12.0/19.85 TS1/TS2

For the free energies, you can see that TS2 is the rate limiting step for the first two electron donating substituents, and the last two electron withdrawing ones, whilst TS1 represents the rate limiting step for the middle substituents. This represents two changes of rate limiting step over the entire range of substituents. A different picture emerges if only the enthalpies are used. Now TS1 is rate limiting for essentially all the substituents. The difference of course arises because of significant changes to the entropy of the transition states. The Hammett equation, and its use of  σR constants to try to infer the electronic response of a reaction mechanism, does not really factor in entropic responses. Nor is it often if at all applied using a really wide range of substituents. So any linearity or indeed non-linearity in Hammett plots may correspond only very loosely to the underlying mechanisms involved.

Starting in the 1940s and lasting perhaps 40-50 years, thousands of different reaction mechanisms were subjected to the Hammett treatment during the golden era of physical organic chemistry, but very few have been followed up by exploring the computed free energies, as set out above. One wonders how many of the original interpretations will fully withstand such new scrutiny and in general how influential the role of entropy is.

References

  1. C.D. Nielsen, W.J. Mooij, D. Sale, H.S. Rzepa, J. Burés, and A.C. Spivey, "Reversibility and reactivity in an acid catalyzed cyclocondensation to give furanochromanes – a reaction at the ‘oxonium-Prins’ <i>vs.</i> ‘<i>ortho</i>-quinone methide cycloaddition’ mechanistic nexus", Chemical Science, vol. 10, pp. 406-412, 2019. https://doi.org/10.1039/c8sc04302g

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Early "curly" (reaction) arrows. Those of Ingold in 1926.

Wednesday, August 22nd, 2018

In 2012, I wrote a story of the first ever reaction curly arrows, attributed to Robert Robinson in 1924. At the time there was a great rivalry between him and another UK chemist, Christopher Ingold, with the latter also asserting his claim for their use. As part of the move to White City a lot of bookshelves were cleared out from the old buildings in South Kensington, with the result that yesterday a colleague brought me a slim volume they had found entitled The Journal of the Imperial College Chemical Society (Volume 6).‡ 

This journal is a record of lectures given to the chemistry department by visiting speakers, this one dating from 1926, about two years after the article by Robinson noted above.

There are a number of points of interest.

  1. Early on, Ingold introduces the topic of atoms in combination. Lewis (who is acknowledged to have introduced this concept in 1916) is mentioned in parentheses, if not actually in passing, as generalizing (Lewis) from this case, … As was the practice at the time, referencing one’s sources was not always common, and you do not here get an actual citation for Lewis!
  2. Next comes the topic changes in molecular structure (which could be a synonym for reactions) and here you get this diagramA modern version is shown below, scarcely different!
  3. Whilst the first example has examples such as SN1 ionizations, the second is perhaps not as common as might be imagined. It would only work if atom C (assuming it to be carbon) was e.g. a carbene (with six valence electrons) converting to a vinyl carbanion (with eight). Although we may speculate that Ingold thought that the second example might relate to common reactions, in the event both curly arrows are still entirely valid by modern standards. There is no acknowledgement of Robinson’s 1924 effort.
  4. Ingold goes on to discuss substitution patterns in benzene derivatives, and the o/p or m-directing abilities of substituents. He concludes that the Dewar formula for benzene is the most satisfactory vehicle for expressing the theory that electrical disturbances readily reach the o- and p-position, whilst only a small second order effect can reach the m-position. Here I think we can conclude that this approach has not survived into modern thinking. Robinson in his 1924 arrows had of course striven to explain the apparent propensity of nitrosobenzene towards electrophilic substitution in the p-position. Henry Armstrong some thirty years earlier in 1887[1] had arguably already made a pretty decent start, without requiring the use of Dewar benzene.

I suspect those who have dug through the historical archives to cast light on the Robinson/Ingold rivalry may not have appreciated that the Journal of the Imperial College Chemical Society might have been an interesting source!

‡There were nine volumes produced during 1921-1930. It then morphed into The Scientific Journal of the Royal College of Science which continued for an unknown number of years.

References

  1. H.E. Armstrong, "XXVIII.—An explanation of the laws which govern substitution in the case of benzenoid compounds", J. Chem. Soc., Trans., vol. 51, pp. 258-268, 1887. https://doi.org/10.1039/ct8875100258

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Early “curly” (reaction) arrows. Those of Ingold in 1926.

Wednesday, August 22nd, 2018

In 2012, I wrote a story of the first ever reaction curly arrows, attributed to Robert Robinson in 1924. At the time there was a great rivalry between him and another UK chemist, Christopher Ingold, with the latter also asserting his claim for their use. As part of the move to White City a lot of bookshelves were cleared out from the old buildings in South Kensington, with the result that yesterday a colleague brought me a slim volume they had found entitled The Journal of the Imperial College Chemical Society (Volume 6).‡ 

This journal is a record of lectures given to the chemistry department by visiting speakers, this one dating from 1926, about two years after the article by Robinson noted above.

There are a number of points of interest.

  1. Early on, Ingold introduces the topic of atoms in combination. Lewis (who is acknowledged to have introduced this concept in 1916) is mentioned in parentheses, if not actually in passing, as generalizing (Lewis) from this case, … As was the practice at the time, referencing one’s sources was not always common, and you do not here get an actual citation for Lewis!
  2. Next comes the topic changes in molecular structure (which could be a synonym for reactions) and here you get this diagramA modern version is shown below, scarcely different!
  3. Whilst the first example has examples such as SN1 ionizations, the second is perhaps not as common as might be imagined. It would only work if atom C (assuming it to be carbon) was e.g. a carbene (with six valence electrons) converting to a vinyl carbanion (with eight). Although we may speculate that Ingold thought that the second example might relate to common reactions, in the event both curly arrows are still entirely valid by modern standards. There is no acknowledgement of Robinson’s 1924 effort.
  4. Ingold goes on to discuss substitution patterns in benzene derivatives, and the o/p or m-directing abilities of substituents. He concludes that the Dewar formula for benzene is the most satisfactory vehicle for expressing the theory that electrical disturbances readily reach the o- and p-position, whilst only a small second order effect can reach the m-position. Here I think we can conclude that this approach has not survived into modern thinking. Robinson in his 1924 arrows had of course striven to explain the apparent propensity of nitrosobenzene towards electrophilic substitution in the p-position. Henry Armstrong some thirty years earlier in 1887[1] had arguably already made a pretty decent start, without requiring the use of Dewar benzene.

I suspect those who have dug through the historical archives to cast light on the Robinson/Ingold rivalry may not have appreciated that the Journal of the Imperial College Chemical Society might have been an interesting source!

‡There were nine volumes produced during 1921-1930. It then morphed into The Scientific Journal of the Royal College of Science which continued for an unknown number of years.

References

  1. H.E. Armstrong, "XXVIII.—An explanation of the laws which govern substitution in the case of benzenoid compounds", J. Chem. Soc., Trans., vol. 51, pp. 258-268, 1887. https://doi.org/10.1039/ct8875100258

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Is (hν)3 an allotrope of light?

Friday, February 23rd, 2018

A little while ago I pondered allotropic bromine, or Br(Br)3. But this is a far wackier report[1] of a molecule of light.

The preparation and detection of dimer and trimer bound photon states is pure physics; probably considered by the physicists themselves as NOT chemistry. It is certainly true, as a chemist,  that I understood only a little of the article. But chemistry uses photons extensively in the area we call photochemistry. We represent photons as hν, and hence (hν)3.

This molecular light has some fascinating properties. One is that it travels around 100,000 times slower than the usual speed of light. Another is the estimate of the photon-photon binding energies, which are ~1010 times smaller than in diatomic molecules such as NaCl and H2. I await with interest to see whether this new state of light will achieve any interesting chemistry.

References

  1. Q. Liang, A.V. Venkatramani, S.H. Cantu, T.L. Nicholson, M.J. Gullans, A.V. Gorshkov, J.D. Thompson, C. Chin, M.D. Lukin, and V. Vuletić, "Observation of three-photon bound states in a quantum nonlinear medium", Science, vol. 359, pp. 783-786, 2018. https://doi.org/10.1126/science.aao7293

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PIDapalooza 2018: the open festival for persistent identifiers.

Tuesday, November 14th, 2017

PIDapalooza is a new forum concerned with discussing all things persistent, hence PID. You might wonder what possible interest a chemist might have in such an apparently arcane subject, but think of it in terms of how to find the proverbial needle in a haystack in a time when needles might look all very similar. Even needles need descriptions, they are not all alike and PIDs are a way of providing high quality information (metadata) about a digital object.  

The topics for discussion along with descriptions are now available at https://pidapalooza18.sched.com/list/descriptions/ and yes, before you ask, the event has its own PID (DOI: 10.5438/11.0002). Check out the speakers at https://pidapalooza18.sched.com/directory/speakers. I will be telling some stories from chemistry, and who knows, even some of the posts on this blog might feature. And if you do not brush up on the topic, no doubt your librarian, your funding body and your publisher will be telling you about it soon!

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OpenCon (2016)

Friday, November 25th, 2016

Another conference, a Cambridge satellite meeting of OpenCon, and I quote here its mission: “OpenCon is a platform for the next generation to learn about Open Access, Open Education, and Open Data, develop critical skills, and catalyze action toward a more open system of research and education” targeted at students and early career academic professionals. But they do allow a few “late career” professionals to attend as well!

I could only attend the morning session, for which the keynote speaker was Erin McKiernanorcid The presentation was entitled How open science helps researchers succeed, presented as an exploration of an article written by Erin and colleagues with the same name and published in eLife[1] Erin has created a support page at http://whyopenresearch.org to augment the presentation and it’s well worth a visit.

One striking point made was the assertion that Open publications get more citations! 
Open publications get more citations

As with many metrics of the impacts of the science publication processes, a citation itself lacks the context of why it was made (see this post for further discussion), but the expectation is that a citation is “good”. From my perspective as a chemist, I did wonder why molecular science was missing from the graphic above. Do open chemistry publications also get more citations?

Which brings me to another point made during the talk, the increasingly controversial aspect of (journal) impact factors and the pressure placed on early career researchers to publish only in those with “high” impact factors, and for their careers to be assessed at least in part based on these and the anticipated “h-index”. The audience was indeed encouraged to go visit http://www.ascb.org/Dora/ (Declaration on Research Assessment, or Putting science into the assessment of research). Have you signed it yet?

Another manifestation of the modern trend to analyse impact metrics is the site Impactstory.org. This is a scripted resource that starts from your ORCID identifier and (optionally) your Twitter account (yes, apparently Tweets matter!) to derive a more complex alternative metric of a individual’s impacts. I had not tried this one before and so I submitted my ORCID and my Twitter account, and watched as the system went off to http://orcid.scopusfeedback.com (Scopus is an Elsevier product) to attempt to create my profile. It ground for quite a while, reporting initially that I had no publications! This was followed by an unexpected error; I did not get my impact back! But this experiment served to highlight one aspect that was discussed at the meeting; data and other research objects. The graphic above refers only to the citation of journal articles, it does not yet include the citation of data. However ORCID DOES include data and research objects as works.  And because the granularity of my data and research objects is very fine (one molecule = one work), I have quite a few. In fact ~200,000! ORCID gets to about 8000 before it gives up. I suspect http://orcid.scopusfeedback.com queries ORCID, gets back ~8000 entries and crashes. No doubt the programmer tasked with implementing this resource did not anticipate that any individual could accumulate 8000+ entries! Or probably factor in that the vast majority of these would of course not be journal articles but data. If the site gets back to me about the crash I experienced, I will update here.

Simon Deakin was the next speaker with (open) data as the focus and the worries many researchers have in being scooped by others who have re-used your open data without proper attributions. The discussion teased out that if data is properly deposited, it will indeed have full associated metadata and in particular a date stamp that could help protect an author’s interests.

It was really good to meet so many early career researchers who espouse the open ethos. Perhaps, in 20 years time,  another graphic akin to the one above might demonstrate that open researchers get more promotions!

References

  1. E.C. McKiernan, P.E. Bourne, C.T. Brown, S. Buck, A. Kenall, J. Lin, D. McDougall, B.A. Nosek, K. Ram, C.K. Soderberg, J.R. Spies, K. Thaney, A. Updegrove, K.H. Woo, and T. Yarkoni, "How open science helps researchers succeed", eLife, vol. 5, 2016. https://doi.org/10.7554/elife.16800

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Posted in Chemical IT, General | 3 Comments »

The demographics of a blog readership – updated

Thursday, January 8th, 2015

About two years ago, I posted on the distribution of readership of this blog. The passage of time has increased this from 144 to 176 countries. There are apparently between 189-196 such, so not quite yet complete coverage! 2015
Of course, it is the nature of the beast that whilst we can track countries, very little else is known about such readerships. Is the readership young or old, student or professor, chemist or not (although I fancy the latter is less likely). Another way of keeping tabs on some of the activity are aggregators such as Chemical Blogspace, which has been rather quiet recently. Perhaps we have become too obsessed by metrics, and with the Internet-of-things apparently the “next-big-thing”, the metrics are only likely to increase. This will only encourage “game playing“, and I urge you to see a prime example of this in the UK REF (research excellence framework), the measure which attempts to rank UK universities in terms of their “excellence”.

Ah well, I had better leave this blog and go off and check on my h-index just in case it has notched up another integer.

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Chemistry in the early 1960s: a reminiscence.

Monday, December 22nd, 2014

I started chemistry with a boxed set in 1962. In those days they contained serious amounts of chemicals, but I very soon ran out of most of them. Two discoveries turned what might have been a typical discarded christmas present into a lifelong career and hobby.

The first was 60 Stoke Newington High Street in north London, the home of Albert N. Beck, Chemist (or his son; my information comes from a historical listing of the shops present on the high street in 1921). I would set out from our home in London SW6 on the #73 bus route (top deck) and it would take about an hour to arrive. On entering the shop, I ventured down a set of stairs into the basement to replenish the chemicals with sensible stocks, and purchase the odd glassware, filter paper, etc. And then venture back across London carrying the proceeds of many weeks, possibly months worth of hoarded pocket-money (apart that is from 1 shilling every two weeks which I reserved for football at Craven Cottage). At some stage, health and safety legislated against 12-year-old boys (and certainly also girls) purchasing chemicals in this manner! However, I can assure you all that I never came to any harm with anything I purchased at A. N. Beck and Sons. Apart that is from giving my parents a good fright.

The second was coming across this book by A. J. Mee. I had thought it was well and truly lost; imagine my delight when I recently found it at home, complete with chemical stains, and dated as from a reprint in 1959.

IFOn the inside cover, I found one shopping list from my expeditions to A. N. Beck and Sons. The price 1/6 is the representation of one shilling and six pence (more than the price of a football match, or perhaps £50 in today’s money? I think football was much cheaper then! Oh, 1/6 is 7.5p in the decimal currency of today, or £0.075). Note that iodine was one of the items purchased. And note the wish list at the bottom! I was clearly starting to do organic chemistry.

shopping-list

The pages of this book list 289 experiments, and I assiduously recorded a tick against all the ones I actually did. This is a typical page (click to expand).

IFThus expt 205 is the preparation of 1,3,5-tribromobenzene from 1,3,5-tribromoaniline (ticked), followed by that of o-cresol from o-toluidine (ticked). You can see how all the aromatic rings are still represented by what now looks like cyclohexane. This book gave me many hours of delightful recreation (I have not counted the ticks, but I think I attempted around half the experiments). Note in particular the huge scale these experiments were done at; 18g of product (I suspect I must have scaled them down a fair bit in order to preserve pocket money). Expt 198 was that of benzidine, of which I do recollect preparing  ~2g. No warnings then about the extremely carcinogenic nature of this substance! Chemistry has certainly changed since then.

Lost unfortunately is the laboratory book where I recorded my results, but one or two samples still exist!

 

 

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Posted in Historical | 60 Comments »

Ribulose-1,5-bisphosphate + carbon dioxide → carbon fixation!

Sunday, April 20th, 2014

Ribulose-1,5-bisphosphate reacts with carbon dioxide to produce 3-keto-2-carboxyarabinitol 1,5-bisphosphate as the first step in the biochemical process of carbon fixation. It needs an enzyme to do this (Ribulose-1,5-bisphosphate carboxylase/oxygenase, or RuBisCO) and lots of ATP (adenosine triphosphate, produced by photosynthesis). Here I ask what the nature of the uncatalysed transition state is, and hence the task that might be facing the catalyst in reducing the activation barrier to that of a facile thermal reaction. I present my process in the order it was done‡.

carboxFirstly, I will hypothesize that since C3 needs to lose a hydrogen, the easiest way of doing so is to form the enol of Ribulose-1,5-bisphosphate. I am going to start by reducing the above model to its core; C1 and the attached phosphate is replaced by a methyl, and C4-5 likewise. In this model, it takes 13.1 kcal/mol of free energy to enolize.[1],[2] This species can then react with CO2 (potentially with an accompanying proton transfer) to give 3-keto-2-carboxyarabinitol 1,5-bisphosphate directly. The transition state at the ωB97XD/6-311G(d,p)/SCRF=water level[3] has an IRC (intrinsic reaction coordinate)[4] that reveals the activation barrier is ~17 kcal/mol with respect to the enol (19.5 in ΔG298), with the overall reaction[5] being exo-energic by -2.6 kcal/mol with respect to the enol, but endo-energic by +10.5 kcal/mol with respect to keto-Ribulose-1,5-bisphosphate + carbon dioxide. Note the characteristic feature at IRC -3.0 of a hidden zwitterionic intermediate, which marks a belated proton transfer occurring AFTER the transition state for C-C bond formation. The reaction is asynchronous for this basic model.
carbox
carboxE
carboxG
For this very basic (phosphate-free) model of Ribulose-1,5-bisphosphate, the total computed free energy barrier@298K is 32.6 kcal/mol (standard state of 0.041M; reduced by ~1.9 kcal/mol for more concentrated, e.g. 1M solutions). This is ~13 kcal/mol too high to correspond to a uncatalysed fast process at room temperatures, a gap that the phosphate end-groups and the enzyme have to address (a challenge typically enzymes do manage to achieve).

With a basic model in place, it is time to restore those truncated phosphate end-groups to see what their contribution might be (treated as dianions each for the time being, and stabilized by using a continuum solvent field for water). First, the energies:

System ΔΔG Data DOI
Ribulose-1,5-bisphosphate as keto + CO2  0.0 [6]
Ribulose-1,5-bisphosphate as enol + CO2 13.0 [7]
Transition state 34.8 [8]
Acyclic 3-keto-2-carboxyarabinitol 1,5-bisphosphate 11.5 [9]
Cyclic 3-keto-2-carboxyarabinitol 1,5-bisphosphate -7.3 [10]

Note the network of hydrogen bonds formed at the transition state geometry (below) and the various gauche stereo-electronic alignments[11] which you should really explore in the Jmol 3D model invoked by clicking below.

carbox-TS

Click for 3D

  1. Addition of the phosphate groups has little effect on the energetics of the keto/enol equilibrium,
  2. or on the barrier to reaction with  carbon dioxide.
  3. But, they DO provide a new low energy sink I have not seen described before for the reaction (below), which makes the overall process from Ribulose-1,5-bisphosphate + CO2 exo-energic by -7.3 kcal/mol. Thus the phosphates provide the overall thermodynamic driving force for the carbon fixation.

    Click for 3D

    Click for 3D. Cyclic low-energy cyclic chair isomer of 3-keto-2-carboxyarabinitol 1,5-bisphosphate

  4. Which leaves the role of the enzyme as one of reducing the overall activation barrier. The reaction MUST be enzymatically favoured, since the enzyme also needs to control when the cycle occurs, via a light-sensitive switch. If no enzyme-catalysis were needed, then carbon-fixation would occur in the dark, and consume all available ATP in the process. Inferred purely from the results in the table above, two functions can be listed:
    • The enzyme can help increase the effective molarity of the bimolecular reaction between Ribulose-1,5-bisphosphate + CO2. As noted above, increasing the concentration from e.g. 1 atmosphere (0.041M) to 1M reduces ΔG† by 1.9 kcal/mol.
    • The most influential role the enzyme could play is to bind the enol form of Ribulose-1,5-bisphosphate preferentially over the keto form. If most of the substrate is bound in this form, that would reduce the overall barrier by 13 kcal/mol, more than enough to enable a room temperature reaction.
    • There may of course be many other subtle effects in operation, such as preferential stabilisation of the transition state, which cannot be inferred here without a detailed knowledge of the enzyme. I have deliberately tried to avoid doing that, since I wanted to see what might be concluded purely from the energetics found above.

There is one final step required; a very rapid decomposition of the 3-keto-2-carboxyarabinitol 1,5-bisphosphate (cyclic or not) to produce two molecules of 3-phosphoglycerate. I will leave my computational-energetic analysis and mechanism of that step to another post.

Postscript. An IRC on the full phosphate model took three days to run and has only just finished.[12] The profile is similar to that obtained for the phosphate-free model, with the exception of the IRC feature at -13, where one phosphate group rotates and starts to H-bond to the 3-keto-2-carboxyarabinitol, resulting in a lower energy conformation than that reported above. The energy of this new conformation[13] relative to the starting point (labelled as 0.0 above) is +2.3 kcal/mol (c.f. +11.5 for the previous conformation). The phosphates clearly remain a strong driving force for the reaction. It is quite possible that even more stable forms of this product could be found (by varying where the acidic protons reside) but at least we now know that the product can be more stable than the reactant (by at least -7.3 kcal/mol), which is the important conclusion.
carbox-prod1E
carbox-prod1G

Postscript 1. Yet another lower energy isomer of the product has popped out[14] being -13.1 kcal/mol lower than the initial reactants.

‡I do not describe much molecular biology on this blog, but an urge to rectify this was inspired by a TV program I watched four days ago charting how the pathway chronologically known first as the Calvin, then the Calvin-Benson and now the Calvin-Benson-Bassham cycle for carbon fixation became known (and how it gradually gathered attribution). As a chemist who was trained to try to understand reaction mechanisms, my immediate question (unsurprisingly not addressed at all in the TV program) was: what is the key carbon-carbon bond forming step? Here, I simply wanted initially to answer that one simple question and perhaps the aspect of the relative timing of any C-C bond formation and associated proton transfer. This latter idea in turn was hovering in the background of my mind from association with our previous project in proline-catalysed aldol reactions, where a similar question can be posed and indeed has been answered.[15] The rest of what you see here led directly from trying to answer that initial question. Peter Medawar’s 1963 talk Is the scientific paper a fraud? presented the argument that scientific journal articles give a misleading idea of the actual process of scientific discovery[16]. I hope that perhaps as a blog post, the above does give a little insight into the scientific process I experienced for myself over a period of the last two days (and with conclusions which may of course turn out to be quite wrong).

References

  1. H.S. Rzepa, "Gaussian Job Archive for C5H8O4", 2014. https://doi.org/10.6084/m9.figshare.1004015
  2. H.S. Rzepa, "Gaussian Job Archive for C5H8O4", 2014. https://doi.org/10.6084/m9.figshare.1004023
  3. H.S. Rzepa, "Gaussian Job Archive for C5H8O4", 2014. https://doi.org/10.6084/m9.figshare.1004011
  4. H.S. Rzepa, "Gaussian Job Archive for C5H8O4", 2014. https://doi.org/10.6084/m9.figshare.1004037
  5. H.S. Rzepa, "Gaussian Job Archive for C5H8O4", 2014. https://doi.org/10.6084/m9.figshare.1004038
  6. H.S. Rzepa, "Gaussian Job Archive for C6H8O13P2(4-)", 2014. https://doi.org/10.6084/m9.figshare.1004086
  7. H.S. Rzepa, "Gaussian Job Archive for C6H8O13P2(4-)", 2014. https://doi.org/10.6084/m9.figshare.1004066
  8. H.S. Rzepa, "Gaussian Job Archive for C6H8O13P2(4-)", 2014. https://doi.org/10.6084/m9.figshare.1004112
  9. H.S. Rzepa, "Gaussian Job Archive for C6H8O13P2(4-)", 2014. https://doi.org/10.6084/m9.figshare.1004085
  10. H.S. Rzepa, "Gaussian Job Archive for C6H8O13P2(4-)", 2014. https://doi.org/10.6084/m9.figshare.1004111
  11. H.S. Rzepa, "Gaussian Job Archive for C6H8O13P2(4-)", 2014. https://doi.org/10.6084/m9.figshare.1004026
  12. H.S. Rzepa, "Gaussian Job Archive for C6H8O13P2(4-)", 2014. https://doi.org/10.6084/m9.figshare.1004557
  13. H.S. Rzepa, "Gaussian Job Archive for C6H8O13P2(4-)", 2014. https://doi.org/10.6084/m9.figshare.1004614
  14. H.S. Rzepa, "Gaussian Job Archive for C6H8O13P2(4-)", 2014. https://doi.org/10.6084/m9.figshare.1004778
  15. A. Armstrong, R.A. Boto, P. Dingwall, J. Contreras-García, M.J. Harvey, N.J. Mason, and H.S. Rzepa, "The Houk–List transition states for organocatalytic mechanisms revisited", Chem. Sci., vol. 5, pp. 2057-2071, 2014. https://doi.org/10.1039/c3sc53416b
  16. S.M. Howitt, and A.N. Wilson, "Revisiting “Is the scientific paper a fraud?”", EMBO reports, vol. 15, pp. 481-484, 2014. https://doi.org/10.1002/embr.201338302

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More joining up of pieces. Stereocontrol in the ring opening of cyclopropenes.

Thursday, July 12th, 2012

Years ago, I was travelling from Cambridge to London on a train. I found myself sitting next to a chemist, and (as chemists do), he scribbled the following on a piece of paper. When I got to work the next day Vera (my student) was unleashed on the problem, and our thoughts were published[1]. That was then.

This is now. I have just finished a post on ring-opening reactions of oxirene, a 4n electron anti-aromatic ring. I was casting around for an example of a calculation done just before the modern Internet era, and happened upon the above. Although this was a mere 20 years ago, much of the detail had faded; I had not thought much about it in the intervening years, but I did recollect that although we had attributed the high stereoselectivity shown above to a stereoelectronic orbital alignment, I was not entirely happy with the interpretation. Put simply, we had relied on a molecular orbital diagram, and this diagram (in resplendent colour in the journal, one of the few being so published at that time, and for no colour charge to boot) was just too complicated. Arguably it was the fixated complexity (I remember at the time that it looked complicated no matter what the viewing angle was) that set me on the road to the use of the Web, and ultimately here to this blog. So I thought a re-analysis using modern algorithms and presentation might help simplify. The newly recalculated transition state (ωB97XD/6-311G(d,p) looks like:

Transition state for ring opening of a cyclopropene. Click for 3D.

  1. The reaction is a 4n (n=1) electron electrocyclic ring opening, and so according to the rules, should proceed with the formation/cleavage of an antarafacial bond. You might think that there are not quite enough substituents to reveal this stereochemistry, but there are if the carbene lone pair is included. So how to add the lone pair?
  2. Well, its coordinates can be computed using the ELF (electron localisation function). The relevant lone pair is ringed in red below. Using (old technology, i.e. a static figure) you may choose to believe me when I argue that this lone pair is above the plane of the forming ring from the perspective shown, whilst the terminus of the bond it forms is to the bottom. This defines an antarafacial component. Well, I might have carefully manipulated the viewing angle to show this. Now, in 2012 rather than 1992, you can load the 3D coordinates by clicking below, and check for yourself!

    Lone pair centroid for the transition state. Click for 3D

  3. What about the stereo-control? Take a look at the angle between the axis of the C-Cl bond (atoms ringed in blue) and the centroid of the carbene lone pair (red). It is about 162°, or almost anti-periplanar. A magic orientation in organic chemistry. Time to attack the orbitals again. Our published diagram looked as below. It shows the HOMO aligning with the LUMO+2 (if your eyes are not distracted by all the other detail).
    But we can now simplify such a complex molecular orbital by using instead a localized version, an NBO. A little explanation is needed. The NBO orbital shown with red/blue phases is antibonding for the C-Cl bond. That with orange/purple is the carbene lone pair. Where orange overlaps with red, we have a positive overlap that stabilises the system. The NBO E2 perturbation energy is around 4.6 kcal/mol. Although this may seem small, it is actually quite large for a through-space interaction of this type. It is this stabilisation (amounting to ~ 1.6 kcal/mol in free energy) that accounts for the high selectivity for the stereoisomer shown above.

    NBO for transition state. Click for 3D.

Well, I think that the passage of 20 years has enabled us to tidy up the origins of the stereoelectronic effect responsible for controlling this reaction, and to produce clearer diagrams which the reader can interactively explore for themselves. It did take 20 years to join things up though!

References

  1. M.S. Baird, J.R. Al Dulayymi, H.S. Rzepa, and V. Thoss, "An unusual example of stereoelectronic control in the ring opening of 3,3-disubstituted 1,2-dichlorocyclopropenes", Journal of the Chemical Society, Chemical Communications, pp. 1323, 1992. https://doi.org/10.1039/c39920001323

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