Posts Tagged ‘chemical reaction’

Smoke and mirrors. All is not what it seems with this Sn2 reaction!

Thursday, April 4th, 2019

Previously, I explored the Graham reaction to form a diazirine. The second phase of the reaction involved an Sn2′ displacement of N-Cl forming C-Cl. Here I ask how facile the simpler displacement of C-Cl by another chlorine might be and whether the mechanism is Sn2 or the alternative Sn1. The reason for posing this question is that as an Sn1 reaction, simply ionizing off the chlorine to form a diazacyclopropenium cation might be a very easy process. Why? Because the resulting cation is analogous to the cyclopropenium cation, famously proposed by Breslow as the first example of a 4n+2 aromatic ring for which the value of n is zero and not 1 as for benzene.[1] Another example of a famous “Sn1” reaction is the solvolysis of t-butyl chloride to form the very stable tertiary carbocation and chloride anion (except in fact that it is not an Sn1 reaction but an Sn2 one!)

Here is the located transition state for the above, using Na+.6H2O as the counter-ion to the chloride. The calculated free energy of this transition state is 3.2 kcal/mol lower than the previous Sn2′ version (FAIR data collection, 10.14469/hpc/5045), with an overall barrier to reaction of 26.5 kcal/mol. This compares to ~24.5 kcal/mol obtained by Breslow for solvolysis of the cyclopropenyl tosylate. Given the relatively simple solvation model I used in the calculation (only six waters to solvate all the ions, and a continuum solvent field for water), the agreement is not too bad.

The animation above is of a normal vibrational mode known as the transition mode (click on the image above to get a 3D rotatable animated model). The calculated vectors for this mode (its energy being an eigenvalue of the force constant matrix) are regularly used to “characterise” a transition state. I will digress with a quick bit of history here, starting in 1972 when another famous article appeared.[2] The key aspect of this study was the derivation of the first derivatives of the energy of a molecule with respect to the (3N) geometrical coordinates of the atoms, using a relatively simply quantum mechanical method (MINDO/2) to obtain that energy. Analytical first derivatives of the MINDO/2 Hamiltonian were then used to both locate the transition state for a simple reaction and then to evaluate the second derivatives (the force constant matrix) using a finite difference method. That force constant matrix, when diagonalized, reveals one negative root (eigenvalue) which is characteristic of a transition state. The vectors reveal how the atoms displace along the vibration, and should of course approximate to the path to either reactant or product.

Since that time, it has been a more or less mandatory requirement for any study reporting transition state models to characterise them using the vectors of the negative eigenvalue. The eigenvalue invariably expressed as a wavenumber. Because this comes from the square root of the mass-weighted negative force constant, it is often called the imaginary mode. Thus in this example, 115i cm-1, the i indicating it is an imaginary number. The vectors are derived from quadratic force constants, which is a parabolic potential surface for the molecule. Since most potential surfaces are not quadratic, it is recognized as an approximation, but nonetheless good enough to serve to characterise the transition state as the one connecting the assumed reactant and product. Thousands of published studies in the literature have used this approach.

So now to the animation above. If you look closely you will see that it is a nitrogen and not a carbon that is oscillating between two chlorines (here it is the lighter atoms that move most). The vectors confirm that, with a large one at N and only a small one at C. So it is Sn2 displacement at nitrogen that we have located? 

Not so fast. This is a reminder that we have to explore a larger region of the potential energy surface, beyond the quadratic region of the transition state from which the vectors above are derived. This is done using an IRC (intrinsic reaction coordinate). Here it is, and you see something remarkable.

The Cl…N…Cl motions seen above in the transition state mode change very strongly in regions away from the transition state. On one side of the transition state, it forms a Cl…C bond, on the other side a Cl…N.

It is also reasonable to ask why the paths either side of the transition state are not the same? That may be because with only six explicit water molecules, three of which solvate the sodium ion, there are not enough to solvate equally the chloride anions either side of the transition state. As a result one chlorine does not behave in quite the same way as the other. The addition of an extra water molecule or two may well change the resulting reaction coordinate significantly.

The overall message is that there are two ways to characterise a computed reaction path. One involves looking at the motions of all the atoms just in the narrow region of the transition state. Most reported literature studies do only this. When the full path is explored with an IRC, a different picture can emerge, as here. The Cl…N…Cl Sn2 mode is replaced by a Cl…C/N…Cl mode. This example however is probably rare, with most reactions the transition state vibration and the IRC do actually agree!

References

  1. R. Breslow, "SYNTHESIS OF THE s-TRIPHENYLCYCLOPROPENYL CATION", Journal of the American Chemical Society, vol. 79, pp. 5318-5318, 1957. https://doi.org/10.1021/ja01576a067
  2. J.W. McIver, and A. Komornicki, "Structure of transition states in organic reactions. General theory and an application to the cyclobutene-butadiene isomerization using a semiempirical molecular orbital method", Journal of the American Chemical Society, vol. 94, pp. 2625-2633, 1972. https://doi.org/10.1021/ja00763a011

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The Graham reaction: Deciding upon a reasonable mechanism and curly arrow representation.

Monday, February 18th, 2019

Students learning organic chemistry are often asked in examinations and tutorials to devise the mechanisms (as represented by curly arrows) for the core corpus of important reactions, with the purpose of learning skills that allow them to go on to improvise mechanisms for new reactions. A common question asked by students is how should such mechanisms be presented in an exam in order to gain full credit? Alternatively, is there a single correct mechanism for any given reaction? To which the lecturer or tutor will often respond that any reasonable mechanism will receive such credit. The implication is that a mechanism is “reasonable” if it “follows the rules”. The rules are rarely declared fully, but seem to be part of the absorbed but often mysterious skill acquired in learning the subject. These rules also include those governing how the curly arrows should be drawn.† Here I explore this topic using the Graham reaction.[1]‡

I start by noting the year in which the Graham procedure was published, 1965. Although the routine representation of mechanism using curly arrows had been established for about 5-10 years by then, the quality of such representations in many articles was patchy. Thus, this one (the publisher will need payment for me to reproduce the diagram here, so I leave you to get it yourself) needs some modern tidying up. In the scheme below, I have also made a small change, using water itself as a base to remove a NH proton, rather than hydroxide anion as used in the article (I will return to the anion later). The immediate reason is that water is a much simpler molecule to use at the start of our investigation than solvated sodium hydroxide. You might want to start with comparing the mechanism above with the literature version[1] to discover any differences. 

The next stage is to compute all of this using quantum mechanics, which will tell us about the energy of the system as it evolves and also identify the free energy of the transition states for the reaction. I am not going to go into any detail of how these energies are obtained, suffice to say that all the calculations can be found at the following DOI: 10.14469/hpc/5045 The results of this exercise are represented by the following alternative mechanism.♥

How was this new scheme obtained? The key step is locating a transition state in the energy surface, a point where the first derivatives of the energy with respect to all the 3N-6 coordinates defining the geometry (the derivative vector) are zero and where the second derivative matrix has just one negative eigenvalue (check up on your Maths for what these terms mean). Each located transition state (which is an energy maximum in just one of the 3N-6 coordinates) can be followed downhill in energy to two energy minima, one of which is declared the reactant of the reaction and the other the product, using a process known as an IRC (intrinsic reaction coordinate). The coordinates of these minima are then inspected so they can be mapped to the conventional representations shown above. New bonds in the formalism above are shown with dashed lines and have an arrow-head ending at their mid-point; breaking bonds (more generally, bonds reducing their bond order) have an arrow starting from their mid-point. The change in geometry along the IRC for TS1 can then be shown as an animation of the reaction coordinate, which you can see below.

Don’t worry too much about when bonds appear to connect or disconnect, the animation program simply uses a simple bond length rule to do this. The major difference with the original mechanism is that it is the chlorine on the nitrogen also bearing a proton that gets removed. Also, the N-N bond is formed as part of the same concerted process, rather than as a separate step.

Shown above is the computed energy along the reaction path. Here a “reality check” can be carried out. The activation free energy (the difference between the transition state and the reactant) emerges as a rather unsavoury ΔG‡=40.8 kcal/mol. Why is this unsavoury? Well, according to transition state theory, the rate of a (unimolecular) reaction is given by the expression: Ln(k/T) = 23.76 – ΔG‡/RT where T is temperature (~323K in this example), R = is the gas constant and k is the unimolecular rate constant. When you solve it for ΔG‡=40.8, it turns out to be a very slow reaction indeed. More typically, a reaction that occurs in a few minutes at this sort of temperature has ΔG‡= ~15 kcal/mol. So this turns out to be an “unreasonable” mechanism, but based on the quantum mechanically predicted rate and not on the nature of the “curly arrows”. And no, one cannot do this sort of thing in an examination (not even on a mobile phone; there is no app for it, yet!) I must also mention that the “curly arrows” used in the above representation are, like the bonds, based on simple rules of connecting a breaking with a forming bond with such an arrow. There IS a method of computing both their number and their coordinates “realistically”, but I will defer this to a future post. So be patient!

The next thing to note is that the energy plot shows this stage of the reaction as being endothermic. Time to locate TS2, which it turns out corresponds to the N to C migration of the chlorine to complete the Graham reaction. As it happens, TS2 is computed to be 10.6 kcal/mol lower than TS1 in free energy, so it is not “rate limiting”.

To provide insight into the properties of this reaction path, a plot of the calculated dipole moment along the reaction path is shown. At the transition state (IRC value = 0), the dipole moment is a maximum, which suggests it is trying to form an ion-pair, part of which is the diazacylopropenium cation shown in the first scheme above. The ion-pair is however not fully formed, probably because it is not solvated properly.

We can add the two reaction paths together to get the overall reaction energy, which is no longer endothermic but approximately thermoneutral. Things are still not quite “reasonable” because the actual reaction is exothermic.

Time then to move on to hydroxide anion as the catalytic base, in the form of sodium hydroxide. To do this, we need to include lots of water molecules (here six), primarily to solvate the Na+ (shown in purple below) but also any liberated Cl–. You can see the water molecules moving around a lot as the reaction proceeds, via again TS1 to end at a similar point as before.

The energy plot is now rather different. The activation energy is now lower than the 15 kcal/mol requirement for a fast reaction; in fact ΔG‡= 9.5 kcal/mol and overall it is already showing exothermicity. What a difference replacing a proton (from water) by a sodium cation makes!

Take a look also at this dipole moment plot as the reaction proceeds! TS1 is almost entirely non-ionic!

To complete the reaction, the chlorines have to rearrange. This time a rather different mode is adopted, as shown below, termed an Sn2′ reaction. The energy of TS2′ is again lower than TS1, by 9.2 kcal/mol. Again no explicit diazacylopropenium cation-anion pair (an aromatic 4n+2, n=0 Hückel system) is formed.



Combing both stages of the reaction as before. The discontinuity in the centre is due to further solvent reorganisation not picked up at the ends of the two individual IRCs which were joined to make this plot. Note also that the reaction is now appropriately exothermic overall.

So what have we learnt?

  1. That a “reasonable” mechanism as shown in a journal article, and perhaps reproduced in a text-book, lecture or tutorial notes or even an examination, can be subjected in a non-arbitrary manner to a reality check using modern quantum mechanical calculations.
  2. For the Graham reaction, this results in a somewhat different pathway for the reaction compared to the original suggestion.
    1. In particular, the removal of chlorine occurs from the same nitrogen as the initial deprotonation
    2. This process does not result in an intermediate nitrene being formed, rather the chlorine removal is concerted with N-N bond formation.
    3. The resulting 1-chloro-1H-diazirine does not directly ionize to form a diazacyclopropenium cation-chloride anion ion pair, but instead can undertake an Sn2′ reaction to form the final 3-chloro-3-methyl-3H-diazirine.
  3. A simple change in the conditions, such as replacing water as a catalytic agent with Na+OH–(5H2O) can have a large impact on the energetics and indeed pathways involved. In this case, the reaction is conducted in NaOCl or NaOBr solutions, for which the pH is ~13.5,♣ indicating [OH–] is ~0.3M.
  4. The curly arrows here are “reasonable” for the computed pathway, but are determined by some simple formalisms which I have adopted (such as terminating an arrow-head at the mid-point of a newly forming bond). As I hinted above, these curly arrows can also be subjected to quantum mechanical scrutiny and I hope to illustrate this process in a future post.

But do not think I am suggesting here that this is the “correct” mechanism, it is merely one mechanism for which the relative energies of the various postulated species involved have been calculated relatively accurately. It does not preclude that other, perhaps different, routes could be identified in the future where the energetics of the process are even lower. 

†This blog is inspired by the two students who recently asked such questions. ‡In fact, you also have to acquire this completely unrelated article[2] for reasons I leave you to discover yourself. ♥You might want to consider the merits or demerits of an alternative way of showing the curly arrows. Is this representation “more reasonable”? ♣I thank Ed Smith for measuring this value for NaOBr and for suggesting the Graham reaction in the first place as an interesting one to model.

References

  1. W.H. Graham, "The Halogenation of Amidines. I. Synthesis of 3-Halo- and Other Negatively Substituted Diazirines<sup>1</sup>", Journal of the American Chemical Society, vol. 87, pp. 4396-4397, 1965. https://doi.org/10.1021/ja00947a040
  2. E.W. Abel, B.C. Crosse, and D.B. Brady, "Trimeric Alkylthiotricarbonyls of Manganese and Rhenium", Journal of the American Chemical Society, vol. 87, pp. 4397-4398, 1965. https://doi.org/10.1021/ja00947a041

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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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Epoxidation of ethene: a new substituent twist.

Friday, December 21st, 2018

Five years back, I speculated about the mechanism of the epoxidation of ethene by a peracid, concluding that kinetic isotope effects provided interesting evidence that this mechanism is highly asynchronous and involves a so-called “hidden intermediate”. Here I revisit this reaction in which a small change is applied to the atoms involved.

Below are two representations of the mechanism. The synchronous mechanism involves five “curly arrows”, two of which are involved in forming a bond between oxygen and carbon, and three of which transfer a proton to the group X (X=O). The second variation asynchronously stops at the half way stage to form a pseudo ion-pair (the “hidden intermediate”) and the proton transfer only occurs in the second stage. If the ethene is substituted with deuterium, experimentally an inverse kinetic isotope effect is observed, which provides strong evidence that at the transition state, no proton transfer is occurring

Before I go on, I should say that you will not find the mechanism as shown in either variation above in very many text books, which tend to practice “curly arrow economy” by employing only four arrows. I will not pursue this aspect here, except to note that as drawn above, the synchronous mechanism resembles that of a pericyclic reaction in a variation known as coarctate, as I noted in the original post (DOI: 10.14469/hpc/4807).

Now I introduce a veritable variation into this reaction, known as Payne epoxidation[1],† which replaces the peracid with a reagent generated by adding hydrogen peroxide to a nitrile to generate a transient species which can be represented by X=NH above. How does this change things? The model below also uses propene rather than ethene (M062X/Def2-TZVPPD/SCRF=dichloromethane).‡ This transition state (ΔG298 31.3 kcal/mol) shows two C-O bond formations, and as before the proton is clearly not yet transferred to the nitrogen (X=NH). Because of this asynchrony, the reaction could also be called a coarctate pseudo-pericyclic reaction.

Asynchronous concerted mechanism. Click for 3D

However, the proton transfer is nonetheless part of a concerted mechanism, as shown by the IRC profile.

The gradient norm most clearly shows the “hidden ion-pair intermediate” at IRC = -1, and the proton transfer only occurs after this point is passed.

This is even more spectacularly illustrated with a plot of dipole moment along the IRC;

In truth, no real differences are yet revealed between the Payne reagent and the peracid. In fact, this is a real surprise, since the NH of the Payne reagent should be very much more basic than the carbonyl oxygen of the peracid. But more exploration of the potential energy surface reveals another transition state!

Stepwise mechanism. Click for 3D

This is seen forming the two C-O bonds AFTER the proton transfer from oxygen to nitrogen. It is 4.2 kcal/mol lower than the first transition state, which corresponds to the scheme below.

The new ion-pair shown above is 7.1 kcal/mol higher than the previous reactant, but is so much more basic than before that the overall activation energy is indeed lowered. Two distinctly separate IRCs can be constructed for this alternative, the first a pure proton transfer (not shown) and the second a pure C-O bond forming process (below). This second step is both concerted and almost purely synchronous.

So now we see how a small change to the reactant molecules (X=O to X=NH) can induce a reaction for which two quite different mechanisms can operate, an asynchronous one albeit with a hidden intermediate and a fully stepwise one in which a quite different, but this time real, intermediate is involved. Nevertheless for both the peracid mechanism and the peroxyimine variation shown here, the proton transfer is NOT involved in the rate limiting step. So for this variation too, inverse kinetic isotope effects would be expected.

‡FAIR data for the calculations at DOI: 10.14469/hpc/4909 †Thanks Ed for pointing this out.

References

  1. G.B. PAYNE, P.H. DEMING, and P.H. WILLIAMS, "Reactions of Hydrogen Peroxide. VII. Alkali-Catalyzed Epoxidation and Oxidation Using a Nitrile as Co-reactant", The Journal of Organic Chemistry, vol. 26, pp. 659-663, 1961. https://doi.org/10.1021/jo01062a004

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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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Reaction coordinates vs Dynamic trajectories as illustrated by an example reaction mechanism.

Monday, March 20th, 2017

The example a few posts back of how methane might invert its configuration by transposing two hydrogen atoms illustrated the reaction mechanism by locating a transition state and following it down in energy using an intrinsic reaction coordinate (IRC). Here I explore an alternative method based instead on computing a molecular dynamics trajectory (MD).

I have used ethane instead of methane, since it is now possible to envisage two outcomes:

An animation of the IRC starting from the located transition state is shown below (DOI: 10.14469/hpc/2331). This is based purely on the computed potential energy surface of the molecule. The IRC is computed from the forces experienced on the atoms as they are displaced from an initial set of coordinates corresponding to the located transition state and then following the direction indicated by the eigenvectors of the negative force constant required of a transition state. Importantly, there is no time component; the path is based entirely on energies and forces.

Next, a molecular dynamics simulation (ωB97XD/6-31G(d,p), DOI: 10.14469/hpc/2330).  This uses the ADMP method, which requests a classical trajectory calculation using the “atom-centered density matrix propagation molecular dynamics model”. This integrates kinetic energy contributions from the molecular vibrations and so explicitly now includes a time component. In this example the evolution of the system from the transition state is charted over a period of 100 femtoseconds (1000 integrated steps). As it happens this is a relatively short period of evolution; sometimes periods of picoseconds may be required to get a realistic model, especially if one is also dealing with explicit solvent molecules (of which perhaps 500 might be required).

Such explicit inclusion of the kinetic energy from molecular vibrations in effect allows the molecule to “jump” over shallow barriers. In this case, the barrier for a [1,2] hydrogen shift from the methyl group to the adjacent carbene (watch atom 8). Simultaneously, the path taken by two hydrogens no longer corresponds to their transposition but to their elimination as a hydrogen molecule. So this quite different outcome from the IRC is very probably also a much more realistic one.

If the MD method is so much more realistic than the IRC, then why is it not always used? The simple answer is computational time! For this very small molecule and using quite a modest basis set (6-31G(d,p)), the relatively short 1000 time steps took about three times as long to compute as the IRC. The factor gets worse as the size of the molecule increases and the number of time steps for a realistic result increases. Perhaps, as technology gets better and new computer architectures emerge, MD simulations of ever increasingly complex reactions will become far more common. In ten years time, I expect most of the examples on this blog will use this method!

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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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Secrets of a university tutor: dissection of a reaction mechanism.

Wednesday, January 25th, 2012

Its a bit like a jigsaw puzzle in reverse, finding out to disassemble a chemical reaction into the pieces it is made from, and learning the rules that such reaction jigsaws follow. The following takes about 45-50 minutes to follow through with a group of students.

The problem is initially posed as the above (ignore the wavy bonds for now). The challenge is to identify the basic components that the reaction is built from and the rules these follow. It can be usefully salami-sliced as follows

  1. You are told the puzzle may consist of one or more (consecutive) pericyclic reactions. This should load up in your mind (from lecture notes) the various basic types of such reactions (the basic shapes of the jigsaw puzzle if you like).
  2. Rules from other areas of chemistry may be needed. Thus from your knowledge of the chemistry of benzene and its aromaticity, you need to remind yourself that there are two resonance forms (the Kekule forms) which are entirely equivalent. Problems such as the above may however be posed using either one or both of these forms. We will find out if this matters or not shortly.
  3. We need to clearly identify exactly what changes when the reaction occurs. To do this, it is useful to number what you think might be the key atoms.
  4. Notice that some atoms are not numbered. It keeps things simple, but in fact numbering them all will not do any damage. The atoms not numbered are the methyl groups (it does seem as if they emerge from the reaction unchanged) and the benzo group on the left. Only time will tell if this scheme needs changing.
  5. And now we are in a position to create a checklist of changes that occur during the reaction.
    1. A σ-bond between 1-6 clearly forms
    2. A π-bond between 5-6 decreases to a σ
    3. The π-bonds in the (un-numbered) benzo group rotate. We recognise this as a benzene resonance rather than a (pericyclic) reaction.
    4. And now for the elephant in the room, the atoms that we (as chemists) know are there, but which are not explicitly shown. These are the hydrogens. We know a rule for this, which is that any structure shown without hydrogens is assumed to have as many attached as are required to achieve a four valent carbon. This is in fact a fuzzy rule, because some carbons can be divalent (carbenes) and some trivalent (carbocations). Normally the former have a : glyph appended to them, and the latter a + charge, and we can see neither here so our rule stands. Time to count the elephants, and to draw the significant hydrogens explicitly (drawing them all would only clutter). We only select those hydrogens that appear to have moved during the reaction. Thus:
    5. A σ-bond between 5-7 clearly forms
    6. A σ-bond between 1-7 clearly breaks
  6. We have four significant bonds that change, 1-6, 5-6, 5-7 and 1-7. The task now is to partition them into groups that might correspond to one of the basic types of pericyclic reaction, and these tend to be defined by how many σ-bonds make or break during the reaction
    1. Thus an electrocyclic reaction either forms or breaks just one σ-bond
    2. A cycloaddition forms two (or more) σ-bonds and its reverse, a cyclo-elimination breaks two (or more) σ-bonds
    3. A sigmatropic reaction forms one σ-bond and breaks another.
    4. Ene reactions break at least one σ-bond and form at least one other, but in unequal numbers that distinguish them from a sigmatropic reaction.
  7. Juggling with these pieces soon reveals that items 5.5 and 5.6 above can comprise a sigmatropic reaction, and that item 5.1 above constitutes an electrocyclic reaction. Item 5.2 above, involving only a π-bond is not counted.
  8. The next task is to decide which comes first! To do this, we need to again recollect carbon tetravalency, and the sacrosanct need not to exceed it. Clearly forming the 1-6 bond as our first action would violate this rule by creating a pentavalent carbon atom. So this leaves 5-7/1-7 as our first action, which is going to be a sigma tropic reaction.
  9. We might recognise at this point that 5-7/1-7 share a common atom (7). We can probably pencil in that this sigma tropic reaction is going to be of the type [1,?] from this observation. From the numbering above (which in fact was deliberately chosen to achieve this effect) we infer that hydrogen 7 moves along a chain of 5 carbon atoms, and so our nomenclature is complete; it is going to be a [1,5] hydrogen migration or sigmatropic shift. Had the numbering been different, we would have had to spot that the non-common bonds differed by five atoms.
  10. The arrow pushing to achieve this transformation is shown below. Notice that the arrows rotate anti-clockwise. It is a feature of pericyclic reactions that it does not matter which clock-direction they rotate in (mostly). Hence pushing them the other way would achieve exactly the same result.
  11. This brings a surprise; we needed five arrows, or ten electrons. Is that a unique solution? Well no. Had we remembered point 5.3 above, then another initial resonance form for the benzo-ring is possible, and this form requires us to push only three arrows, or six electrons.
  12. Is there a common factor between 6 and 10 electrons? Yes, it is the famous Hückel aromaticity 4n+2 rule, for which n =1 or 2. So we get the result we really wanted, which is does not matter which of the two resonance forms for the benzo group we start with, we end up with arrow pushing that either way merely conforms to the 4n+2 rule. In other words, the transition state for this first reaction is aromatic. The stereochemistry implied by this result is going to be deferred to a second tutorial on this topic (and this is where the wavy lines will also come in).
  13. There is another observation we can make. The product of the [1,5] sigmatropic hydrogen shift no longer carries an aromatic ring on the left. We might infer that it will only be a transient intermediate, and will be very inclined to restore the aromaticity at the first opportunity.
  14. We are now in a position to create the 1-6 bond without violating the valency of either atom.
  15. The arrows shown above are two (black) to which can be followed either one more (green) or three more (red), making two possibilities carrying either 6 or 10 electrons. Again, both conform to the 4n+2 rule and so it does not matter which set is followed; the electrocyclic reaction will have an aromatic transition state (again we ignore stereochemistry for the time being).
  16. And hey, we have also recovered the aromaticity of our benzo group on the left.
Well, it is now time to finish up this first tutorial on the topic. In the follow up, I will show these aromatic transition state I have referred to here, and also include discussion of the stereochemistry.

 

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