Posts Tagged ‘relative energy’

Organocatalytic cyclopropanation of an enal: (computational) mechanistic understanding.

Saturday, August 25th, 2018

Symbiosis between computation and experiment is increasingly evident in pedagogic journals such as J. Chemical Education. Thus an example of original laboratory experiments[1],[2] that later became twinned with a computational counterpart.[3] So when I spotted this recent lab experiment[4] I felt another twinning approaching.

The reaction under consideration is that between dec-2-enal and 2,4-dinitrobenzyl chloride as catalysed by an α,α-diphenylprolinol trimethylsilyl ester with addition of further base (di-isopropylamine?). The proposed mechanism can be seen in figure 7‡ of the journal article[4] and also scheme 2 of an earlier article.[5] The following is my interpretation of their published mechanism (the compound numbering is the same as in Figure 7).

  1. The initiating step is the condensation between the alkyl enal (1) and the prolinol derivative (3), with elimination of water and the formation of a positive iminium cation (5). One might wonder at this stage what the counter ion to this cation is.
  2. 5 then reacts with 2,4-dinitrobenzyl chloride (2) with apparent elimination of HCl to form 6. This corresponds to 1,4-Michael addition to 5 with the formation of the first new  C-C bond and the creation of two new stereogenic centres.
  3. 6 then cyclises to form a second new C-C bond and a third new stereogenic centre as in 7.
  4. 7 is then hydrolysed to give the final product 4.

A total of three (starred) stereogenic centres are therefore created in 4, implying 23 = 8 steroisomers, arranged as four diastereomers and their enantiomers. A computational mechanistic analysis might strive to cast light on the following questions.

  • Is the sequence shown in figure 7 reasonable? If not can a more reasonable cycle be constructed that has energetics corresponding to a facile reaction at 0°C?
  • What are the predicted relative yields of the four possible diastereomeric products and do they match those observed?
  • If  R=α,α-diphenylprolinol trimethylsilyl ester, then this fourth chiral centre increases the total number of stereoisomers to 16, arranged in eight pairs of diastereomers. Does this result in the diastereomers of 4 forming with an excess of one enantiomer over the other (an ee ≠ 0)?

This post addresses just the first question (R=R’=H, R”=isopropylamine) leaving the other two questions for later analysis.

My analysis (figure above)♥ of the mechanism, as cast for computational analysis†, differs in various details from Figure 7/Scheme 2 of the published articles.[4],[5]

  1. The issue of defining a counterion to 5 is solved by in fact starting the cycle with proton abstraction from 2 by di-isopropylamine♦ to form a benzylic anion, as stabilized by the 2,4-dinitro groups and with the positive counter-ion being the protonated amine base.
  2. The next step is reaction between 1 and 3 to form an aminol 10, a tetrahedral intermediate.
  3. To remove water from this to form an iminium cation 5, one has to protonate the hydroxy group and this can now be done using the cationic ammonium species formed in step 5 above.
  4. The benzylic anion can now react with the iminium cation to form the first C-C bond and the first two stereocentres via 1,4-Michael addition to form 6
  5. The species 6 can now eliminate chloride anion to form the cyclopropyl iminium cation/anion pair 7, generating the 3rd stereogenic centre.
  6. Hydrolysis forms the product 4 and returns the system to the starting point in the catalytic cycle.
  7. Also included is whether an alternative mechanism is viable, involving elimination of Cl– from 8 to form a “carbene”, which could then potentially add to the alkene in 1.

Species (transition state)

FAIR Data DOI
10.14469/hpc/4642

ΔG273.15, Hartree
(ΔΔG‡273.15, kcal/mol)

Structure
(click for 3D model)
Reactants -1837.174744♣ (0.0)
TS1 -1837.150502 (15.2)
TS2 -1837.154923 (12.4)
TS3 -1837.147927 (16.8)
TS4 -1837.175723 (-0.6)
TS5 -1837.101534 (45.9)

The (relative) free energies of the transition states at the B3LYP+GD3BJ/6-311G(d,p)/SCRF=chloroform level shown in the table above (click on the thumbnail images to show the 3D model of each transition state) reveal that the highest point corresponds to TS3, a C-C bond forming reaction. This is noteworthy because it constitutes the reaction between an ion-pair, albeit ions which are both heavily stabilized by delocalisation. Since the reaction is known to proceed over 3 hours at 0°C, the activation barrier of 16.8 kcal/mol is also entirely reasonable. TS5, the putative formation of a carbene from the benzyl chloride, has a very high barrier and in fact cyclises to form 9. This pathway can therefore be safely ignored.

The next stage would be to investigate the stereochemical implications of this mechanism (atoms in 4 marked with a *) using the actual substituents for R and R’. Because the mechanism includes ion-pairs throughout, this does actually present some tricky issues. Unlike molecules with covalent bonds, where the shapes are relatively easy to predict, ion-pairs are more flexible and can often adopt a variety of poses, the relative energy of which is frequently determined simply by the magnitudes of their dipole moments.[6] If I manage to sort this out, I will report back here.

‡I would love to show you figure 7 here, but the publisher asserts that I would need to pay them $87.75 to do so and so you will have to acquire the article yourself to see it.

†Various guiding rules include constructing the entire catalytic cycle using exactly the same number of atoms so that the cycle can show only relative (free) energies and using neutral ion-pair models rather than just charged species alone.

♥Almost all the chemical diagrams on this blog for some ten years now have been in SVG (scalable vector graphics) format. Most modern web browsers for a number of years now have had excellent support for SVG. Until recently SVG could not be generated directly from a drawing program such as e.g. ChemDraw. Instead I saved as EPS (encapsulated postscript) and then used a program called Scribus to convert to SVG. In fact with Chemdraw V18.0, the direct conversion to SVG seems to be working very well, including honoring color maps. To scale up a diagram, click on it to open a new browser window containing only it and then use the browser zoom-in control to magnify it. Unlike e.g. a pixel image, SVG images magnify/scale correctly.

♣This relates to metadata as described in this post in performing a global search of any species matching this Gibbs Energy.

♦If the mechanism is set up without any base, then proton abstraction must occur directly from the benzyl chloride. Under these circumstances, the barrier for proton removal is 27.5 kcal/mol, whilst that for C-C bond formation is only 13.6.

References

  1. A. Burke, P. Dillon, K. Martin, and T.W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", Journal of Chemical Education, vol. 77, pp. 271, 2000. https://doi.org/10.1021/ed077p271
  2. J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", Journal of Chemical Education, vol. 78, pp. 1266, 2001. https://doi.org/10.1021/ed078p1266
  3. K.K.(. Hii, H.S. Rzepa, and E.H. Smith, "Asymmetric Epoxidation: A Twinned Laboratory and Molecular Modeling Experiment for Upper-Level Organic Chemistry Students", Journal of Chemical Education, vol. 92, pp. 1385-1389, 2015. https://doi.org/10.1021/ed500398e
  4. M. Meazza, A. Kowalczuk, S. Watkins, S. Holland, T.A. Logothetis, and R. Rios, "Organocatalytic Cyclopropanation of (<i>E</i>)-Dec-2-enal: Synthesis, Spectral Analysis and Mechanistic Understanding", Journal of Chemical Education, vol. 95, pp. 1832-1839, 2018. https://doi.org/10.1021/acs.jchemed.7b00566
  5. M. Meazza, M. Ashe, H.Y. Shin, H.S. Yang, A. Mazzanti, J.W. Yang, and R. Rios, "Enantioselective Organocatalytic Cyclopropanation of Enals Using Benzyl Chlorides", The Journal of Organic Chemistry, vol. 81, pp. 3488-3500, 2016. https://doi.org/10.1021/acs.joc.5b02801
  6. J. Clarke, K.J. Bonney, M. Yaqoob, S. Solanki, H.S. Rzepa, A.J.P. White, D.S. Millan, and D.C. Braddock, "Epimeric Face-Selective Oxidations and Diastereodivergent Transannular Oxonium Ion Formation Fragmentations: Computational Modeling and Total Syntheses of 12-Epoxyobtusallene IV, 12-Epoxyobtusallene II, Obtusallene X, Marilzabicycloallene C, and Marilzabicycloallene D", The Journal of Organic Chemistry, vol. 81, pp. 9539-9552, 2016. https://doi.org/10.1021/acs.joc.6b02008

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I’ve started so I’ll finish. The mechanism of diazo coupling to indoles – forty (three) years on!

Thursday, December 24th, 2015

The BBC TV quiz series Mastermind was first broadcast in the UK in 1972, the same time I was starting to investigate the mechanism of diazocoupling to substituted indoles as part of my Ph.D. researches. The BBC program became known for the catch phrase I've started so I'll finish; here I will try to follow this precept with the project I started then.

Indole diazocoupling

In 1972, one measured the rates of chemical reactions to gain insights into the transition state kinetic model. To obtain more data, we used isotopes such as 2H or 3H, together with substituents such as R-t-butyl to modify the potential energy surfaces of the reactions by inducing steric effects.[1],[2] We found that the kinetics for this reaction were actually complex‡ (in part because of pH dependence) involving a Wheland intermediate (the formation of which is shown with red curly arrows above) followed by the collapse of this intermediate to the diazo-coupled product (blue arrows). Coupling to 2-methyl indole (R=X=H, R'=Me), 2-t-butyl indole (R=H, R'=t-butyl) and 4-methyl-2-t-butyl indole (R=Me, R'=t-butyl) revealed that the kinetic isotope effects induced by replacing H by D or T were "not apparent" (i.e. close to 1), the inference being that the rate constant k1 for those systems was slower than k2; the formation of the Wheland intermediate was rate determining (the rds) for the reaction. But with 2-methyl-4,6-di-t-butyl indole (R=t-butyl, R'=Me) this changed and a deuterium isotope effect of ~7 was observed. The rate determining proton removal from the Wheland intermediate k2 was now slower than k1. With 2,4,6-tri-t-butyl indole, we ended by noting that the reaction become almost too slow to observe and furthermore was accompanied by loss of a t-butyl cation as well as a proton.

At this point we attempted to infer some transition state models consistent with these observations. Note that we had relatively little data with which to derive our 3D models (one needs to define a geometry using 3N-6 variables, along with its relative energy and force constants). The text and diagram of our attempt is shown below.

TS1

The main points of this argument were;

  1. That the Wheland complex is asymmetric, with the diazonium ion adopting a pseudo-axial line of attack.
  2. In contrast, the leaving proton lies closer to the plane of the indole ring
  3. The abstracting base experiences "steric hindrance" if R = t-butyl but not if R' = t-butyl.

I was eager to find out how one might test these models by quantum computation and my next stop in 1974 was to Austin Texas, where Michael Dewar's  group was soon to break the record for computing the geometry of a molecule with 49 atoms (similar in size to the reactions shown above) using the then very new semi-empirical MINDO/3 valence-shell quantum theory. The theory still needed much improvement in a great many aspects and the last forty years has brought us features such as density functional theories, far more accurate all-electron basis sets, superior geometry optimisation methods for transition states, code parallelisation, solvation treatments and increasing recognition that a particular form of electron correlation associated with dispersion energies needed specific attention. These methods would not have become applicable to molecules of this size had the computers themselves not become perhaps 10 million times faster during this period, with a commensurate increase in the digital memories required and decrease in cost.

Time then to apply a B3LYP+D3/Def2-TZVP/SCRF=water quantum model to the problem. Four species were computed for each set of substituents; the reactant, a transition state for C…N bond formation (TS1), a Wheland intermediate and a transition state for C-H bond cleavage (TS2). The relative free energies of the last three with respect to the first are shown in the table below. An IRC for R=R'=H (below) was used to show that a bona-fide† Wheland intermediate is indeed formed.[3]

IRC animation for TS1, R=R'=H
TS1 IRC
IRC for TS2, R=R'=H
TS2

The relative free energies (kcal/mol) are shown in the table below and the following conclusions can be drawn from this computed model:

  1. For R=R'=H, ΔG298‡ for TS1 is higher than TS2 (✔ with expt)
  2. With R=t-butyl,R'=Me, ΔG298‡ of TS1 is 3.1 kcal/mol lower than with R=R'=H. This indicates that t-butyl and methyl groups actually activate electrophilic addition by stabiisation of the induced positive charge, and have no steric effect upon the first step (✔ with our conclusions).
  3. For R= t-butyl,R'=Me, ΔG298‡ of TS1 is lower than TS2 (✔ with expt).
  4. With R=R'= t-butyl, ΔG298‡ of TS2 is 4.9 kcal/mol higher than with R=R'=H and is 3.1 kcal/molhigher with R=t-butyl,R'=Me, indicating the steric effect acts on this stage.
  5. The angle of approach of the diazonium electrophile is ~123-118° for R=R'=H and R=R'=t-butyl, about 30° away from a strict pseudo-axial "reactant-like" approach as implied in our sketch above (❌ with diagram above)
  6. The angle of proton abstraction with the plane of the indole ring is 107° for R=R'=H and 100.3° for R=R'=t-butyl, the hydrogen being closer to pseudo-axial than equatorial, relative to the plane of the indole ring  (❌ with diagram above).
  7. The position along the reaction path for proton abstraction is much later with R=R'=t-butyl (rC-H ~1.42Å) than R=R'=H (rC-H ~1.27Å),  (❌ with the statement above: a reactant-like transition state even for the proton expulsion step).
  8. The cross-over between TS1/TS2 as the rds is in the region of the substituents R=Me,R'=t-butyl (~✔ with expt).
  9. The steric interaction occurs not so much between the incoming base and the t-butyl groups, but because of enforced proximity between the t-butyl group and the diazo group induced during the proton removal stage.
  10. The steric effect induced by R=t-butyl is greater than when  R'=t-butyl.
  11. The Wheland intermediate is in a relatively shallow minimum.
R, R'

TS1,
ΔG298‡ 

k1

 ∠ N1-C3-N2

ΔG298 

TS2,
ΔG298‡ 

k2

 ∠ N1-C3-H

ΔΔG‡
(TS2-TS1)

 kH/kD
(calc)
[4],[5]
R=R'=H 21.4[6],[7] 122.9 19.6[8] 18.6[9] 107.0 -1.8 0.925 (TS1)
R=Me,R'=t-butyl 16.9[10],[11] 121.8 15.2[12] 18.4[13] 101.8 +1.5 0.900 (TS1)
6.4 (TS2)
R=t-butyl,R'=Me 18.3[14],[15] 115.2 16.0[16] 21.7[17] 100.9 +3.4 6.8 (TS2)
R=R'=t-butyl 17.8[18],[19] 117.6 17.8[20] 23.5[21] 100.4 +5.2 6.9 (TS2)

Possible errors in the model:

  1. I have not included any explicit solvent water in which hydrogen bonds to the base (the chloride anion) might moderate its properties.
  2. The ion-pair reactant complex between the phenyl diazonium chloride and the indole has many possible orientations, and these have not been optimised.
  3. The free energies are subject to the usual errors due to the rigid-rotor approximations and other artefacts of partition functions.
  4. Other DFT functionals have not been explored, nor have better basis sets.
  5. This current study is confined to formation of the cis-diazo product.

But even such a model seems to reproduce much of what we learnt about diazocoupling to 2,4-substituted indoles. The calculations you see above took about a week to set up and complete; the original experimental work took (in real-time) ~150 weeks (interleaved with two other mechanistic studies). Also efficient implementation of the quantum theories, together with the computer resources to evaluate the molecular energies and geometries, was almost entirely lacking in 1972 and this has probably only become a realistic project in the last five years or so. So that 43 year wait to finish what I started seems not unreasonable. Nowadays of course, combining experimental kinetic measurements with computational models very often goes hand in hand.

It is also worth speculating about the wealth of mechanistic data garnered during the heyday of physical organic chemistry during  the period ~1940-1980. The experiments were not then informed by feedback from computational modelling. However, it seems unlikely that very many of these mechanistic studies will ever be retrospectively augmented with computed models; the funding for the resources to do so is unlikely to ever be seen as a priority.

‡A little more complex than the scheme above, since the reaction also exhibits dependency on acid concentration. Nowadays, there are a number of computer programs available for analysing such complex kinetics, but in 1972 I had to write my own non-linear least squares fitting analysis of the steady state equation to the measured rates[2] This replaced the use of graph paper to analyse (of necessity much simpler) rate equations. †The related diazo coupling to activated aryls such as phenol or aniline shows a mechanistic cross-over between an entirely synchronous path in which no Wheland intermediate is involved (e.g. phenol)[22] to one where the intermediate does form (e.g. aniline).[23] Diazo coupling to e.g. benzofuran rather than indole will be reported in a future post.

References

  1. B.C. Challis, and H.S. Rzepa, "The mechanism of diazo-coupling to indoles and the effect of steric hindrance on the rate-limiting step", Journal of the Chemical Society, Perkin Transactions 2, pp. 1209, 1975. https://doi.org/10.1039/p29750001209
  2. H.S. Rzepa, "Hydrogen Transfer Reactions Of Indoles", Zenodo, 1974. https://doi.org/10.5281/zenodo.18777
  3. H.S. Rzepa, "C14H12ClN3", 2015. https://doi.org/10.14469/ch/191707
  4. H.S. Rzepa, "KINISOT. A basic program to calculate kinetic isotope effects using normal coordinate analysis of transition state and reactants.", 2015. https://doi.org/10.5281/zenodo.19272
  5. H. Rzepa, "The mechanism of diazo coupling to indoles", 2015. https://doi.org/10.14469/hpc/176
  6. H.S. Rzepa, "C 14 H 12 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191705
  7. H.S. Rzepa, "C 14 H 12 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191698
  8. H.S. Rzepa, "C 14 H 12 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191713
  9. H.S. Rzepa, "C14H12ClN3", 2015. https://doi.org/10.14469/ch/191712
  10. H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191723
  11. H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191719
  12. H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191721
  13. H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191720
  14. H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191722
  15. H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191717
  16. H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191726
  17. H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191714
  18. H.S. Rzepa, "C22H28ClN3", 2015. https://doi.org/10.14469/ch/191715
  19. H.S. Rzepa, "C 22 H 28 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191706
  20. H.S. Rzepa, "C 22 H 28 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191709
  21. H.S. Rzepa, "C22H28ClN3", 2015. https://doi.org/10.14469/ch/191718
  22. H.S. Rzepa, "C12H11ClN2O", 2015. https://doi.org/10.14469/ch/191700
  23. H.S. Rzepa, "C12H12ClN3", 2015. https://doi.org/10.14469/ch/191699

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Posted in Historical, Interesting chemistry, reaction mechanism | No Comments »

I've started so I'll finish. The mechanism of diazo coupling to indoles – forty (three) years on!

Thursday, December 24th, 2015

The BBC TV quiz series Mastermind was first broadcast in the UK in 1972, the same time I was starting to investigate the mechanism of diazocoupling to substituted indoles as part of my Ph.D. researches. The BBC program became known for the catch phrase I've started so I'll finish; here I will try to follow this precept with the project I started then. Indole diazocoupling In 1972, one measured the rates of chemical reactions to gain insights into the transition state kinetic model. To obtain more data, we used isotopes such as 2H or 3H, together with substituents such as R-t-butyl to modify the potential energy surfaces of the reactions by inducing steric effects.[1],[2] We found that the kinetics for this reaction were actually complex‡ (in part because of pH dependence) involving a Wheland intermediate (the formation of which is shown with red curly arrows above) followed by the collapse of this intermediate to the diazo-coupled product (blue arrows). Coupling to 2-methyl indole (R=X=H, R'=Me), 2-t-butyl indole (R=H, R'=t-butyl) and 4-methyl-2-t-butyl indole (R=Me, R'=t-butyl) revealed that the kinetic isotope effects induced by replacing H by D or T were "not apparent" (i.e. close to 1), the inference being that the rate constant k1 for those systems was slower than k2; the formation of the Wheland intermediate was rate determining (the rds) for the reaction. But with 2-methyl-4,6-di-t-butyl indole (R=t-butyl, R'=Me) this changed and a deuterium isotope effect of ~7 was observed. The rate determining proton removal from the Wheland intermediate k2 was now slower than k1. With 2,4,6-tri-t-butyl indole, we ended by noting that the reaction become almost too slow to observe and furthermore was accompanied by loss of a t-butyl cation as well as a proton. At this point we attempted to infer some transition state models consistent with these observations. Note that we had relatively little data with which to derive our 3D models (one needs to define a geometry using 3N-6 variables, along with its relative energy and force constants). The text and diagram of our attempt is shown below. TS1 The main points of this argument were;

  1. That the Wheland complex is asymmetric, with the diazonium ion adopting a pseudo-axial line of attack.
  2. In contrast, the leaving proton lies closer to the plane of the indole ring
  3. The abstracting base experiences "steric hindrance" if R = t-butyl but not if R' = t-butyl.

I was eager to find out how one might test these models by quantum computation and my next stop in 1974 was to Austin Texas, where Michael Dewar's  group was soon to break the record for computing the geometry of a molecule with 49 atoms (similar in size to the reactions shown above) using the then very new semi-empirical MINDO/3 valence-shell quantum theory. The theory still needed much improvement in a great many aspects and the last forty years has brought us features such as density functional theories, far more accurate all-electron basis sets, superior geometry optimisation methods for transition states, code parallelisation, solvation treatments and increasing recognition that a particular form of electron correlation associated with dispersion energies needed specific attention. These methods would not have become applicable to molecules of this size had the computers themselves not become perhaps 10 million times faster during this period, with a commensurate increase in the digital memories required and decrease in cost. Time then to apply a B3LYP+D3/Def2-TZVP/SCRF=water quantum model to the problem. Four species were computed for each set of substituents; the reactant, a transition state for C…N bond formation (TS1), a Wheland intermediate and a transition state for C-H bond cleavage (TS2). The relative free energies of the last three with respect to the first are shown in the table below. An IRC for R=R'=H (below) was used to show that a bona-fide† Wheland intermediate is indeed formed.[3]

IRC animation for TS1, R=R'=H
TS1 IRC
IRC for TS2, R=R'=H
TS2

The relative free energies (kcal/mol) are shown in the table below and the following conclusions can be drawn from this computed model:

  1. For R=R'=H, ΔG298‡ for TS1 is higher than TS2 (✔ with expt)
  2. With R=t-butyl,R'=Me, ΔG298‡ of TS1 is 3.1 kcal/mol lower than with R=R'=H. This indicates that t-butyl and methyl groups actually activate electrophilic addition by stabiisation of the induced positive charge, and have no steric effect upon the first step (✔ with our conclusions).
  3. For R= t-butyl,R'=Me, ΔG298‡ of TS1 is lower than TS2 (✔ with expt).
  4. With R=R'= t-butyl, ΔG298‡ of TS2 is 4.9 kcal/mol higher than with R=R'=H and is 3.1 kcal/mol higher with R=t-butyl,R'=Me, indicating the steric effect acts on this stage.
  5. The angle of approach of the diazonium electrophile is ~123-118° for R=R'=H and R=R'=t-butyl, about 30° away from a strict pseudo-axial "reactant-like" approach as implied in our sketch above (❌ with diagram above)
  6. The angle of proton abstraction with the plane of the indole ring is 107° for R=R'=H and 100.3° for R=R'=t-butyl, the hydrogen being closer to pseudo-axial than equatorial, relative to the plane of the indole ring  (❌ with diagram above).
  7. The position along the reaction path for proton abstraction is much later with R=R'=t-butyl (rC-H ~1.42Å) than R=R'=H (rC-H ~1.27Å),  (❌ with the statement above: a reactant-like transition state even for the proton expulsion step).
  8. The cross-over between TS1/TS2 as the rds is in the region of the substituents R=Me,R'=t-butyl (~✔ with expt).
  9. The steric interaction occurs not so much between the incoming base and the t-butyl groups, but because of enforced proximity between the t-butyl group and the diazo group induced during the proton removal stage.
  10. The steric effect induced by R=t-butyl is greater than when  R'=t-butyl.
  11. The Wheland intermediate is in a relatively shallow minimum.
R, R' TS1,
ΔG298‡  k1 		∠ N1-C3-N2 Int
ΔG298  		TS2,
ΔG298‡  k2 		∠ N1-C3-H ΔΔG‡
(TS2-TS1) 		kH/kD
(calc)
[4],[5]
R=R'=H 21.4[6],[7] 122.9 19.6[8] 18.6[9] 107.0 -1.8 0.925 (TS1)
R=Me,R'=t-butyl 16.9[10],[11] 121.8 15.2[12] 18.4[13] 101.8 +1.5 0.900 (TS1)
6.4 (TS2)
R=t-butyl,R'=Me 18.3[14],[15] 115.2 16.0[16] 21.7[17] 100.9 +3.4 6.8 (TS2)
R=R'=t-butyl 17.8[18],[19] 117.6 17.8[20] 23.5[21] 100.4 +5.2 6.9 (TS2)

Possible errors in the model:

  1. I have not included any explicit solvent water in which hydrogen bonds to the base (the chloride anion) might moderate its properties.
  2. The ion-pair reactant complex between the phenyl diazonium chloride and the indole has many possible orientations, and these have not been optimised.
  3. The free energies are subject to the usual errors due to the rigid-rotor approximations and other artefacts of partition functions.
  4. Other DFT functionals have not been explored, nor have better basis sets.
  5. This current study is confined to formation of the cis-diazo product.

But even such a model seems to reproduce much of what we learnt about diazocoupling to 2,4-substituted indoles. The calculations you see above took about a week to set up and complete; the original experimental work took (in real-time) ~150 weeks (interleaved with two other mechanistic studies). Also efficient implementation of the quantum theories, together with the computer resources to evaluate the molecular energies and geometries, was almost entirely lacking in 1972 and this has probably only become a realistic project in the last five years or so. So that 43 year wait to finish what I started seems not unreasonable. Nowadays of course, combining experimental kinetic measurements with computational models very often goes hand in hand. It is also worth speculating about the wealth of mechanistic data garnered during the heyday of physical organic chemistry during  the period ~1940-1980. The experiments were not then informed by feedback from computational modelling. However, it seems unlikely that very many of these mechanistic studies will ever be retrospectively augmented with computed models; the funding for the resources to do so is unlikely to ever be seen as a priority.

‡A little more complex than the scheme above, since the reaction also exhibits dependency on acid concentration. Nowadays, there are a number of computer programs available for analysing such complex kinetics, but in 1972 I had to write my own non-linear least squares fitting analysis of the steady state equation to the measured rates[2] This replaced the use of graph paper to analyse (of necessity much simpler) rate equations. I note that mentions of non-linear least squares methods in kinetic analyses start around 1986[22] Even by 1992, the topic was considered novel enough to warrant a publication[23]

†The related diazo coupling to activated aryls such as phenol or aniline shows a mechanistic cross-over between an entirely synchronous path in which no Wheland intermediate is involved (e.g. phenol)[24] to one where the intermediate does form (e.g. aniline).[25] Diazo coupling to e.g. benzofuran rather than indole by the way is also stepwise, but via a very shallow Wheland intermediate[26] and with a higher barrier than indole, making it a very slow reaction.

 

References

  1. B.C. Challis, and H.S. Rzepa, "The mechanism of diazo-coupling to indoles and the effect of steric hindrance on the rate-limiting step", Journal of the Chemical Society, Perkin Transactions 2, pp. 1209, 1975. https://doi.org/10.1039/p29750001209
  2. H.S. Rzepa, "Hydrogen Transfer Reactions Of Indoles", Zenodo, 1974. https://doi.org/10.5281/zenodo.18777
  3. H.S. Rzepa, "C14H12ClN3", 2015. https://doi.org/10.14469/ch/191707
  4. H.S. Rzepa, "KINISOT. A basic program to calculate kinetic isotope effects using normal coordinate analysis of transition state and reactants.", 2015. https://doi.org/10.5281/zenodo.19272
  5. H. Rzepa, "The mechanism of diazo coupling to indoles", 2015. https://doi.org/10.14469/hpc/176
  6. H.S. Rzepa, "C 14 H 12 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191705
  7. H.S. Rzepa, "C 14 H 12 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191698
  8. H.S. Rzepa, "C 14 H 12 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191713
  9. H.S. Rzepa, "C14H12ClN3", 2015. https://doi.org/10.14469/ch/191712
  10. H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191723
  11. H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191719
  12. H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191721
  13. H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191720
  14. H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191722
  15. H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191717
  16. H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191726
  17. H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191714
  18. H.S. Rzepa, "C22H28ClN3", 2015. https://doi.org/10.14469/ch/191715
  19. H.S. Rzepa, "C 22 H 28 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191706
  20. H.S. Rzepa, "C 22 H 28 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191709
  21. H.S. Rzepa, "C22H28ClN3", 2015. https://doi.org/10.14469/ch/191718
  22. R. Ambrosetti, G. Bellucci, and R. Bianchini, "Direct numerical approach to complex reaction kinetics: the addition of bromine to cyclohexene in the presence of pyridine", The Journal of Physical Chemistry, vol. 90, pp. 6261-6266, 1986. https://doi.org/10.1021/j100281a038
  23. N.H. Chen, and R. Aris, "Determination of Arrhenius constants by linear and nonlinear fitting", AIChE Journal, vol. 38, pp. 626-628, 1992. https://doi.org/10.1002/aic.690380419
  24. H.S. Rzepa, "C12H11ClN2O", 2015. https://doi.org/10.14469/ch/191700
  25. H.S. Rzepa, "C12H12ClN3", 2015. https://doi.org/10.14469/ch/191699
  26. H.S. Rzepa, "C14H11ClN2O", 2015. https://doi.org/10.14469/ch/191730

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Modelling the geometry of unbranched alkanes.

Saturday, March 29th, 2014

By about C17H36, the geometry of “cold-isolated” unbranched saturated alkenes is supposed not to contain any fully anti-periplanar conformations. [1] Indeed, a (co-crystal) of C16H34 shows it to have two-gauche bends.[2]. Surprisingly, the longest linear alkane I was able to find a crystal structure for, C28H58 appears to be fully extended[3],[4] (an early report of a low quality structure for C36H74[5] also appears to show it as linear).‡ Here I explore how standard DFT theories cope with these structures.

I start with noting the use of a TZVP basis set. In a recent article[6] we noted that the basis-set-superposition-errors for this basis were about a quarter of that for the standard Pople-type 6-311G(d,p) basis that I tend to use for modelling in this blog. This matters, since the relative energy of a folded-conformation vs an extended linear one might depend on the quality of the basis set and its inherent BSSE. The DFT method is the classical B3LYP. I also modelled C58H118 as the hydrocarbon as being well beyond the region anticipated above for folding of the chain to have started (no, there is no crystal structure). The geometries of linear and bent forms are shown below.

003001

The relative free energy of the V-shaped bent form[7] emerges as 3.5 kcal/mol higher than the linear form[8]. Now, to add a Grimme-D3 dispersion correction to the energies. The V-shape of the bent form now adopts the hairpin mode,[9] and its energy is now 2.5 kcal/mol lower than the linear form.[10]

002

Note in the above the very slight strange oscillation (kink) that appears about 11 atoms away from the hairpin bend. I repeated this with the wB97XD DFT procedure (in which dispersion is implicit) and found the same result.

As triple-ζ basis quality modelling of molecules with >100 atoms becomes increasingly common, it is worth repeating yet again that the model should always contain dispersion (and solvent if appropriate) corrections as default. Indeed, it is probably also worth re-investigating much early modelling (by this I mean modelling done ten or more years ago) to see if such corrections significantly influence the conclusions.[6]

‡The searches cannot be carried out according to the formula CnH2n+2, but must be done individually for the value of n. I gave up at C50.

References

  1. N.O.B. Lüttschwager, T.N. Wassermann, R.A. Mata, and M.A. Suhm, "The Last Globally Stable Extended Alkane", Angewandte Chemie International Edition, vol. 52, pp. 463-466, 2012. https://doi.org/10.1002/anie.201202894
  2. N. Cocherel, C. Poriel, J. Rault‐Berthelot, F. Barrière, N. Audebrand, A. Slawin, and L. Vignau, "New 3π‐2Spiro Ladder‐Type Phenylene Materials: Synthesis, Physicochemical Properties and Applications in OLEDs", Chemistry – A European Journal, vol. 14, pp. 11328-11342, 2008. https://doi.org/10.1002/chem.200801428
  3. S.C. Nyburg, and A.R. Gerson, "Crystallography of the even <i>n</i>-alkanes: structure of C<sub>20</sub>H<sub>42</sub>", Acta Crystallographica Section B Structural Science, vol. 48, pp. 103-106, 1992. https://doi.org/10.1107/s0108768191011059
  4. R. Boistelle, B. Simon, and G. Pèpe, "Polytypic structures of n-C28H58 (octacosane) and n-C36H74 (hexatriacontane)", Acta Crystallographica Section B Structural Crystallography and Crystal Chemistry, vol. 32, pp. 1240-1243, 1976. https://doi.org/10.1107/s0567740876005025
  5. H.M.M. Shearer, and V. Vand, "The crystal structure of the monoclinic form of n-hexatriacontant", Acta Crystallographica, vol. 9, pp. 379-384, 1956. https://doi.org/10.1107/s0365110x5600111x
  6. 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
  7. H.S. Rzepa, "Gaussian Job Archive for C58H118", 2014. https://doi.org/10.6084/m9.figshare.978501
  8. H.S. Rzepa, "Gaussian Job Archive for C58H118", 2014. https://doi.org/10.6084/m9.figshare.978502
  9. H.S. Rzepa, "Gaussian Job Archive for C58H118", 2014. https://doi.org/10.6084/m9.figshare.978832
  10. H.S. Rzepa, "Gaussian Job Archive for C58H118", 2014. https://doi.org/10.6084/m9.figshare.978833

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