Physical organic chemistry « Henry Rzepa's blog

Posts Tagged ‘Physical organic chemistry’

A molecular balance for dispersion energy?

Sunday, February 7th, 2016

The geometry of cyclo-octatetraenes differs fundamentally from the lower homologue benzene in exhibiting slow (nuclear) valence bond isomerism rather than rapid (electronic) bond-equalising resonance. In 1992 Anderson and Kirsch[1] exploited this property to describe a simple molecular balance for estimating how two alkyl substituents on the ring might interact via the (currently very topical) mechanism of dispersion (induced-dipole-induced-dipole) attractions. These electron correlation effects are exceptionally difficult to model using formal quantum mechanics and are nowadays normally replaced by more empirical functions such as Grimme's D3BJ correction.[2] Here I explore aspects of how the small molecule below might be used to investigate the accuracy of such estimates of dispersion energies.

The concentration of the two forms shown above can be readily estimated by NMR spectroscopy (the barrier is slow enough to allow peaks for both isomers to be integrated). This shows that the 1,6 form is present in greater concentrations than the 1,4 form, equivalent to a difference in free energy ΔΔG₂₉₈ of 0.39 kcal/mol in favour of the former. Why is this? Because, it is claimed, in the 1,6 isomer the two t-butyl groups are close enough to experience mutual dispersion attractions not experienced by the 1,4 form. This can be illustrated using the NCI display below for the two forms.

Click for 3D. Addition NCI interactions ringed in red.

Click for 3D. 1,6-isomer: Additional NCI interactions ringed in red.

Click for 3D, 1,4 isomer.

Method	Equilibrium constant, 298K	ΔΔE	ΔΔH₂₉₈	ΔΔS₂₉₈	ΔΔG₂₉₈	Source
Experiment	1.93	–	1.14	-2.5	0.387	[1]
B3LYP/Def2-TZVPP/CDCl3 (no dispersion)	1.906^‡	0.05	0.00	+1.3^‡	0.382^‡	[3],[4]
B3LYP/Def2-TZVPP/CDCl3 (gd3bj dispersion)	8.36	0.75	0.66	+2.0	1.25	[5],[6]

^‡This contains a contribution of RTLn 2 (= 0.410 kcal/mol = 1.04 in ΔS), where 2 is the symmetry number for a species with C₂ rotational symmetry, to the 1,4-isomer only.

The interpretation of these results, as is often found, is non-trivial.

The relative concentrations of species in equilibrium equates with their relative free energies, ΔG₂₉₈and not ΔE (the difference in total energy computed using either quantum or molecular mechanics).
ΔG₂₉₈ has a component derived from the entropy of the system, and this in turn has contributions from symmetry (numbers). Only the 1,6-isomer has two-fold rotational symmetry for the lowest energy pose of the two t-butyl groups, and this contributes 0.41 kcal/mol to ΔG₂₉₈. This aspect is not discussed in the original article.[1]
The B3LYP/Def2-TZVPP DFT method predicts ΔΔE to be +0.05 kcal/mol without the inclusion of the D3BJ dispersion correction but +0.75 kcal/mol with. One might approximately equate the latter to the contributions ringed in red in the NCI distributions shown above. The enthalpies (where ΔΔE is corrected for zero point energies) are very similar.
Conversion to ΔG₂₉₈involves use of the vibrational frequencies to obtain the entropy; here one encounters a difference between the two double bond isomers. The lowest energy vibration for C₂-symmetric 1,4 is 23 cm^-1, whereas that for the 1,6 is only 7 cm^-1 (a value which also depends on round-off errors and accuracies in the calculation). These errors in the RRHO (rigid-rotor-harmonic-oscillator) approximations makes meaningful calculation of ΔS₂₉₈and henceΔG₂₉₈ problematic at this small energy difference level. In both cases, this approach suggests that the entropy of the 1,6 form is slightly larger than the 1,4 isomer, whereas the reverse is apparently true by experimental measurement. It might all boil down to those low-frequency vibrations!

So we may conclude that whereas the dispersion uncorrected method gets the right answer for the equilibrium constant for probably the wrong reasons, inclusion of a dispersion correction would get the right answer were it not for the error in the entropy. Agreement with experiment would be obtained if the calculated entropy difference were to be -0.9 kcal/mol K^-1 instead of +2.0. Thus the 1,6 isomer has the two t-butyl groups weakly interacting (red circle above), which intuition tends to suggest would reduce the entropy (reduce the disorder) of the system and not increase it.

At least in this relatively small molecule, we now have a handle for estimating these sorts of effects in terms of variables such as the basis set used, the energy Hamiltonian (e.g. type of functional etc) and of course the dispersion correction.

References

J.E. Anderson, and P.A. Kirsch, "Structural equilibria determined by attractive steric interactions. 1,6-Dialkylcyclooctatetraenes and their bond-shift and ring inversion investigated by dynamic NMR spectroscopy and molecular mechanics calculations", Journal of the Chemical Society, Perkin Transactions 2, pp. 1951, 1992. https://doi.org/10.1039/p29920001951
S. Grimme, S. Ehrlich, and L. Goerigk, "Effect of the damping function in dispersion corrected density functional theory", Journal of Computational Chemistry, vol. 32, pp. 1456-1465, 2011. https://doi.org/10.1002/jcc.21759
H.S. Rzepa, "C 16 H 24", 2016. https://doi.org/10.14469/ch/191875
H.S. Rzepa, "C 16 H 24", 2016. https://doi.org/10.14469/ch/191876
H.S. Rzepa, "C 16 H 24", 2016. https://doi.org/10.14469/ch/191874
H.S. Rzepa, and H.S. Rzepa, "C 16 H 24", 2016. https://doi.org/10.14469/ch/191880

Tags:dispersion, energy, Entropy, lowest energy, lowest energy pose, Physical organic chemistry, Potential theory
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Kinetic isotope effect models as a function of ring substituent for indole-3-carboxylic acids and indolin-2-ones.

Wednesday, January 20th, 2016

The original strategic objective of my PhD researches in 1972-74 was to explore how primary kinetic hydrogen isotope effects might be influenced by the underlying structures of the transition states involved. Earlier posts dealt with how one can construct quantum-chemical models of these transition states that fit the known properties of the reactions. Now, one can reverse the strategy by computing the expected variation with structure to see if anything interesting might emerge, and then if it does, open up the prospect of further exploration by experiment. Here I will use the base-catalysed enolisation of 1,3-dimethylindolin-2-ones and the decarboxylation of 3-indole carboxylates to explore this aspect.

The systems and results are shown in the table below, summarised by the points:

1,3-dimethyl-indolinones:

The free energy barriers are very low, but show an overall increase when changing the substituent from nitro to amino, with the 6-position being more sensitive than the 5. However, the increase is not consistent.
The transition state mode changes regularly, the wavenumber more than doubling along the progression.
The basic structure of the proton transfer evolves smoothly, from being an early transition state with 6-nitro to being a late one with 6-amino.
The primary kinetic isotope effect shows less variation, but the trend is to increase as the transition state gets later, even beyond the point where the two bond lengths associated with the tranferring hydrogen are equal in length.
As Dan Singleton has pointed out on this blog, the observed KIE is a combination of effects based purely on the transition state structure and effects resulting from the sharpness of the barrier inducing proton tunneling and this is itself related to the magnitude of ν_i. The KIE ratios tabulated below derive purely from the former and do not take into account any such tunneling. We can see from the variation in ν_i that such tunnelling contributions are likely to vary substantially across this range of substituents. As a result, deconvoluting the KIE due to the symmetry of the proton transfer from the contribution due to tunnelling is going to be difficult.
There are other computational errors which might contribute, such as solvent reorganisations due to specific substituents, only partially taken into acount here. In effect the unsubstituted reaction geometry was used as the template for the others, followed of course by a re-optimisation which might not explore other more favourable orientations brought about by the substituents.

Indole-3-carboxylic acids:

The free energy barriers are now much higher than the indolinones, but show a consistent decrease along the series from 6-nitro to 6-amino. This matches with the idea that the indole is a base and the basicity is increased by electron donation and decreased by electron withdrawal.
The transition state mode again changes regularly, increasing as the barrier decreases.
For 5-H, the computed free energy barrier matches that measured remarkably well.
The calculated KIE increase regularly along the series 6-nitro to 6-amino.
The calculated KIE for 5-H matches that measured very well, but that for the 5-chloro does not. One might safely conclude that the outlier is probably the experimental value. The KIE are not obtained by direct measurement of the rate of reaction, but inferred from solving the relatively complex rate equation with inclusion of some approximations and assumptions. Perhaps one of these approximations is not valid for this substituent, or possibly an experimental error has encroached. Were this work to ever be repeated, this entry should be prioritised.
The overall variation in KIE is in fact quite small, but if the KIE can be measured very accurately, then they should be useful for comparison with such calculations.
We cannot really conclude whether the magnitude of the KIE closely reflects the symmetry of the transition state. For all the examples below, the C-H bond is always shorter than the H-O bond. More extreme and probably multiple substituents on the ring (5,6-dinitro? 5,6-diamino?) might have to be used to probe a wider variation in transition state symmetry. For example, the maximum value for proton transfer from a hydronium ion was stated a long time ago to be around 3.6, [1] and it would be of interest to see if that value is attained when the proton transfer becomes fully symmetry.

1,3-dimethylindolin-2-ones[2]
Model	ΔG^‡₂₉₈ (ΔH^‡₂₉₈)	k^H/k^D (298K)	r_C-H, r_H-O	ν_i	DataDOIs
6-nitro	1.94	3.22	1.256, 1.417	611	[3],[4]
5-nitro	1.82	3.65	1.289, 1.364	895	[5],[6]
H	2.48	4.40	1.326, 1.316	1130	[7],[8]
5-amino	6.73	3.86	1.337, 1.304	1182	[9],[10]
6-amino	3.19	4.43	1.349, 1.291	1226	[11],[12]
Indole-3-carboxylic acids[13]
6-nitro	25.1	2.72	1.279,1.391	706	[14],[15]
5-chloro	23.1	2.80 (2.23)	1.300,1.361	873	[16],[17]
5-H	22.1 (22.0)^a[18]	2.87 (2.72)[18]	1.304,1.354	921	[19],[20]
6-amino	20.5	3.04	1.308,1.348	950	[21],[22]

^aThe barrier is higher than previously reported because a significantly lower isomer of the ionised reactant was subsequently located.[21] Use of this new isomer also has a modest knock-on effect on the computed isotope effect for this system, bringing it into line with the other substituents and also with experiment.

Overall, this study of variation in kinetic isotope effects for proton transfer as induced by variation of ring substitution shows the viability of such computation. The total elapsed time since the start of this project is about three weeks, very much shorter than the original time taken to synthesize the molecules and measure their kinetics. Importantly, these were very much reactions occuring in aqueous solution, where solvation and general acid or general base catalysis occurred. Such reactions have long been thought to be very difficult to model in a non-dynamic discrete sense. The results obtained here tends towards optimism that such calculations may have a useful role to play in understanding such mechanisms.

I would like to express my enormous gratitude to my Ph.D. supervisor, Brian Challis, for starting me along this life-long exploration of reaction mechanisms. I hope the above gives him satisfaction that the endeavour back in 1972 has borne some more fruits.

References

C.G. Swain, D.A. Kuhn, and R.L. Schowen, "Effect of Structural Changes in Reactants on the Position of Hydrogen-Bonding Hydrogens and Solvating Molecules in Transition States. The Mechanism of Tetrahydrofuran Formation from 4-Chlorobutanol1", Journal of the American Chemical Society, vol. 87, pp. 1553-1561, 1965. https://doi.org/10.1021/ja01085a025
H. Rzepa, "Kinetic isotope effects for the ionisation of 5- and 6-substituted 1,3-dimethyl indolinones.", 2016. https://doi.org/10.14469/hpc/208
H.S. Rzepa, "C 10 H 19 N 2 Na 1 O 8", 2016. https://doi.org/10.14469/ch/191802
H.S. Rzepa, "C 10 H 19 N 2 Na 1 O 8", 2016. https://doi.org/10.14469/ch/191796
H.S. Rzepa, "C 10 H 19 N 2 Na 1 O 8", 2016. https://doi.org/10.14469/ch/191800
H.S. Rzepa, "C 10 H 19 N 2 Na 1 O 8", 2016. https://doi.org/10.14469/ch/191789
H.S. Rzepa, "C 10 H 20 N 1 Na 1 O 6", 2016. https://doi.org/10.14469/ch/191787
H.S. Rzepa, "C 10 H 20 N 1 Na 1 O 6", 2016. https://doi.org/10.14469/ch/191782
H.S. Rzepa, "C 10 H 21 N 2 Na 1 O 6", 2016. https://doi.org/10.14469/ch/191803
H.S. Rzepa, "C 10 H 21 N 2 Na 1 O 6", 2016. https://doi.org/10.14469/ch/191797
H.S. Rzepa, "C 10 H 21 N 2 Na 1 O 6", 2016. https://doi.org/10.14469/ch/191804
H.S. Rzepa, "C 10 H 21 N 2 Na 1 O 6", 2016. https://doi.org/10.14469/ch/191799
H. Rzepa, "Decarboxylation of 5- and 6-substituted indole-3-carboxylic acids", 2016. https://doi.org/10.14469/hpc/220
H.S. Rzepa, "C 9 H 15 Cl 1 N 2 O 8", 2016. https://doi.org/10.14469/ch/191807
H.S. Rzepa, and H.S. Rzepa, "C 9 H 15 Cl 1 N 2 O 8", 2016. https://doi.org/10.14469/ch/191805
H.S. Rzepa, "C 9 H 15 Cl 2 N 1 O 6", 2016. https://doi.org/10.14469/ch/191822
H.S. Rzepa, "C 9 H 15 Cl 2 N 1 O 6", 2016. https://doi.org/10.14469/ch/191825
B.C. Challis, and H.S. Rzepa, "Heteroaromatic hydrogen exchange reactions. Part 9. Acid catalysed decarboxylation of indole-3-carboxylic acids", Journal of the Chemical Society, Perkin Transactions 2, pp. 281, 1977. https://doi.org/10.1039/p29770000281
H.S. Rzepa, "C 9 H 16 Cl 1 N 1 O 6", 2016. https://doi.org/10.14469/ch/191828
H.S. Rzepa, "C 9 H 16 Cl 1 N 1 O 6", 2016. https://doi.org/10.14469/ch/191790
H.S. Rzepa, "C 9 H 17 Cl 1 N 2 O 6", 2016. https://doi.org/10.14469/ch/191810
H.S. Rzepa, "C 9 H 17 Cl 1 N 2 O 6", 2016. https://doi.org/10.14469/ch/191806

Tags:aqueous solution, Brian Challis, can construct quantum-chemical models, computed free energy barrier matches, Dan Singleton, free energy barrier, free energy barriers, Kinetic isotope effect, Organic chemistry, Physical organic chemistry, quantum-chemical models, supervisor
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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. 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; theformation 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;

That the Wheland complex is asymmetric, with the diazonium ion adopting a pseudo-axial line of attack.
In contrast, the leaving proton lies closer to the plane of the indole ring
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

IRC for TS2, R=R'=H

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

For R=R'=H, ΔG₂₉₈^‡ for TS1 is higher than TS2 (✔ with expt)
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).
For R= t-butyl,R'=Me, ΔG₂₉₈^‡ of TS1 is lower than TS2 (✔ with expt).
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.
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)
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).
The position along the reaction path for proton abstraction is much later with R=R'=t-butyl (r_C-H ~1.42Å) than R=R'=H (r_C-H ~1.27Å), (❌ with the statement above: a reactant-like transition state even for the proton expulsion step).
The cross-over between TS1/TS2 as the rds is in the region of the substituents R=Me,R'=t-butyl (~✔ with expt).
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.
The steric effect induced by R=t-butyl is greater than when R'=t-butyl.
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)	k^H/k^D (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:

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

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
H.S. Rzepa, "Hydrogen Transfer Reactions Of Indoles", Zenodo, 1974. https://doi.org/10.5281/zenodo.18777
H.S. Rzepa, "C14H12ClN3", 2015. https://doi.org/10.14469/ch/191707
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
H. Rzepa, "The mechanism of diazo coupling to indoles", 2015. https://doi.org/10.14469/hpc/176
H.S. Rzepa, "C 14 H 12 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191705
H.S. Rzepa, "C 14 H 12 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191698
H.S. Rzepa, "C 14 H 12 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191713
H.S. Rzepa, "C14H12ClN3", 2015. https://doi.org/10.14469/ch/191712
H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191723
H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191719
H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191721
H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191720
H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191722
H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191717
H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191726
H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191714
H.S. Rzepa, "C22H28ClN3", 2015. https://doi.org/10.14469/ch/191715
H.S. Rzepa, "C 22 H 28 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191706
H.S. Rzepa, "C 22 H 28 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191709
H.S. Rzepa, "C22H28ClN3", 2015. https://doi.org/10.14469/ch/191718
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
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
H.S. Rzepa, "C12H11ClN2O", 2015. https://doi.org/10.14469/ch/191700
H.S. Rzepa, "C12H12ClN3", 2015. https://doi.org/10.14469/ch/191699
H.S. Rzepa, "C14H11ClN2O", 2015. https://doi.org/10.14469/ch/191730

Tags:Butyl, chemical reactions, Indole, Kinetic isotope effect, Organic chemistry, Physical organic chemistry, potential energy surfaces, relative energy
Posted in Historical, Interesting chemistry, reaction mechanism | 1 Comment »

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

Thursday, December 24th, 2015

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; theformation 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;

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

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

IRC for TS2, R=R'=H

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

For R=R'=H, ΔG₂₉₈^‡ for TS1 is higher than TS2 (✔ with expt)
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).
For R= t-butyl,R'=Me, ΔG₂₉₈^‡ of TS1 is lower than TS2 (✔ with expt).
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.
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)
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).
The position along the reaction path for proton abstraction is much later with R=R'=t-butyl (r_C-H ~1.42Å) than R=R'=H (r_C-H ~1.27Å), (❌ with the statement above: a reactant-like transition state even for the proton expulsion step).
The cross-over between TS1/TS2 as the rds is in the region of the substituents R=Me,R'=t-butyl (~✔ with expt).
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.
The steric effect induced by R=t-butyl is greater than when R'=t-butyl.
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)	k^H/k^D (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:

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

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

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
H.S. Rzepa, "Hydrogen Transfer Reactions Of Indoles", Zenodo, 1974. https://doi.org/10.5281/zenodo.18777
H.S. Rzepa, "C14H12ClN3", 2015. https://doi.org/10.14469/ch/191707
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
H. Rzepa, "The mechanism of diazo coupling to indoles", 2015. https://doi.org/10.14469/hpc/176
H.S. Rzepa, "C 14 H 12 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191705
H.S. Rzepa, "C 14 H 12 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191698
H.S. Rzepa, "C 14 H 12 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191713
H.S. Rzepa, "C14H12ClN3", 2015. https://doi.org/10.14469/ch/191712
H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191723
H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191719
H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191721
H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191720
H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191722
H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191717
H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191726
H.S. Rzepa, "C 19 H 22 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191714
H.S. Rzepa, "C22H28ClN3", 2015. https://doi.org/10.14469/ch/191715
H.S. Rzepa, "C 22 H 28 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191706
H.S. Rzepa, "C 22 H 28 Cl 1 N 3", 2015. https://doi.org/10.14469/ch/191709
H.S. Rzepa, "C22H28ClN3", 2015. https://doi.org/10.14469/ch/191718
H.S. Rzepa, "C12H11ClN2O", 2015. https://doi.org/10.14469/ch/191700
H.S. Rzepa, "C12H12ClN3", 2015. https://doi.org/10.14469/ch/191699

π-Resonance in amides: a crystallographic reality check.

Saturday, September 5th, 2015

The π-resonance in amides famously helped Pauling to his proposal of a helical structure for proteins. Here I explore some geometric properties of amides related to the C-N bond and the torsions about it.

Scheme

The key aspect of amides is that a lone pair of electrons on the nitrogen can conjugate with the C=O carbonyl only if the lone pair orbital is parallel to the C-O π-system. We can define this with the O=C-N-R torsion angle (and equate 0 or 180° with the p-orbitals being parallel). In the above definition, each R can be either 4-coordinate C (to avoid alternative conjugations) or H and the C-N bond is specified as being cyclic. As usual the R-factor is < 5%, no errors, no disorder.

First, the C-N torsion, which adopts values of either 0 or 180°. Notice that whilst the anti R-group shows no more than about 20° deviation from 180°, it does have a small tail tending towards longer C-N distances of >1.4Å. The hotspot is for the syn R-group. Here there is a strong trend that as the dihedral deviates from 0° the C-N bond very clearly elongates. As the π-π overlap decreases, the bond elongates from the hot spot value of ~1.34Å to 1.41Å at 50°. The greater propensity of the syn-R to twist may be because it incurs more steric hindrance or perhaps because we have defined the C-N bond to be part of a cycle.

Scheme

Next, we plot the C-N distance against the torsion R-N-C-R’, which defines how planar the nitrogen is. A value of 180° is planar and the hot-spot is here. But as the planarity decreases down to almost tetrahedral (110°) the C-N bond elongates to 1.41Å. Notice one rather intriguing aspect; from 180° to 160° or so, there is little response from the C-N bond, but the elongation really accelerates from 140° to 110°. A little twisting hardly affects the π-π overlap, but it really starts to matter for twists of >50°.

Scheme

Finally a plot of the C-N vs the C-O distances. As the C-N increases, the C-O contracts, this being a nice summary of the π resonance in amides.

Scheme

We have not seen any surprises, but this statistical exploration of crystal structures at least puts some numbers on the changes in bond lengths as a result of conjugative resonance.

Tags:Amide, chemical bonding, Conjugated system, Physical organic chemistry, Resonance
Posted in Chemical IT, crystal_structure_mining | 1 Comment »

A visualization of the anomeric effect from crystal structures.

Thursday, August 27th, 2015

The anomeric effect is best known in sugars, occuring in sub-structures such as RO-C-OR. Its origins relate to how the lone pairs on each oxygen atom align with the adjacent C-O bonds. When the alignment is 180°, one oxygen lone pair can donate into the C-O σ* empty orbital and a stabilisation occurs. Here I explore whether crystal structures reflect this effect.

Scheme

The torsion angles along each O-C bond are specified, along with the two C-O distances. All the bonds are declared acyclic, and the usual R < 5%, no disorder and no errors specified.

You can see from the plot below that the hotspot occurs when both RO-CO torsions are ~65°. From this we will assume that the two (unseen)^‡ lone pairs at any one of the oxygens are distributed approximately tetrahedrally around each oxygen, and if this is true then one of them must by definition be oriented ~ 180° with respect to the same RO-CO bond (the other is therefore oriented -60°). This allows it to be antiperiplanar to the adjacent C-O bond and hence interact with its σ* empty orbital. So the hotspot corresponds to structures where BOTH oxygen atoms have lone pairs which interact with the adjacent O-C anti bond.
There is a tiny cluster for which both RO-CO torsions are ~180° and hence neither oxygen has an antiperiplanar lone pair.
Only slightly larger are clusters where one torsion is ~65° and the other ~180°, meaning that only one oxygen has an antiperiplanar lone pair.
A plot of the two C-O lengths indeed shows an overall hotspot at ~1.40Å for both distances. If the search is filtered to include only torsions in the range 150-180°, the hotspot value increases to 1.415Å for both. If one torsion is restricted to 40-80° and the other to 150-180° the hotspot shows one C-O bond is about 0.012Å shorter than the other.

Scheme

I also include a further constraint, that the diffraction data must be collected below 140K. The hotspot moves to ~ 55/60° indicating values free of some vibrational noise.

Scheme

Interestingly, replacing oxygen with nitrogen reveals relatively few examples of the effect (C(NR₂)₄ is an exception). Replacing O by divalent S produces only 13 hits, with the surprising result (below) that in all of them only one S sets up an anomeric interaction. Arguably, the number of examples is too low to draw any firm conclusions from this observation.

Scheme

^‡Most diffractometers measure low angle scattering of X-rays by high density electrons. These are the core electrons associated with a nucleus rather than the valence electrons associated with lone pairs. Hence very few positions of valence lone pairs have ever been crystallographically measured.

Tags:Alkane stereochemistry, Anomeric effect, Carbohydrate chemistry, Carbohydrates, Carbon–oxygen bond, Chemical bond, Ether, Lone pair, Physical organic chemistry, Quantum chemistry, Stereochemistry, Technology/Internet
Posted in Chemical IT, crystal_structure_mining | No Comments »

Reproducibility in science: calculated kinetic isotope effects for cyclopropyl carbinyl radical.

Saturday, July 11th, 2015

Previously on the kinetic isotope effects for the Baeyer-Villiger reaction, I was discussing whether a realistic computed model could be constructed for the mechanism. The measured KIE or kinetic isotope effects (along with the approximate rate of the reaction) were to be our reality check. I had used ΔΔG energy differences and then HRR (harmonic rate ratios) to compute[1] the KIE, and Dan Singleton asked if I had included heavy atom tunnelling corrections in the calculation, which I had not. His group has shown these are not negligible for low-barrier reactions such as ring opening of cyclopropyl carbinyl radical.[2] As a prelude to configuring his suggested programs for computing tunnelling (GAUSSRATE and POLYRATE), it was important I learnt how to reproduce his KIE values.[2] Hence the title of this post. Now, read on.

I felt I could contribute to the cause by extending the published results in two respects:

The reported[2] calculations are for the model B3LYP/6-31G(d) but the article does not report the tolerance to e.g. basis set variation (6-31G(d), a modest basis set by 2015 standards),
or to the quantum model used (B3LYP, a veritable DFT method).

These two model chemistries can both be tested by “increasing” their accuracy. The Def2-QZVPP basis set is nearing the CBS, or complete basis set limit. The coupled-cluster CCSD(T) method is regarded as the gold standard for single reference calculations. The CASSCF method tests the response to a multi-reference wave function. Each is applied separately to ensure only one variable is being changed at a time.

Method	Expt. KIE[2]^‡	Pred. KIE (my result)	Pred. ΔG₂₉₈^‡	Pred. KIE[2]	KIE + Tunnelling correction[2]
B3LYP/6-31G(d)[3],[4]	1.079₂₉₅	1.0582	8.0	1.058	1.073
B3LYP/6-31G(d)[3],[4]	1.163₁₇₃	1.1067	8.0	1.106	1.169
B3LYP/Def2-QZVPP[5],[6]	1.079₂₉₅	1.0563	6.6	1.058	1.073
B3LYP/Def2-QZVPP[5],[6]	1.163₁₇₃	1.1031	6.6	1.106	1.169
CASSCF(5,5)/6-31G(d)[7],[8]	1.079₂₉₅	1.0572	8.2	1.058	1.073
CASSCF(5,5)/6-31G(d)[7],[8]	1.163₁₇₃	1.1050	8.2	1.106	1.169
CASSCF(5,5)/Def2-TZVPP[9],[10]	1.079₂₉₅	1.0561	7.9	1.058	1.073
CASSCF(5,5)/Def2-TZVPP[9],[10]	1.163₁₇₃	1.1028	7.9	1.106	1.169
CCSD(T)/6-31G(d)[11],[12]	1.079₂₉₅	1.0597^†	9.7	1.058	1.073
CCSD(T)/6-31G(d)[11],[12]	1.163₁₇₃	1.1099	9.7	1.106	1.169

†Actually separate ratios of ¹³C/¹²C(C-4)/¹³C/¹²C(C-3) since C-3 and C-4 are not equivalent in the reactant species because of the methylene group pyramidalisation. The KIE calculation input and outputs are archived.[13]

The first two rows of table are my attempt at an exact replication of the literature. The start point of such a project would be the supporting information or SI[2] which contains coordinates for the program GAUSSRATE and defines key structures in the form of a double-column, page thrown (broken might be a better word) PDF file. It was going to be a bit of a struggle to reconstitute this format into the structure required for a Gaussian calculation, so I simply constructed the models from scratch and optimised to the ring-opening transition state[4] and reactant.[3] I used a more recent version of the Gaussian program (G09/D.01 rather than G03/D.02) to do this, and tightened up some of the criteria to modern cutoff standards. A continuum solvent model could have been specified (the solvent used in the experiments was 1,2-dichlorobenzene) but since no mention was made of solvent, I assumed a gas phase calculation had originally been done. The starting geometry of the reactant deliberately had no symmetry, but during optimisation it converged to having a plane of symmetry using the B3LYP/6-31G(d) level of theory (the SI does not note this symmetry, it is implicit). I then used my code[1] to compute the isotope effects. The KIE program used in the original literature calculation was not directly mentioned in the supporting information but is presumed to be Quiver. Dan Singleton has recently sent me these codes, but they still need to be compiled and tested at my end. I ended up with splendid agreement for the KIE as you can see above (top two lines). Its reproducible! Hence the various assumptions I made in achieving this appear justified.

Returning to the geometry of the cyclopropyl carbinyl radical as having a plane of symmetry, two of the other methods, CCSD(T)/6-31G(d) and CASSCF(5,5)/6-31G(d), as well as CASSCF(5,5) at the better Def2-TZVPP basis all predicted that the methylene radical is twisted by about 20° with respect to the Cs plane of the ring.

It is useful to check whether this twisting has any impact on the predicted KIE. The answer is clear (Table). ALL the methods predict similar KIE to ± 0.003,^† which is as about as accurate as can be measured experimentally at the 1σ level of confidence. This is a remarkable result; few other computed molecular properties turn out to be so insensitive to the quantum procedure used. The next stage will be to check if the tunnelling corrections required to bring the calculation into congruence with the measured values are similarly insensitive.

^‡ The “barrier height” is quoted as 7 kcal/mol[2]. This is probably NOT the activation free energy.

References

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
O.M. Gonzalez-James, X. Zhang, A. Datta, D.A. Hrovat, W.T. Borden, and D.A. Singleton, "Experimental Evidence for Heavy-Atom Tunneling in the Ring-Opening of Cyclopropylcarbinyl Radical from Intramolecular 12C/13C Kinetic Isotope Effects", Journal of the American Chemical Society, vol. 132, pp. 12548-12549, 2010. https://doi.org/10.1021/ja1055593
H.S. Rzepa, "C4H7(2)", 2015. https://doi.org/10.14469/ch/191357
H.S. Rzepa, "C4H7(2)", 2015. https://doi.org/10.14469/ch/191358
H.S. Rzepa, "C 4 H 7", 2015. https://doi.org/10.14469/ch/191353
H.S. Rzepa, "C 4 H 7", 2015. https://doi.org/10.14469/ch/191352
H.S. Rzepa, "C 4 H 7", 2015. https://doi.org/10.14469/ch/191361
H.S. Rzepa, "C 4 H 7", 2015. https://doi.org/10.14469/ch/191364
H.S. Rzepa, "C 4 H 7", 2015. https://doi.org/10.14469/ch/191363
H.S. Rzepa, "C 4 H 7", 2015. https://doi.org/10.14469/ch/191362
H.S. Rzepa, "C 4 H 7", 2015. https://doi.org/10.14469/ch/191367
H.S. Rzepa, "C 4 H 7", 2015. https://doi.org/10.14469/ch/191356
H.S. Rzepa, "Reproducibility In Science: Calculated Kinetic Isotope Effects For Cyclopropyl Carbonyl Radical.", 2015. https://doi.org/10.5281/zenodo.19949

Tags:activation free energy, Basis set, Dan Singleton, energy differences, gas phase calculation, Kinetic isotope effect, PDF, Physical organic chemistry
Posted in reaction mechanism | 2 Comments »

Reproducibility in science: calculated kinetic isotope effects for the Baeyer-Villiger reaction.

Wednesday, July 1st, 2015

Recollect this earlier post on the topic of the Baeyer-Villiger reaction. In 1999 natural abundance kinetic isotope effects were reported[1] and I set out to calculate the values predicted for a particular model constructed using Quantum mechanics. This comparison of measurement and calculation is nowadays a standard verification of both experiment and theory. When the two disagree either the computational model is wrong or incomplete, or the remoter possibility that there is something not understood about the experiment.

In this case, as you can see above, the measured ¹³C KIE at the carbonyl carbon was in the range 1.045-1.051, whereas the theory (ωB97XD/Def2-TZVP/SCRF=DCM) predicted a significantly smaller value of 1.023 for the first kinetic step, the formation of the tetrahedral intermediate. This was the step suggested by Singleton as rate limiting in the forward direction (there was also a larger disagreement on the ²H KIE at C3/C5, measured as 0.97 and calculated as 0.997 but this might simply be a typographical error).

Now we have to find an explanation, and it was contingent upon myself to show that the theory was properly executed. At this stage, Dan Singleton offered some suggestions on this blog. This one related to how I had calculated the KIE, with Dan suggesting that the method I had used might be too inaccurate to draw any conclusions from. It was up to me to reproduce my results using the method suggested by Dan as the more accurate. And this is where this story really starts.

I had used the Free energy method, which involves calculating the free energies of reactant and product using the built-in thermochemical component of the Gaussian code. Dan’s concern was that such free energies are only reported to an accuracy of 0.000001 Hartree. Since the isotope effect is calculated from differences in these free energies, was this degree of precision high enough to ensure reliable calculated KIE? Better to solve the equations directly and these involve the so-called Bigeleisen-Mayer terms derived from the classical partition functions. I recollected we had used this method back in 1975[2], but I assumed the computer code used was long since lost by myself. Instead Quiver was suggested (first written around 1988 by Keith Laidig at Yale) and I added the comment that the modern version of Quiver is called THERMISTP[3]. All that needed to be done was to acquire a copy of an appropriate code and re-run the KIE calculation using it.

And now comes the true purpose of this post, which is reproducing a calculation that might have been done ~20 years ago using computer code. Issues such as:

Does the code still exist in either Source form or Executable form?
If it does, will it still run correctly on a modern computer?
Is it documented sufficiently to allow someone not immersed in the code to run it. After ~20 years, it might not be possible to talk to the original coders for explanations.

So this is what happened when I investigated.

Requests for the THERMISTP code of its authors, by email, have not yet brought a response. They may still, but one has to recognise that they may not. For example (unless I missed it), the article in which THERMISTP is cited[3] does not document how the code described in that article might be obtained (but the authors’ emails are provided).
I then followed up Dan’s suggestion to use Quiver. A copy was tracked down at http://www.chem.ucla.edu/~mccarren/houkGroup.html and a tar archive was available. The program comes as Quiver itself and a pre-program called qcrunch is used to prepare the data for Quiver.
It comes with pretty good (and brief!) documentation.
Fortran source code for Quiver (quiver.f) is available which is good, since one can compile it for one’s favourite machine (in my case a Mac running OS X). One can also read the comments to discover information beyond that provided by the documentation.
qcrunch however is only provided as an executable, and that means running it on Linux. One cannot read the comments!
When I ran qcrunch, it complained that an auxiliary program was not available to it. It wanted to run something associated with Gaussian 94, sadly long since gone from our systems. With no source code available I would have to fool qcrunch into thinking that Gaussian09 was really Gaussian94. It involves symbolic links and such and needs a little Unix expertise.
That done, I gave it its first input data, which is the normal mode analysis of the reactant involved in the reaction above, in the form of a formatted checkpoint file (a .fchk file). It seemed happy, and so I proceeded to the next step
which was to run quiver. This needed compilation. Here we encounter interesting issues. Most Fortran code can have “dependencies” which relate to the compiler used by its developer. The compiler however is rarely stated in the documentation, and I decided to use GFortran, which I obtained from http://hpc.sourceforge.net and installed on my Mac. And using this compiler, the compilation failed with about 3 syntax errors. You have to know enough Fortran to correct them all and obtain your executable.
Now I could run quiver to get the Bigeleisen-Mayer functions. It appeared to happily run, but produced rubbish (the anticipated frequencies had silly values of -10,000 cm^-1 etc).
Now you go back to the code, and discover that the dimension statement (yes, Fortran required you to specify the size of your arrays in the code) is limited to 40 atoms! The Baeyer-Villiger system has 48. Easily fixed. Still rubbish out!
So now you go back to the start and create data for a tiny molecule, water in this case, and again qcrunch and quiver are run. Now sensible results, in the shape of normal mode frequencies of the anticipated values.
Conclusion: That qcrunch is probably also dimensioned to 40 atoms, but I now have no way of correcting this because I do not (yet?) have the source code for it. It might indeed be lost. If it is, it will have to be re-written from scratch.
Time elapsed thus far: ~2 weeks of intermittent work on the problem.
It was at this point I had one of those happy moments of accidental discovery. I updated the OS on my Mac to 10.10.4 (this was released yesterday). One of the new features was TRIM support for solid state third party disks (SSDs). I installed it and decided to test an external SSD connected to my machine. It happened to have lots of old stuff on it. In an idle moment, I decided to search its file base for the program we had written back in 1975 and which I had convinced myself was long-lost. Hey presto, there it was (KINISOT.f). I even found example input and output files. These take the form of frequencies for reactant (normal isotopes), reactant (new isotope), transition state (normal isotope) and transition state (new isotope). Not as elegant as quiver, but entirely fit for my purpose here.
The results:
1. ¹³C KIE for the carbonyl carbon using the free energy method: 1.023 (see diagram above)
2. ¹³C KIE using the Bigeleisen-Mayer partition function ratios: 1.0226
3. ²H KIE for the axial α protons using the free energy method: 0.928
4. ²H KIE for the axial α protons using the Bigeleisen-Mayer partition function ratios: 0.92831
The agreement enables me to conclude that the free energy method does not in fact suffer from significant round-off errors and other inaccuracies induced by the subtraction of two very similar energies.

What I have I learnt from this experience?

That reproducing a calculation using old computer codes (in this case ~18 years) can be a difficult and complex procedure, relying on being able to contact people and ask for copies of the code, coping with possibly non-existent documentation, and with no access to the original coder who may be the only person able to explain it.
That 20 years of continuous improvement in the computer industry means that a problem that would require impossibly enormous amounts of computer time then might be easily feasible now. The limit of 40 atoms in 1997 for quiver and qcrunch must have seemed future proof then, but alas it did not prove so.
That if the source code for a program dimensioned too small is lost, one may have no option but to re-write it from scratch. It would indeed be a good test of reproducibility if the answers are unchanged!
Keep good archives of your old work. You never know when they might come in useful!

Lessons for the future?

Document your code! Put yourself in the position of someone in 20 years time trying to make sense of it! And record the compiler used (along with flags), and also the OS.
Archive it in Zenodo or Github, and include that documentation.[4] You might not be contactable by email in 20 years time!
include test inputs and outputs (OK, that is mostly done nowadays).
I intend to do the above for my program. But I will use the immediate excuse often used by others for not archiving their codes: it is not yet documented sufficiently! But surely this would only take an hour or so? Watch this space. And please forgive the coding, it was done in 1975, when I was very inexperienced (another oft-used excuse!).

What about the Baeyer-Villiger isotope effects? Well, the above merely establishes that the free energy method (which requires no extra codes) has sufficient accuracy for computing KIEs. An explanation for the difference between the reported ¹³C KIE at the carbonyl carbon and its calculation still needs identifying. I state at the outset that (heavy atom) tunnelling corrections are NOT yet applied, and I might try the small-curvature tunneling model suggested by Dan, since he and Borden[5] have shown it can indeed be important. It would be exciting if the hydrogen isotope effects can be reproduced without tunnelling but that the carbon KIEs do require it.

I have received much help in the above saga from Jordi Bures Amat here, Erik Plata in Donna Blackmond’s group and information about another useful system for calculating KIE, the ISOEFF program.[6]

References

D.A. Singleton, and M.J. Szymanski, "Simultaneous Determination of Intermolecular and Intramolecular 13C and 2H Kinetic Isotope Effects at Natural Abundance", Journal of the American Chemical Society, vol. 121, pp. 9455-9456, 1999. https://doi.org/10.1021/ja992016z
M.J.S. Dewar, S. Olivella, and H.S. Rzepa, "Ground states of molecules. 49. MINDO/3 study of the retro-Diels-Alder reaction of cyclohexene", Journal of the American Chemical Society, vol. 100, pp. 5650-5659, 1978. https://doi.org/10.1021/ja00486a013
M. Saunders, M. Wolfsberg, F.A.L. Anet, and O. Kronja, "A Steric Deuterium Isotope Effect in 1,1,3,3-Tetramethylcyclohexane", Journal of the American Chemical Society, vol. 129, pp. 10276-10281, 2007. https://doi.org/10.1021/ja072375r
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
O.M. Gonzalez-James, X. Zhang, A. Datta, D.A. Hrovat, W.T. Borden, and D.A. Singleton, "Experimental Evidence for Heavy-Atom Tunneling in the Ring-Opening of Cyclopropylcarbinyl Radical from Intramolecular 12C/13C Kinetic Isotope Effects", Journal of the American Chemical Society, vol. 132, pp. 12548-12549, 2010. https://doi.org/10.1021/ja1055593
V. Anisimov, and P. Paneth, "ISOEFF98. A program for studies of isotope effects using Hessian modifications", Journal of Mathematical Chemistry, vol. 26, pp. 75-86, 1999. https://doi.org/10.1023/a:1019173509273

Tags:Dan Singleton, Donna Blackmond, energy method, Erik Plata, free energy method, Jordi Bures Amat, Keith Laidig, Kinetic isotope effect, Physical organic chemistry, Yale
Posted in reaction mechanism | 4 Comments »

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

Wednesday, June 10th, 2015

I have blogged before about the mechanism of this classical oxidation reaction. Here I further explore computed models, and whether they match the observed kinetic isotope effects (KIE) obtained using the natural-abundance method described in the previous post.

There is much previous study of this rearrangement, and the issue can be reduced to deciding whether TS1 or TS2 is rate-limiting. The conventional text-book wisdom is that the carbon migration step TS2 is the “rds” and it was therefore quite a surprise when Singleton and Szymanski[1] obtained KIE which seemed to clearly point instead to TS1 as being rate limiting, inferred from a large ¹³C effect (~1.05) at the carbonyl carbon (blue star) and none at the α-carbon (red star). This result (for this specific reaction and conditions, which is dichloromethane as solvent) is now routinely quoted[2] when the mechanism is discussed. This latter article reports[2] calculated energetics for TS1 and TS2 (see Table 1 in this article) and after exploring various models, the conclusion is that TS1 and TS2 are essentially isoenergic. However, no isotope effects are computed for their models, and so we do not know if TS1 or TS2 agrees better with the reported values.[2] Since I had managed to get pretty good agreement with experimental KIEs using the ωB97XD/Def2-TZVPP/SCRF=xylenes model for the Diels-Alder reaction, I thought I would try the same method to see how it performs for the Baeyer-Villiger.

It is in fact non-trivial to set up a consistent model. Using arrow pushing, one can on paper draw three variations for TS1, the formation of the peroxyhemiacetal tetrahedral intermediate (TI) and also often called the Criegee intermediate.

TS1a is the “text-book” variation, involving the production of a zwitterionic intermediate which immediately undergoes a proton transfer (PT). The arrows tend not to be used for this last step, since the direct transfer would involve a 4-membered ring and a highly non-linear geometry at the transferring proton which is understood to be “unfavourable”. Such zwitterions involve a large degree of charge separation and hence a large dipole moment. In a non-protic solvent such as dichloromethane, one is very loath to use such species in a mechanism, and it’s not modelled here either.
Using just cyclohexanone and peracid, it is in fact difficult to avoid ionic species. TS1b is an attempt which shows the proton transfer is done first on the peracid to create a so-called carbonyl ylid, and this then reacts with the ketone
If however a proton transfer agent is introduced as TS1c, one can use this species (shown in red above) to transfer the proton as part of a concerted mechanism; this was in fact the expedient used in the earlier theoretical study[2] and this route tends to avoid much if not all of the charge separation. The acid comes from the product of the reaction, and hence the kinetics may in fact have an induction period when this acid builds up. The initial proton transfer reagent may also be traces of water present in reagents or solvent. Singleton and Szymanski in fact include no supporting information in their article and so we do not know what the concentrations used were (assumed for the present discussion as 1M) whether everything was rigorously dried, or indeed what the kinetic order in [peracid] turned out to be.

The same problem is faced with TS2; how to transfer a proton? Because we want to compare the relative energies of TS1 and TS2, we also have to atom-balance the mechanism, and so the additional acid component introduced into TS1c is also retained in two alternative mechanisms for TS2 (and for TS1b).

TS2a uses just the components of the tetrahedral intermediate (TI), but again in a fashion that requires no charge separation during the reaction. The additional acid component (red) plays a passive role, hydrogen bonding to the TI.
TS2b now incorporates the additional acid by expanding the ring (green) in an active role.

IRCs using the 6-311G(d,p) basis) for TS1[3] and TS2[4] are interesting in revealing relative synchronicity of the proton transfers for TS1 but asynchronicity for TS2 involving a hidden intermediate.

The energy, energy gradient and dipole moment magnitudes for this second step are particularly fascinating. The dipole moment starts off quite small (3.1D) at the TI, and is still so at the TS, but almost immediately afterwards, it shoots up to ~12D as the hidden intermediate develops (IRC ~4) Two successive proton transfers (IRC ~6, 7) then reduce the value down again.

A table of results can now be constructed for these various models, evaluating two different basis sets for the calculation.

system	ΔΔG₂₉₈ (1M) ωB97XD/6-311G(d,p)/SCRF=DCM, kcal/mol	Dipolemoment,D	ΔG₂₉₈ (1M) ωB97XD/Def2-TZVPP/SCRF=DCM
Reactants	+1.4^a	–	-3.3^a[5],[6],[7]
Complexed state	0.0[8]	5.0	0.0[9]
TS1a	n/a	n/a	n/a
TS1b	32.9[10]	8.6	32.2[11]
TS1c	14.9[12]	3.0	16.1[13]
TI	-1.7[14]	3.1	-0.3[15]
TS2a	22.2[16]	9.3	25.0[17]
TS2b	20.2[12]	5.4	22.7[18]
Product	-69.8[19]	5.3	[20]

^aThis value is corrected to a standard state of 1M for a termolecular reaction by 3.78 kcal/mol from the computed free energies at 1 atm as described previously.[21]

Firstly, one must note that the resting state for the reactants depends on the concentration. At 1M at the higher basis set, its the separated reactants, but at the lower it is the hydrogen bonded complex between them. Increasing the concentration would favour the latter.
TS1c is significantly lower in free energy than TS2b, a result somewhat at variance with the earlier report.[2] The functional used in the present calculation, the basis set, the dispersion model and the solvation model are all improvements on the original work.
Likewise, the energy of TI, the Criegee intermediate emerges as similar to the reactants. Coupled with the magnitude of the barrier for TS1c this does tend to point to a relatively rapid pre-equilibrium and that TS2b determines the rate of reaction.

Kinetic isotope effects for our models

Having constructed models, we can now subject them to testing against the measured kinetic isotope effects.[1]

The measured values are shown above. The first set (a) are what are described as intermolecular isotope effects and result from measuring changes in the isotopic abundance obtained by recovering unreacted starting material after a large proportion of the reaction has gone to completion. This was interpreted as indicating TS1 was rate limiting. Using instead the uncomplexed cyclohexanone has only a small effect (C1: 1.023 complexed, 1.021 uncomplexed).
The values in parentheses were obtained using the TS1c model above and are relative to the complexed reactant involving hydrogen bonds between the cyclohexanone, the peracid and the acid catalyst. The agreement can only be described as partial.
- The predicted ¹³C isotope effect at C1 is about half of the measured value. The previous calibration of the method being used had resulted in agreement within experimental error for the Diels Alder reaction, and so this large disagreement is unexpected.
- The ²H KIE at C2 is within experimental error.
- The ²H KIE at C3 is badly out. Here, it is the experimental result that seems wrong, since there is no reason to expect any KIE at this position especially since the ¹³C at the same position is 1.00 for both measured and calculated values.
So we might infer an inconclusive result. I can only speculate on the computed model here, and invoke in effect the variation principle. If the model is wrong, we would expect a more correct model to have a lower rather than higher energy relative to reactants. The free energy of activation however is already low, corresponding to a very fast room temperature reaction; too fast indeed to easily recover any unreacted starting material if that were to be rate limiting!
Set (b) corresponds to what is described as an intramolecular KIE as defined by TS2, since it is measured from isotopic ratio changes in the product rather than reactant as the reaction progresses.
- The value in (…) is relative to the complexed reactants and the value in […] is relative to TI.
- The predicted ¹³C isotope effect at C2m (the migrating carbon) agrees within experimental error with the measured value if the TI is used as the reference. This nicely shows how isotope effects for what may not be a rate limiting step can be measured by this technique.
- The predicted ¹³C isotope effect at C1 (which is not reported in the original article) relative to TI is significant, and it would be nice to confirm the computed model by a measurement at this position.
- The other KIE also agree reasonably with experiment when TI is specified as the reactant for this step.

So is there support from the calculations for the formation of the semi-peroxyacetal being rate limiting, as claimed by Singleton and Szymanski[1]? There is no doubt that the KIE obtained from measuring the product is different from measuring the reactant, but the lack of agreement for two of the measured values for TS1 is a concern. Perhaps one might conclude that this is an experiment well worth repeating. Of the two computed models, TS1 and TS2, the variation principle would again lead us to suspecting that the one with higher energy can only be decreased by improvement, whereas improvement of the one with the lower energy cannot also increase its relative energy. So if a new model for the carbon migration step can be found, its activation free energy must be lower than that already identified. But the excellent agreement between TS2b shown in (b) suggests that this model is already pretty good! Lowering its energy by >7kcal/mol to make TS1 rate limiting would probably require quite a different model.

What I think is more certain is the value of subjecting the measured KIE to computed models, in the knowledge that if the model is indeed realistic a good agreement should be expected. And it is a shame that the natural abundance KIE method cannot be applied to oxygen isotope effects, which would surely settle the issue.^‡ And I should end by reminding that there is evidence that the mechanism may be quite sensitive to variation of solvent, ketone, peracid, pH, etc, and so these conclusions only apply to this specific reaction in dichloromethane.

^‡ For TI > TS2, the ¹⁸O KIE is predicted as 1.048 (peroxy oxygen) and 1.032 (acyl oxygen). For Reactant > TS1, the values are respectively 0.998 and 1.003.

References

D.A. Singleton, and M.J. Szymanski, "Simultaneous Determination of Intermolecular and Intramolecular 13C and 2H Kinetic Isotope Effects at Natural Abundance", Journal of the American Chemical Society, vol. 121, pp. 9455-9456, 1999. https://doi.org/10.1021/ja992016z
J.R. Alvarez-Idaboy, and L. Reyes, "Reinvestigating the Role of Multiple Hydrogen Transfers in Baeyer−Villiger Reactions", The Journal of Organic Chemistry, vol. 72, pp. 6580-6583, 2007. https://doi.org/10.1021/jo070956t
H.S. Rzepa, "C20H20Cl2O6", 2015. https://doi.org/10.14469/ch/191318
H.S. Rzepa, "C20H20Cl2O6", 2015. https://doi.org/10.14469/ch/191317
H.S. Rzepa, "C 7 H 5 Cl 1 O 2", 2015. https://doi.org/10.14469/ch/191322
H.S. Rzepa, "C 7 H 5 Cl 1 O 3", 2015. https://doi.org/10.14469/ch/191323
H.S. Rzepa, "C 6 H 10 O 1", 2015. https://doi.org/10.14469/ch/191324
H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191307
H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191315
H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191313
H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191325
H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191306
H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191312
H.S. Rzepa, "C20H20Cl2O6", 2015. https://doi.org/10.14469/ch/191311
H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191319
H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191314
H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191321
H.S. Rzepa, and H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191320
H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191310
H.S. Rzepa, "C 20 H 20 Cl 2 O 6", 2015. https://doi.org/10.14469/ch/191327
J.R. Alvarez-Idaboy, L. Reyes, and J. Cruz, "A New Specific Mechanism for the Acid Catalysis of the Addition Step in the Baeyer−Villiger Rearrangement", Organic Letters, vol. 8, pp. 1763-1765, 2006. https://doi.org/10.1021/ol060261z

Tags:ATM, Baeyer–Villiger oxidation, Chemistry, Dipole, energy, energy gradient, Kinetic isotope effect, Physical organic chemistry
Posted in reaction mechanism | 4 Comments »

Natural abundance kinetic isotope effects: expt. vs theory.

Wednesday, June 3rd, 2015

My PhD thesis involved determining kinetic isotope effects (KIE) for aromatic electrophilic substitution reactions in an effort to learn more about the nature of the transition states involved.[1] I learnt relatively little, mostly because a transition state geometry is defined by 3N-6 variables (N = number of atoms) and its force constants by even more and you get only one or two measured KIE per reaction; a rather under-defined problem in terms of data! So I decided to spend a PostDoc learning how to invert the problem by computing the anticipated isotope effects using quantum mechanics and then comparing the predictions with measured KIE.[2] Although such computation allows access to ALL possible isotope effects, the problem is still under-defined because of the lack of measured KIE to compare the predictions with. In 1995 Dan Singleton and Allen Thomas reported an elegant strategy to this very problem by proposing a remarkably simple method for obtaining KIE using natural isotopic abundances.[3] It allows isotope effects to be measured for all the positions in one of the reactant molecules by running the reaction close to completion and then recovering unreacted reactant and measuring the changes in its isotope abundances using NMR. The method has since been widely applied[4],[5] and improved.[6] Here I explore how measured and calculated KIE can be reconciled.

The original example uses the Diels-Alder cycloaddition as an example, with the 2-methylbutadiene component being subjected to the isotopic abundance. Although comparison with calculation on related systems was done at the time[7] the computational methods in use then did not allow effects such as solvation to be included. I thought it might be worth re-investigating this specific reaction using more modern methodology (ωB97XD/Def2-TZVPP/SCRF=xylenes), giving an opportunity for testing one key assumption made by Singleton and Allen, viz the use of an internal isotope reference for a site where the KIE is assumed to be exactly 1.000 (the 2-methyl group in this instance). This assumption made me recollect my post on how methyl groups might not be entirely passive by rotating (methyl “flags”) in the Diels-Alder reaction between cis-butene and 1,4-dimethylbutadiene. I had concluded that post by remarking that Rotating methyl groups should be looked at more often as harbingers of interesting effects, which in this context may mean that such rotations may not be entirely isotope agnostic.

To start, I note that the endo (closed shell, i.e. non-biradical; the wavefunction is STABLE to open shell solutions) transition state obtained for this reaction[8],[9] has a computed dipole moment of 6.1D, just verging into the region where solvation starts to make an impact. Perhaps the most important conclusion drawn from Singleton and Allen’s original article[2] was that the presence of an apparently innocuous 2-methyl substituent is sufficient to render the reaction asynchronous, which means that one C-C bond forms faster than the other. They drew this conclusion from observing that the inverse deuterium isotope effect was larger at C1 than C4, the difference being well outside of their estimated errors. The calculations indicate that the two bonds have predicted lengths of 2.197 (to C1) and 2.294Å (to C4) at the transition state. This means that an asynchronicity as small as Δ0.1Å can be picked up in measured isotope effects!

The calculated activation free energy is 19.2 kcal/mol (0.044M), which is entirely reasonable for a reaction occurring slowly at room temperature. The barrier for the exo isomer is 21.0 kcal/mol, 1.8 kcal/mol higher in free energy.^† The measured isotope effects are shown below with the predicted values in brackets. The colour code is green=within the estimated experimental error, red=outside the error.

The following observations can be made:

The internal isotope reference assumed as 1.000 is reasonable for carbon, but the “rotating methyl groups” resulting from hyper conjugation between the C-H groups and the π system do have a small effect resulting in a predicted KIE of 0.996 rather than the assumed 1.000. This will impact upon all the other measured values to some extent.
All the predicted^‡ ¹³C isotope effects agree with experiment within the error estimated for the latter. The calculation also has its errors, of which the most obvious is that harmonic frequencies are used rather than the more correct anharmonic values.
The ²H isotope effects show more deviation. This might be a combination of the assumption that the internal Me reference has no isotope effect coupled with the use of harmonic frequencies for the calculation.
Although the ²H values differ somewhat beyond the experimental error, the E/Z effects are well reproduced by calculation. The inverse isotope effect for the (Z) configuration is significantly larger in magnitude than for the (E) form, as was indeed noted by Singleton and Thomas.
So too is the asymmetry induced by the methyl group. The inverse isotope effects are greater for the more completely formed bond (to C1) than for the lagging bond (to C4). They are indeed a very sensitive measure of reaction synchronicity.

The pretty good agreement between calculation and experiment provides considerable reassurance that the calculated properties of transition states can indeed be subjected to reality checks using experiment. Indeed, it takes little more than a day to compute a complete set of KIEs, far less than it takes to measure them. One could easily argue that such a computation should accompany measured KIE whenever possible.

^‡This gives me an opportunity to extol the virtues of effective RDM (research data management). The two DOIs for the data include files containing the full coordinates and force constant matrices for both reactant and TS. Using these, one can obtain frequencies for any isotopic substitution you might wish to make in <1 second each, and hence isotope effects not computed here. One option might be to e.g. invert the reactant from the 2-methylbutadiene to the maleic anhydride and hence compute the isotope effects expected on this species (not reported in the original article) or to monitor instead the product.[10]

^†The KIE have only subtle small differences to the endo isomer; too small to assign the stereochemistry with certainty.

References

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
M.J.S. Dewar, S. Olivella, and H.S. Rzepa, "Ground states of molecules. 49. MINDO/3 study of the retro-Diels-Alder reaction of cyclohexene", Journal of the American Chemical Society, vol. 100, pp. 5650-5659, 1978. https://doi.org/10.1021/ja00486a013
D.A. Singleton, and A.A. Thomas, "High-Precision Simultaneous Determination of Multiple Small Kinetic Isotope Effects at Natural Abundance", Journal of the American Chemical Society, vol. 117, pp. 9357-9358, 1995. https://doi.org/10.1021/ja00141a030
https://doi.org/
Y. Wu, R.P. Singh, and L. Deng, "Asymmetric Olefin Isomerization of Butenolides via Proton Transfer Catalysis by an Organic Molecule", Journal of the American Chemical Society, vol. 133, pp. 12458-12461, 2011. https://doi.org/10.1021/ja205674x
J. Chan, A.R. Lewis, M. Gilbert, M. Karwaski, and A.J. Bennet, "A direct NMR method for the measurement of competitive kinetic isotope effects", Nature Chemical Biology, vol. 6, pp. 405-407, 2010. https://doi.org/10.1038/nchembio.352
J.W. Storer, L. Raimondi, and K.N. Houk, "Theoretical Secondary Kinetic Isotope Effects and the Interpretation of Transition State Geometries. 2. The Diels-Alder Reaction Transition State Geometry", Journal of the American Chemical Society, vol. 116, pp. 9675-9683, 1994. https://doi.org/10.1021/ja00100a037
H.S. Rzepa, "C 9 H 10 O 3", 2015. https://doi.org/10.14469/ch/191299
H.S. Rzepa, "C 9 H 10 O 3", 2015. https://doi.org/10.14469/ch/191301
D.E. Frantz, D.A. Singleton, and J.P. Snyder, "13C Kinetic Isotope Effects for the Addition of Lithium Dibutylcuprate to Cyclohexenone. Reductive Elimination Is Rate-Determining", Journal of the American Chemical Society, vol. 119, pp. 3383-3384, 1997. https://doi.org/10.1021/ja9636348

Tags:Allen Thomas, calculated activation free energy, Chemistry, Dan Singleton, Deuterium, Diels–Alder reaction, Isotope, Isotopes, Kinetic isotope effect, Nuclear physics, Physical organic chemistry, shell solutions
Posted in reaction mechanism | 6 Comments »

Henry Rzepa's blog

Posts Tagged ‘Physical organic chemistry’

A molecular balance for dispersion energy?

References

Kinetic isotope effect models as a function of ring substituent for indole-3-carboxylic acids and indolin-2-ones.

1,3-dimethyl-indolinones:

Indole-3-carboxylic acids:

References

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

Possible errors in the model:

References

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

Possible errors in the model:

References

π-Resonance in amides: a crystallographic reality check.

A visualization of the anomeric effect from crystal structures.

Reproducibility in science: calculated kinetic isotope effects for cyclopropyl carbinyl radical.

References

Reproducibility in science: calculated kinetic isotope effects for the Baeyer-Villiger reaction.

References

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

Kinetic isotope effects for our models

References

Natural abundance kinetic isotope effects: expt. vs theory.

References

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