Posts Tagged ‘gas phase calculation’

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.

cp

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

  1. 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),
  2. 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
1.163173 1.1067 1.106 1.169
B3LYP/Def2-QZVPP[5],[6] 1.079295 1.0563 6.6 1.058 1.073
1.163173 1.1031 1.106 1.169
CASSCF(5,5)/6-31G(d)[7],[8] 1.079295 1.0572 8.2 1.058 1.073
1.163173 1.1050 1.106 1.169
CASSCF(5,5)/Def2-TZVPP[9],[10] 1.079295 1.0561 7.9 1.058 1.073
1.163173 1.1028 1.106 1.169
CCSD(T)/6-31G(d)[11],[12] 1.079295 1.0597† 9.7 1.058 1.073
1.163173 1.1099 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.

cp-asymm

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

  1. 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
  2. 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 <sup>12</sup>C/<sup>13</sup>C Kinetic Isotope Effects", Journal of the American Chemical Society, vol. 132, pp. 12548-12549, 2010. https://doi.org/10.1021/ja1055593
  3. H.S. Rzepa, "C4H7(2)", 2015. https://doi.org/10.14469/ch/191357
  4. H.S. Rzepa, "C4H7(2)", 2015. https://doi.org/10.14469/ch/191358
  5. H.S. Rzepa, "C 4 H 7", 2015. https://doi.org/10.14469/ch/191353
  6. H.S. Rzepa, "C 4 H 7", 2015. https://doi.org/10.14469/ch/191352
  7. H.S. Rzepa, "C 4 H 7", 2015. https://doi.org/10.14469/ch/191361
  8. H.S. Rzepa, "C 4 H 7", 2015. https://doi.org/10.14469/ch/191364
  9. H.S. Rzepa, "C 4 H 7", 2015. https://doi.org/10.14469/ch/191363
  10. H.S. Rzepa, "C 4 H 7", 2015. https://doi.org/10.14469/ch/191362
  11. H.S. Rzepa, "C 4 H 7", 2015. https://doi.org/10.14469/ch/191367
  12. H.S. Rzepa, "C 4 H 7", 2015. https://doi.org/10.14469/ch/191356
  13. H.S. Rzepa, "Reproducibility In Science: Calculated Kinetic Isotope Effects For Cyclopropyl Carbonyl Radical.", 2015. https://doi.org/10.5281/zenodo.19949

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Reactions in supramolecular cavities – trapping a cyclobutadiene: ! or ?

Sunday, August 8th, 2010

Cavities promote reactions, and they can also trap the products of reactions. Such (supramolecular) chemistry is used to provide models for how enzymes work, but it also allows un-natural reactions to be undertaken. A famous example is the preparation of P4 (see blog post here), an otherwise highly reactive species which, when trapped in the cavity is now sufficiently protected from the ravages of oxygen for its X-ray structure to be determined. A colleague recently alerted me to a just-published article by Legrand, van der Lee and Barboiu (DOI: 10.1126/science.1188002) who report the use of cavities to trap and stabilize the notoriously (self)reactive 1,3-dimethylcyclobutadiene (3/4 in the scheme below). Again sequestration by the host allowed an x-ray determination of  the captured species!

Scheme for production of 1,3-dimethylcyclobutadiene 3 and CO2.

The colleague tells me he has himself already penned an article on the topic and submitted this to a conventional journal. However, their rules decree that whilst it is being refereed, I could not discuss the article here, or indeed even name its author. Assuming his article is published, I will indeed reveal his identity, so that he gets the credit he deserves! Meanwhile, I will concentrate in this blog purely on two other aspects of this reaction which caught my own eye after he brought the article to my attention.

The reaction involves imobilising a precursor 1 in a crystalline calixarene network as shown above, and then in situ photolysis to form the Dewar lactone 2. Further photolysis then results in extrusion of carbon dioxide and the formation of 1,3-dimethyl cyclobutadiene 3 and CO2, both still trapped in the host crystals. Thus imobilised, here they both apparently remain (at 175K) for long enough for their X-ray structure to be determined. What attracted me to this chemistry was the potential of this reaction as a nice example of a Diels Alder reaction occuring in a cavity. The first example of such catalysis was reported by Endo, Koike, Sawaki, Hayashida, Masuda, and Aoyama (DOI: 10.1021/ja964198s) and I have used this in my lectures for many years. This latter example however illustrates the promotion of a cycloaddition, which inside a cavity is accelerated by a factor of ~105, rather than of the reverse cycloelimination. I explain this to students by invoking entropy. Normally, when two molecules react together, there is an entropic penalty, which can add 8 or more kcal/mol to the free energy of activation of a bimolecular reaction in the absence of the cavity.

Structure of entrapped 1,3-dimethylcyclobutadiene, obtained from the CIF file provided via DOI: 10.1126/science.1188002

By a strange coincidence, my name is also on a recently published article (DOI: 10.1021/ol9024259) with other colleagues on the use of (Lewis) acid catalysts to accelerate a type of reaction known as the Prins. This involves the addition of an alkene to a carbonyl group. Now as it happens, the reaction in the scheme above showing 4 → 2 happens to combine these features; it is both a Diels-Alder cycloaddition and also involves an alkene adding to a carbonyl compound! It is therefore noteworthy that the claimed reaction 1 → 2 → 3 + CO2 is done in the presence of a strong acid catalyst, the guanidinium cation 5, which is itself part of the structure of the calixarene-based host. It is represented as X in the scheme above, and can also be identified in the above 3D model via the light blue atoms.

There are however crucial differences between these two earlier examples I quoted and the reaction of 2 → 3; the latter is in fact a cycloelimination and not a (cyclo)addition. In other words, according to literature precedent, the guanidinium cation-based cavity should act to accelerate the reverse cycloaddition 4 → 2 rather than the forward cycloelimination. Since the isomerisation 3 → 4 is thought to be fast, the question arises: how rapid is the reverse reaction 4 → 2? In particular, is it slow enough to allow X-ray diffraction data to be collected for 3/4 over the necessary period of 24 hours or more? Legrand, van der Lee and Barboiu do not address this point in their article. Nor is there discussion there of how the cavity and the acid catalyst might influence the position of the equilbrium 2 → 3 + CO2.

This is where calculations can help. At the B3LYP/6-311G(d,p) level four different models were selected.

  1. Model A is a simple gas phase calculation for the singlet state, which reveals the free energy barrier for 4 → 2 is already quite modest for a Diels-Alder reaction (more typical values are ~22 kcal/mol), due no doubt to the instability/reactivity of the cyclobutadiene. However, at 175K, that would still be quite sufficient to prevent the reverse reaction from occurring to any extent over the period of X-ray data collection.
  2. Model B adds a condensed phase (water) to the model. This serves in part to simulate the condensed crystal environment (which is pretty ionic being a tetra ion-pair). The barrier drops to 12.1 kcal/mol.
  3. Adding one guanidinium cation to both these models (C and D) which simulate the Prins conditions, drops the barrier to 8.3 kcal/mol (model 4).
  4. You can inspect details of any of the calculations by clicking on the digital repository entry (shown as dr in the table), where full data is available.

None of these models includes the entropic effects of full constraint in a cavity (which I estimated above as capable of reducing the free energy barrier for reaction by ~8 or more kcal/mol). If this correction is applied to model D, it would reduce the barrier to ~0 kcal/mol! The calculations also reveal that the reverse reaction 4 → 2 is exothermic, and this exothermicity is enhanced by the acid catalyst 5. It would be further enhanced by reducing the entropy of reaction by pre-organizing the reactants in the cavity. The tendency must therefore be for 3/4 to revert to 2 on purely thermodyamic grounds, and only the presence of a significant kinetic barrier would allow them to exist as separate species. This barrier, as one might infer from the calculations shown in the table below, may not be a large one. Even a barrier of 8 kcal/mol might require cooling to significantly lower than 175K to render the reaction slow on a ~24 hour timescale.

Model ΔG‡4 → 2
kcal/mol		 ΔGreac 4 → 2 Singlet-triplet
separation
A. Gas phase,X=none dr ts 16.8 dr -3.5dr +5.7 dr
B. Continuum solvent (water),X=none dr ts 12.1dr -6.0 dr +7.7 dr
C. Gas phase,X=guanidinium+ dr ts 6.1 dr -19.5dr +2.1dr
D. Continuum solvent (water),X=guanidinium+ dr ts 8.3 dr -10.1 dr +7.7 dr

So I end my own speculations here on the nature of the reaction reported by Legrand, van der Lee and Barboiu by asking: are the products they claim (1,3-dimethylcyclobutadiene and carbon dioxide) capable of existing as separate species for long enough inside their cavity, even at 175K, to allow for the collection of X-ray data for a structure determination?

I tend to think probably not (? rather than !). But do decide for yourselves.

Archived as http://www.webcitation.org/5rpkn2Z5S on 08/08/2010. See also this post.

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