Posts Tagged ‘energy differences’

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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The mysteries of stereoinduction.

Thursday, July 1st, 2010

Stereo-induction is, lets face it, a subtle phenomenon. The ratio of two stereoisomers formed in a reaction can be detected very accurately by experiment, and when converted to a free energy difference using ΔG = -RT Ln K, this can amount to quite a small value (between 0.5 – 1.5 kcal/mol). Can modelling reproduce effects originating from such small energy differences? Well one system that has been argued about now for several decades is shown below as 1.

Norbornene systems

Way back in 1992, we thought that the explanation for attack by an electrophile on the alkene from the syn face was electrostatic (although it did depend on the nature of the electropile; thus we concluded that attack by Hg(OH)2 was electrostatic, but by BH3 was orbital controlled). Recently, a different explanation has emerged, relating to how the fundamental normal vibrational modes of the molecule interact with the transition normal mode for the reaction. A new example of this, relating to reaction of the isomeric 2 with a peracid has recently been discussed on Steve Bachrach’s blog. Here, the peroxide of the peracid is thought to act as an electrophile (although one must bear in mind that it does bear two electron lone pairs!). The conclusion was pretty clear cut; the experimental preference for syn (92%) over the anti isomer (8%, ΔΔG = 1.4 kcal/mol) was NOT due to electrostatic effects, but due to distorsional asymmetry in the vibrational mode that couples/forms the transition state mode.

I could not resist revisiting this system. As in 1992, a molecular electrostatic potential was calculated for 2. The method used was wB97XD/aug-cc-pvdz, and if you want the archive of this calculation to evaluate it yourself, see here).

MEP for 2. Click on diagram for 3D.

A very clear electrostatic bias for syn attack emerges (orange = attractive to a proton=electrophile). This electrostatic picture is not directly related to any distortional asymmetry, although of course both could arise from the same electronic factors. They may indeed be different manifestations of the same underlying nature of the wavefunction. But I would claim here that to make the clear statement that electrostatic effects are NOT responsible for the discrimination in this reaction is perhaps too simplistic (electrostatic potentials were not reported in the original article). The control experiment is 3, which is known to be far less selective. The calculated electrostatic potential likewise shows much less discrimination.

The norbornene with a four-membered ring

Is there another take on 2? Well, how about an NBO (natural bond order) analysis? The interaction energy between the filled C1-C2 orbital and the antibonding C15-C16 π* bond is 3.24. This could be regarded as pushing electrons into the anti-periplanar syn face of the alkene. The corresponding C2-C9/C15-C16 interaction resulting in an anti-preference is less at 2.55 kcal/mol. This effect arises because the C1-C2 bond (localised as an NBO) is a better donor (E=-17.8eV) than C2-C9 (E=-18.1eV). Because C2 is common to both, it must be the difference between C1 and C9 (i.e. the hybridization of each). Perhaps it’s an orbital effect after all?

Norbornene electrostatic potential

I would conclude by saying that it can be ferociously difficult to identify the fundamental origins of stereo-induction. But I leave the argument in the hands of the reader now. What do you think?

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