In a comment appended to an earlier post, I mused about the magnitude of the force constant relating to the interconversion between a classical and a non-classical structure for the norbornyl cation. Most calculations indicate the force constant for an “isolated” symmetrical cation is +ve, which means it is a true minimum and not a transition state for a [1,2] shift. The latter would have been required if the species equilibrated between two classical carbocations. I then pondered what might happen to both the magnitude and the sign of this force constant if various layers of solvation and eventually a counter-ion were to be applied to the molecule, so that a bridge of sorts between the different states of solid crystals, superacid and aqueous solutions might be built.
I augmented the model in stages. The results are summarised in the table below.
- Firstly, adding a self-consistent-reaction-field (SCRF) continuum model for water.
- Then adding to that four explicit water molecules symmetrically arranged around the four C-H groups mostly likely to be solvated via hydrogen bonds.
- The final model added a chloride anion to complete the ion pair and a further three water molecules to act as its solvation sphere. A search of the Cambridge structure database for any instances of a molecule with a designated C+ and a nucleophilic halide– with zero coordination number (a free halide anion) reveals no hits; such ion-pairs are clearly very unstable towards covalent bond formation, existing if at all only as transient species or when the counter-ion is non-nucleophilic such as R4B–.
| Calculated geometries, Def2-TZVPP/SCRF=water | ||||
|---|---|---|---|---|
|
Model |
Apical C-C distance,Å |
Basal C-C distance,Å |
ν [1,2] cm-1 |
DataDOI |
| Vacuum, cation B3LYP+D3BJ |
1.888 | 1.388 | +140 | 10.14469/hpc/2410 |
| Vacuum, cation ωB97XD |
1.830 | 1.388 | +235 | 10.14469/hpc/2409 |
| Vacuum, cation B2PLYPD3 |
1.872 | 1.390 | +194 | 10.14469/hpc/2238 |
| SCRF, cation ωB97XD |
1.819 | 1.387 | +236 | 10.14469/hpc/2413 |
| SCRF, cation B2PLYPD3 |
1.858 | 1.388 | +202 | 10.14469/hpc/2243 |
| SCRF+4H2O, cation B2PLYPD3 |
1.838 | 1.390 | +254 | 10.14469/hpc/2246 |
| SCRF+7H2O+Cl– ion pair B3LYP+D3BJ |
1.593, 2.485 | 1.510 | – | 10.14469/hpc/2408 |
| SCRF+7H2O+Cl– ion pair ωB97XD |
1.795, 1.817 | 1.385 | +249 | 10.14469/hpc/2411 |
As the solvation and environment of the cationic model improves, the apical distance shortens significantly. But the crunch comes when a chloride counter-anion is added to desymmetrise this environment. Using the veritable B3LYP functional, but with an added dispersion term (D3BJ) and starting from a partially optimised ion-pair geometry, this geometry optimisation (shown animated below) rapidly quenches the ion-pair to form a covalent norbornyl chloride. It is noteworthy that the magnitude of the [1,2] vibration force constant (140 cm-1) is rather smaller using B3LYP than the other methods explored.
The next method tried was ωB97XD, which contains a built-in dispersion term (D2) and also reveals a larger force constant for the gas phase [1,2] shift (≡235 cm-1). Starting from the same initial geometry as the B3LYP calculation, optimisation of the ion-pair proceeds remarkably slowly‡ (even using the recalcfc=5 keyword to recompute the force constant matrix/search direction every five cycles to improve behaviour), suggesting that the potential energy surface is very flat indeed. The final geometry retains the ion-pair character (dipole moment 23D) but reveals distinct asymmetry in the resulting bridged structure, for which the [1,2] shift is ν 249 cm-1.
It is clear that the structure of the norbornyl ion-pair is balanced on a knife-edge. Perturbations such as change of density functional (e.g. B3LYP+D3BJ) can topple it over that edge. Weaker asymmetry can also be induced by the presence of the contact-anion and water molecules. I have selected just one solvation model, which includes seven water molecules and an explicit anion. Clearly a more statistical and dynamical approach to the number of waters and their orientation around the norbornyl ring system would sample a much larger set of models. It may be that some of them do again topple the symmetric bridge structure off its delicate perch whilst others retain it. Perhaps this is why the results from the enormous range of solvolysis mechanisms are so difficult to always reconcile. A crystal structure may also be a relatively large perturbation to the solution structure of this species!
The title of one of the last articles published (posthumously) with Paul Schleyer as a co-author[1] is “Norbornyl Cation Isomers Still Fascinate“. True indeed.
‡This renders refinement using the B2PLYPD3 double-hybrid method[2] an exceptionally slow process, since computing the force constant matrix using this method is very computationally intensive at the selected triple-ζ level.
References
- P.V.R. Schleyer, V.V. Mainz, and E.T. Strom, "Norbornyl Cation Isomers Still Fascinate", ACS Symposium Series, pp. 139-168, 2015. https://doi.org/10.1021/bk-2015-1209.ch007
- L. Goerigk, and S. Grimme, "Efficient and Accurate Double-Hybrid-Meta-GGA Density Functionals—Evaluation with the Extended GMTKN30 Database for General Main Group Thermochemistry, Kinetics, and Noncovalent Interactions", Journal of Chemical Theory and Computation, vol. 7, pp. 291-309, 2010. https://doi.org/10.1021/ct100466k