Reactions in cavities can adopt quite different characteristics from those in solvents. Thus first example of the catalysis of the Diels-Alder reaction inside an organic scaffold was reported by Endo, Koike, Sawaki, Hayashida, Masuda, and Aoyama (DOI: 10.1021/ja964198s), where the reaction shown below is speeded up very greatly in the presence of a crystalline lattice of the anthracene derivative shown below.
Its difficult to be precise about how much faster, since the kinetics depend on reorganisation of the scaffold, the actual reaction kinetics, and diffusion of the products in and out of the cavity. It does however mean that a poor solution reaction (reflux, many hours, modest yield) can be accomplished in an hour or so at room temperature in high yield.
Some idea of what is going on can be probed using calculation. Because the host and the guest interact though van der Waals or dispersion forces, a new breed of density functional theory which takes these into account is used (ωB97XD). The basic assemblage comprises the reactants shown below, enclosed in a cage formed by four of the anthracene units. A total of 236 atoms. This is a pretty challenging size for a full-blown quantum mechanical calculation. Here, its been done using a reasonable basis set, 6-31G(d) and with a continuum solvation model applied (dichloromethane). If you are interested in this sort of thing, that is 2292 basis functions. I started the calculations in mid September, and its taken more than six weeks to optimise (on 8-processor computers).
Firstly, the results for a control calculation in dichloromethane. The energies of activation of the two isolated reactants coming together at the transition state are calculated as:
ΔG298 29.5, ΔH 15.5, T.ΔS -13.98 kcal mol-1 (ΔS -46.9 cal K-1mol-1)
which are of course the various contributions to the equation ΔG = ΔH – T.ΔS. Note in particular how the last term increases the free energy barrier by ~14 kcal mol-1! Using the equation Ln k/T = 23.76 – ΔG/RT, one can estimate a rate constant of ~4 x 10-6 hour-1 at 298K (i.e. very slow at room temperatures). If the unfavourable -T.ΔS term is ignored (ΔG = ΔH), the rate constant increases to ~9 x 104 hour-1 at 298K (i.e. fast), quite a difference. What about the values when the reactants and transition state are surrounded by the host?
ΔG298 20.0, ΔH 16.5, T.ΔS -3.49 kcal mol-1 (ΔS -11.7 cal K-1 mol-1)
The key difference is that the last term is now much smaller, this reduces the free energy of activation and the estimated rate constant at 298K is now ~ 0.01 s-1 (42.5 hour-1). This magnitude of rate constant corresponds to a reasonably fast reaction at room temperatures.
This post demonstrates that the fascinating area of supermolecular chemistry can be just as amenable to computational exploration as the more conventional reaction.