Modeling the Reaction of Carboxylic Acids and Isonitriles in a Self‐Assembled Capsule

Abstract Quantum chemical calculations were used to study the reaction of carboxylic acids with isonitriles inside a resorcinarene‐based self‐assembled capsule. Experimentally, it has been shown that the reactions between p‐tolylacetic acid and n‐butyl isonitrile or isopropyl isonitrile behave differently in the presence of the capsule compared both with each other and also with their solution counterparts. Herein, the reasons for these divergent behaviors are addressed by comparing the detailed energy profiles for the reactions of the two isonitriles inside and outside the capsule. An energy decomposition analysis was conducted to quantify the different factors affecting the reactivity. The calculations reproduce the experimental findings very well. Thus, encapsulation leads to lowering of the energy barrier for the first step of the reaction, the concerted α‐addition and proton transfer, which in solution is rate‐determining, and this explains the rate acceleration observed in the presence of the capsule. The barrier for the final step of the reaction, the 1,3 O→N acyl transfer, is calculated to be higher with the isopropyl substituent inside the capsule compared with n‐butyl. With the isopropyl substituent, the transition state and the product of this step are significantly shorter than the preceding intermediate, and this results in energetically unfavorable empty spaces inside the capsule, which cause a higher barrier. With the n‐butyl substituent, on the other hand, the carbon chain can untwine and hence uphold an appropriate guest length.

Transition states 7a-TS and 7b-TS result in the cis conformation of the 7a/7b formamides. Interconversion to the respective trans conformers is calculated to have barriers of ca. 22 kcal/mol. The trans conformers are calculated to be ca. 1 kcal/mol more stable than the cis ones in solution.
Note that (Z)-4b-TS and (E)-4b-TS are marked with asterisks (*) in Figures S2 and S3. These geometries have two imaginary frequencies. The additional small (<10i cm -1 ) imaginary frequencies were found to correspond to diffuse vibrations involving the tolyl and propyl moieties. Other conformations of these TSs were found to be several kcal/mol higher. Many attempts were made to eliminate these surplus imaginary frequencies without success. They were therefore replaced by real frequencies of the same magnitudes in the quasi-RRHO calculations. Experience of similar cases shows that the error bar of this treatment is <1 kcal/mol.

Geometries of capsule-formamide complexes
The optimized geometries of the lowest energy complexes of 2·7a@12, 7a·7a@12, 2·7b@12 and 7b·7b@12 are shown in Figure S4. Interestingly, in the complexes with one p-tolylacetic acid and one formamide molecule, i.e. 2·7a@12 and 2·7b@12, the formamide conformation and the interactions between the acid and the formamide differ depending on the formamide substituent. In 2·7a@12, a hydrogen bond is present between the carboxylic acid and the carbonyl oxygen of cis-7a. In the most stable conformation of 2·7b@12, however, trans-7b is encapsulated and an addition guest-guest hydrogen bond is possible, from the amide of 7b to the carbonyl oxygen of 2. There are also interesting differences between the complexes with two formamide guests. In 7a·7a@12 a hydrogen bond exists between the formamides, while the two formamides do not interact in 7b·7b@12.
Energetically, 2·7a@12 and 2·7b@12 are similarly stable relative to their respective reactant complexes (-7.1 and -5.5 kcal/mol). However, an interesting observation is that 7b·7b@12, experimentally observed in a 1:3 ratio to 2·7b@12, [S1] is calculated to be more than 13 kcal/mol higher than 2·7b@12. Even though two formamides cannot fill the capsule as well as the combination of one carboxylic acid and one formamide, this energy difference is overestimated by the computational methods. Comparing 2·7a@12 with 7a·7a@12, the latter is calculated to be only +4.0 kcal/mol higher. Figure S4. Optimized geometries and relative Gibbs energies of encapsulation complexes with 7a or 7b. S6

Energy decomposition analysis
To quantify the different factors affecting the reactivity inside the capsule, an energy decomposition analysis was undertaken following the same procedure as in our previous papers. [S2,S3] First the a-addition step was evaluated. In Figure S5, the analysis is done for three cases: i) nbutyl substituent with reactant structure 2·3a@12 ( Figure S5A), ii) n-butyl substituent with reactant structure (2·3a@12)' (Figure S5B), and iii) isopropyl substituent with reactant structure 2·3b@12 ( Figure S5C). The two reactant complexes 2·3a@12 and (2·3a@12)' differ in that in 2·3a@12, a hydrogen bond is formed between 2 and a carbonyl oxygen at the capsule seam, while in (2·3a@12)', 2 forms a hydrogen bond to the isonitrile moiety of 3a. The two structures differ only by 0.2 kcal/mol.
The energetic effect of the capsule can be roughly divided into enthalpic and entropic contributions. For all cases, it is found that the two parts have similar contributions to the lowering of the barrier: i) DDH ‡ = -4.6 kcal/mol, -TDDS ‡ = -4.3 kcal/mol; ii) DDH ‡ = -3.7 kcal/mol, -TDDS ‡ = -5.4 kcal/mol; and iii) DDH ‡ = -2.5 kcal/mol, -TDDS ‡ = -3.9 kcal/mol ( Figure S5). This is quite similar to the cycloaddition reaction in the same capsule studied previously, for which strain and interaction effects were calculated to lower the barrier by 3.1 kcal/mol and entropic effects were found to further reduce it by 3.3 kcal/mol. [S2] Further decomposition of the enthalpic contribution into contributions from host and guest distortions and host-guest interaction shows that this analysis is quite sensitive to whether 2·3a@12 or (2·3a@12)' is chosen as the reactant complex. With the 2·3a@12 (case i), the host is significantly distorted as one of the hydrogen bonds between the two cavitands is broken. In the decomposition analysis, this shows up as host distortion lowering the barrier significantly (-7.4 kcal/mol) since the host is significantly less distorted in the TS structure. This is compensated by the host-guest interaction energy being greater in the reactant structure than in the TS, giving a host-guest interaction term of +7.5 kcal/mol. When cases ii and iii are compared, however, the enthalpic terms are much more similar.
The fact that the entropic and enthalpic contributions to the barrier lowering of the a-addition step are of similar magnitudes can be rationalized as follows. Enthalpically, the capsule interacts better with the TS than with the reactants. This is in part due to the breaking of the vdW interactions that in solution exist between the aryl group of 2 and the n-butyl or isopropyl moieties in 3a and 3b, respectively (see Figures S1 and S2), thus destabilizing the reactant complex compared to the solution case. The entropic effects contribute to the barrier in solution by 4.4 kcal/mol, while the barrier inside the capsule is hardly affected ( Figure S5). In solution, the ground state of the reaction is the separated reactants, but in presence of capsule the reactant supercomplex becomes the lowest-energy species. The capsule eliminates thus the entropic penalty of bringing the reactants together.

Host and guest volumes
The calculated van der Waals volumes of the guests (calculated with VOIDOO) [S4] and cavity volumes of the host (calculated with the sphere-packing method as in Ref. S2) are given in Table  S1 for all studied host-guest complexes.
The packing coefficients (PCs), [S5] also listed, are quite similar throughout the reaction, with the exception of the 1,3 O→N acyl transfer step with the isopropyl substituent: from (E)-4b@12 to 5b@12, the PC decreases from 0.59 to 0.53. This is due to an increase in the cavity volume of the host, which mainly stems from the lower part of the capsule (as shown in Figure 6 in the paper) widening to accommodate the N-formyl amide product 5b. A related effect is observed in going from (E)-4a@12 to 5a@12, but the decrease in PC is smaller there (from 0.60 to 0.57). This is because the lower part of the capsule (in Figure 3) is already widened in order to accommodate the longer n-butyl group in (E)-4a@12, and thus less distortion is needed in order to make room for product 5a.
For comparison, the cavity volumes were also calculated with BetaVoid. [S6] While volumes estimated with this method are much smaller, the same trend as above is observed: the cavity volume increases from (E)-4@12 to 5@12 (Table S1).

Absolute energies and energy corrections
The calculated energies of all compounds in the article are given in Table S2.  [a] Three-body dispersion correction is included. [b] Corrections for the transfer from ideal gas to solution, +1.9 kcal/mol, are included in the reported solvation Gibbs energies. [c] An imaginary frequency of 9i cm -1 was found in the vibrational analysis and could not be eliminated by further optimization. This was treated as real in the calculations of the thermal correction to Gibbs energy.