Dispersion-corrected density functional theory is used to study the cycloaddition reaction between phenyl acetylene and phenyl azide inside a synthetic, self-assembled capsule. The capsule is first characterized computationally and a previously unrecognized structure is identified as being the most stable. Next, an examination of the free energies of host-guest complexes is conducted, considering all possible reagent, solvent, and solvent impurity combinations as guests. The experimentally observed relative stabilities of host-guest complexes are quite well reproduced, when the experimental concentrations are taken into account. Experimentally, the presence of the host capsule has been shown to accelerate the cycloaddition reaction and to yield exclusively the 1,4-regioisomer product. Both these observations are reproduced by the calculations. A detailed energy decomposition analysis shows that reduction of the entropic cost of bringing together the reactants along with a geometric destabilization of the reactant supercomplex are the major contributors to the rate acceleration compared to the background reaction. Finally, a sensitivity analysis is conducted to assess the stability of the results with respect to the choice of methodology.