The study of supramolecular “host-guest” complexes in solutions is of fundamental and practical significance. The structures and formation enthalpy of supramolecular complexes for the 4-DASPI dye with two cavitands (cucurbit[6]uril and cucurbit[7]uril) have been obtained by the TDDFT quantum chemistry method with a camb3lyp basis. It was shown by visualization of the structures that the size of cucurbit[6]uril is too small and doesn’t allow the dye chromophore to penetrate into the cavitand cavity while the dye stays in the ground state, but the formation of an external complex is possible. On the contrary, formation of an inclusion complex with the cucurbit[7]uril is energetically favorable, and the dye chromophore penetrates into the cavity. Visualization of the complex structure allows us to determine the chromophore position relative to the given cavitand cavity, and thus we can predict the changes in the dye spectra due to complexation. The theoretical results of the work are in good correlation with the experiment.