The quantum-chemical simulation of the interactions underlying the absorption extraction process of hydrogen sulfide from gas streams with diethanolamine (DEA) has been performed. It has been shown that molecular complexes are formed without any barrier in the gas phase, whereas both molecular and ionic complexes are formed in the aqueous phase. It has been found that the use of the IPCM continuum solvation model fails to adequately reproduce the value of the heat of the reaction. A promising method for describing the absorption process of hydrogen sulfide extraction with alkanolamines using the supramolecular approach based on a discrete solvation model has been proposed. The approach takes account of intermolecular interactions in the DEA-H2S-H2O system and makes it possible to determine structural and energy parameters of the resulting associates and the mechanism of the process.