The macrobicyclic mixed-donor N3S3 cage ligand AMME-N3S3sar (1-methyl-8-amino-3,13,16-trithia-6,10,19-triazabicyclo[6.6.6]eicosane) can form complexes with Cu(II) in which it acts as hexadentate (N3S3) or tetradentate (N2S2) donor. These two complexes are in equilibrium that is strongly influenced by the presence of halide ions (Br(-) and Cl(-)) and the nature of the solvent (DMSO, MeCN, and H2O). In the absence of halides the hexadentate coordination mode of the ligand is preferred and the encapsulated complex ("Cu-in(2+)") is formed. Addition of halide ions in organic solvents (DMSO or MeCN) leads to the tetradentate complex ("Cu-out(+)") in a polyphasic kinetic process, but no Cu-out(+) complex is formed when the reaction is performed in water. Here we applied density functional theory calculations to study the mechanism of this interconversion as well as to understand the changes in the reactivity associated with the presence of water. Calculations were performed at the B3LYP/(SDD,6-31G**) level, in combination with continuum (MeCN) or discrete-continuum (H2O) solvent models. Our results show that formation of Cu-out(+) in organic media is exergonic and involves sequential halide-catalyzed inversion of the configuration of a N-donor of the macrocycle, rapid halide coordination, and inversion of the configuration of a S-donor. In aqueous solution the solvent is found to have an effect on both the thermodynamics and the kinetics of the reaction. Thermodynamically, the process becomes endergonic mainly due to the preferential solvation of halide ions by water, while the kinetics is influenced by formation of a network of H-bonded water molecules that surrounds the complex.