Context and results In this study, the heterojunction Cu 2 O/TiO 2 is used for the degradation of a cationic dye, Rhodamine B, under solar light irradiation over a wide pH range. The physical and optical properties of both semiconductors Cu 2 O and TiO 2 are correlated with the photo-electrochemical characterization to establish the energy diagram of the heterojunction Cu 2 O/TiO 2 . X-ray diffraction, UV–visible, SEM, EDX, and BET analyses are conducted for both photocatalysts. The band gap (E g ) of 3.26 eV is obtained for TiO 2 with an indirect optical transition. In the case of Cu 2 O, the transition is directly allowed at 2.05 eV. According to the BET analysis, the specific surface area of TiO 2 particles is higher (82.65 m 2  g −1 ) than that of Cu 2 O (29.81 m 2  g −1 ). The flat band potentials, determined from the Mott-Schottky plots, are 0.3 and − 0.32 V SCE for TiO 2 and Cu 2 O, respectively. The photocatalytic activity is directly proportional to the mass ratio, and the best result is obtained for the mass ratio 1:1 of Cu 2 O/TiO 2 . Computational and theoretical techniques Furthermore, a theoretical study is conducted by using density functional theory to optimize the structure, reactivity sites of the RhB molecule, and physical parameters like the energy of the frontier molecular orbitals and electronegativity and to predict the proposed mechanism of RhB degradation as well as its intermediates. Also, molecular dynamics simulation is used to determine the adsorption behavior of RhB on TiO 2 (101) and Cu 2 O (111) surfaces. The ecotoxicity evaluation showed that degradation products have significantly lower acute toxicity than RhB.