Heterogeneous catalytic hydrogenation of gaseous carbon dioxide to methanol is an important reduction reaction in chemical process engineering, renewable energy industry and emerging green chemistry, as it provides means to harness surplus electrical energy and convert a pollutant and emitted greenhouse gas into a useful building block and biofuel. On industrial operating scale, multifunctional copper/zinc catalysts on various supporting substrates (e.g. CZA with alumina) are most commonly used due to their high selectivity and conversion. In this work, post-Hartree–Fock and density functional theory (DFT) calculations were carried out to assess the thermodynamics and to elucidate the pathway leading to the formation of methanol from CO2 on realistic spinel-type tri-metallic materials. Firstly, a commercial-like Cu/ZnO/Al2O3 was synthesised via co-precipitation and characterised to obtain the active sites’ structure for modelling. Powder X-ray diffraction (XRD), Brunauer–Emmett–Teller (BET) surface area measurement, scanning/transmission electron microscopy (SEM and TEM) and energy-dispersive X-ray spectroscopy (EDS) were performed. Subsequently, the Gibbs free energy, enthalpy, entropy and chemical equilibrium constants of the direct methanol synthesis and the competing reverse water–gas shift (RWGS) reaction at the temperatures of 25°C, 150°C, 200°C, 250°C and 300°C, and the pressures of 1bar, 20bar, 40 bar, 60 bar and 100 bar were evaluated using ab initio quantum chemistry method CCSD(T)/aug-cc-pVQZ. To investigate kinetics, a mechanistic pathway scheme with all established intermediates was constructed, whereas physical/chemical adsorption/desorption energies, geometries, barriers and rates for adsorbate elementary steps were calculated using plane-wave DFT. Results demonstrate that the formate precursor route predominates as the respective transition state activation energies are lower and, thus CH3OH is proposed to form through HCOO, H2COO, H2COOH, CH2O and CH3O species.