The growing concern over the escalating levels of anthropogenic CO2 emissions necessitates effective strategies for its conversion to valuable chemicals and fuels. In this research, we embark on a comprehensive investigation of the nature of zirconia on a copper inverse catalyst under the conditions of CO2 hydrogenation to methanol. We employ density functional theory calculations in combination with the Grand Canonical Basin Hopping method, enabling an exploration of the free energy surface including a variable amount of adsorbates within the relevant reaction conditions. Our focus centers on a model three-atom Zr cluster on a Cu(111) surface decorated with various OH, O, and formate ligands, noted Zr3Ox (OH)y (HCOO)z/Cu(111), revealing major changes in the active site induced by various reaction parameters such as the gas pressure, temperature, conversion levels, and CO2/H2 feed ratios. Through our analysis, we have unveiled insights into the dynamic behavior of the catalyst. Specifically, under reaction conditions, we observe a large number of composition and structures with similar free energy for the catalyst, with respect to changing the type, number, and binding sites of adsorbates, suggesting that the active site should be regarded as a statistical ensemble of diverse structures that interconvert.