where ∆ f H H 2 O = -238.9 kJ mol -1 (ATcT ). Another widely used correction to DFT energies of gas-phase species for catalytic systems was proposed by Peterson et al. for the electrochemical reduction of CO 2 on Cu(111). The authors applied a statistical sensitivity analysis to identify correction factors that align the reaction enthalpies from DFT with the experimental values. To determine these correction factors, they compared the DFTderived reaction enthalpies of 21 hand-picked gas-phase reactions involving CO 2 , CO, H 2 , and H 2 O with experimental values from the NIST database. Perturbing the energy of CO 2 and all species with an OCO backbone by 43.4 kJ mol -1 for the RPBE functional led to a minimum deviation between the experimental and DFT values. However, the agreement with all test reactions is not exact, and a discrepancy of ≈6 kJ mol -1 remained. In the same study, very different correction factors were necessary when using the PBE functional, highlighting the functional dependence of these corrections. In a follow-up study, Studt et al. repeated the same analysis using the BEEF-vdW functional in GPAW, and they obtained the closest agreement when perturbing the CO 2 as well as the H 2 energy by 31.8 kJ mol -1 and 8.7 kJ mol -1 . In a different study by , a slightly different correction value for CO 2 of 39.6 kJ mol -1 was obtained using QuantumEspresso while the H 2 correction remained 8.7 kJ mol -1 . This discrepancy in correction factors highlights the slight differences between different electronic structure codes and numerical settings, making it challenging to generalize correction factors. Following these pioneering studies, a range of corrections for the gas-phase energies were proposed in the literature for nitrogen-containing species , O 2 173 , CO, CO 2 and other species depending on the xc-functional . Urrego-Ortiz et al. reviewed the gas-phase errors and corrections of DFT calculations for computational catalysis. Fig. shows the enthalpy diagram with the applied corrections to CO 2 and H 2 of 31.8 kJ mol -1 and 8.7 kJ mol -1 for the BEEF-vdW functional , respectively. The derivation of the ∆ A H follows the equations described in Section 4.2.2, with corrections added to the DFT gas-phase energies of CO 2 and H 2 O. Notably, the reaction enthalpies will be the same regardless of whether corrections are added before or after anchoring the thermochemical network; however, if corrected species are used as anchors, then the correction will be distributed throughout the network, and the individual ∆ A H will depend on whether the correction was applied before or after anchoring. Thus, it is recommended that corrected species should not be used as anchors to avoid ambiguity about which species have been "corrected". Using these standard corrections, the overall reaction enthalpy with the gasphase corrections is 159.4 kJ mol -1 , which still deviates from the experimental value by 10 kJ mol -1 . This error leads to an equilibrium constant that deviates by a factor of ∼4 from the exact value (see Fig. ). Compared to the "non-corrected" free energy diagram constructed directly from DFT energies, the only change is for the adsorption enthalpy of CO 2 , which is increased by 31.8 kJ mol -1 , making CO * 2 more stable. Since H 2 desorption does not appear in this reaction mechanism, the H 2 correction cancels out, and all other DFT reaction enthalpies are conserved. In general, the approach changes only the reaction energies for the adsorption/desorption steps where corrected molecules are involved.