Impact of Intrinsic Density Functional Theory Errors on the Predictive Power of Nitrogen Cycle Electrocatalysis Models

O nitrogen species can pollute both the atmosphere and water bodies. Their concentrations are worryingly increasing because of anthropogenic activities such as the combustion of fossil fuels and intensive agriculture. An alternative to remediate their negative impact is to reduce them into unharmful molecular nitrogen (N2) or valuable ammonia (NH3), 12−14 thereby dynamizing the nitrogen cycle. In principle, electrocatalysis could be used as a green technology for these processes if the necessary energy input comes from renewable sources. However, the design of active, selective, and stable catalysts for the reduction of nitrogen oxides is not trivial. In that regard, density functional theory (DFT) calculations could serve as a supplement, support, or guide to experiments. DFT is widely used in computational chemistry for the modeling of solids. Specifically, exchange-correlation functionals at the generalized gradient approximation (GGA) have shown high accuracy with low computational requirements when predicting the ground-state properties of bulk and surface metals. However, when predicting gas-phase energetics, the limitations of GGA functionals are wellknown (e.g., overbinding energy of N2 and O2) 25−27 and predictions in line with experiments are only expected on the basis of error cancellation, i.e., when similar compounds appear in opposite sides of chemical reactions. The inaccuracies may be reduced by the use of meta-GGA functionals, which represent a step up in the hierarchy of exchange-correlation approximations. Because functionals at the meta-GGA level take into account the kinetic energy density of the Kohn− Sham orbitals, they are supposedly better than GGAs for molecules, while metals are still accurately described. Gas-phase errors are problematic in heterogeneous catalysis, where an accurate description of the gas phase is paramount for adsorption and desorption steps. Such steps happen each at least once in every catalytic reaction. In spite of their gas-phase errors, GGA functionals are extensively used in catalysis given their low computational requirements. Previous efforts have been devoted to (i) benchmarking their performance for predicting the enthalpies and entropies of adsorption of various systems and (ii) combining different functionals to boost their accuracy. Considering recent error analysis on nitrogen-containing organic compounds, if DFT at the GGA level is used to model reactions involving nitrogen oxides, it is expected that the calculated energies will entail large errors, in particular for highly oxidized species, such as nitrate and nitrite. Thus, accurately assessing the energetics of reactions such as nitrate reduction or electrochemical nitrogen oxidation remains challenging. Herein, we show that large errors are encountered in the GGA and meta-GGA formation enthalpies of 11 oxidized nitrogen species in the gas phase. Importantly, the errors scale with the number of oxygens in the structure and the scaling factor is approximately constant for all the functionals studied. This exposes an intrinsic GGA and meta-GGA limitation that must be overcome if accurate predictions are sought after for the modeling of catalytic redox processes among nitrogencontaining species. Furthermore, we show the effects of intrinsic gas-phase errors on adsorption-energy scaling relations and volcano plots for two electrocatalytic reactions and propose an inexpensive scheme to systematically correct such errors.