Fig. 5: Computational NO₃RR descriptors as calculated by using DFT with optB86b-vdW functional.

a Gibbs free energies (∆_rG) of the reaction for the first two electron transfer steps in the NO₃RR. Processes that generate NO₂⁻ in the bulk electrolyte are shown in blue. Note solid bars indicate no electron transfer, uphill gradient stripes indicate a reductive e⁻ transfer and downhill gradient stripes indicate an oxidative/reverse electron transfer. b Quadrant plot of the ∆_rG for associative adsorption \([{\,\!}^{*}+{{{{{{\rm{NO}}}}}}}_{3}^{-}\to {\,\!}^{*}{{{{{{\rm{NO}}}}}}}_{2}]\) (Y₁-axis), dissociative adsorption \([{\,\!}^{*}+{{{{{{\rm{NO}}}}}}}_{3}^{-}\to {\,\!}^{*}{{{{{{\rm{O}}}}}}+{{{{{\rm{NO}}}}}}}_{2}^{-}]\) (X-axis) and *NO₂ desorption \([{\,\!}^{*}{{{{{{\rm{NO}}}}}}}_{2}\to {\,\!}^{*}+{{{{{{\rm{NO}}}}}}}_{2}^{-}]\) (Y₂-axis), forming sectors where certain reaction pathways are thermodynamically favored. The main quadrants were determined by the X-axis and Y₁-axis. Quadrants III and IV were further divided by the Y₂-axis into III.a, III.b, IV.a and IV.b sub⁻sections. The three reaction coordinates determined two types of NO₃⁻ adsorptions and two types of NO₂⁻ evolutions as shown by the diagram above the figure. For simplified plots correlating two descriptors at a time, see Fig. S63. c Correlation between DFT-derived \({\Delta }_{{{{{{\rm{r}}}}}}}{{{{{\rm{G}}}}}}[{\,\!}^{*}+{{{{{{\rm{NO}}}}}}}_{3}^{-}\to {\,\!}^{*}{{{{{{\rm{NO}}}}}}}_{2}]\) and experiment-derived NO₃RR FE_NH3 at −0.2 V vs. RHE. d Correlation between DFT-derived \({\Delta }_{{{{{{\rm{r}}}}}}}{{{{{\rm{G}}}}}}[{\,\!}^{*}+{{{{{{\rm{NO}}}}}}}_{2}^{-}\to {\,\!}^{*}{{{{{{\rm{NO}}}}}}}_{2}]\) and experiment-derived NO₂RR FE_NH3 at −0.2 V vs. RHE. Oxygenated active sites (O-M) were included for the oxyphilic elements (Mo, La, Ce and W), where R is reported as the absolute value of the correlation coefficient.