Quantifying uncertainty in the prediction of catalytic trends for ammonia synthesis

The probability that the ammonia synthesis TOF of a given catalyst is higher than the TOF of iron step sites (calculated with the self-consistent BEEF-vdW energetics) as a function of nitrogen adsorption energy relative to that of iron. The line corresponds to linear regression between the adsorption energy of nitrogen and other intermediates.

Density functional theory (DFT) has proven to be a valuable tool for atomic-scale understanding and design of catalytic processes. These successes have come in spite of the fact that the accuracy of DFT is typically known only qualitatively. As the field of computational materials design expands it becomes increasingly urgent to develop methods to quantitatively evaluate the accuracy of DFT calculations and assess the implications of uncertain DFT results on the prediction of materials properties.

The recently developed BEEF-vdW exchange-correlation functional utilizes the Bayesian approach to statistics in order to quantitatively estimate the error on DFT energies using “ensembles” of energies that reproduce known errors in DFT calculations and captures correlations between these errors. We have used the ensembles from the BEEF-vdW functional in conjunction with a microkinetic model in order to assess the impact of the uncertainty in energetics on the predicted catalytic rates. The results show that the error on rates exhibits a nontrivial dependence on reaction condition and catalytic surface, but despite relatively large errors in DFT energetics (~0.2 eV) the error on predicted turnover frequencies (1-2 orders of magnitude) is generally smaller than expected. This is shown to result from cancellation of error due to correlations between the energetics of the intermediates in the ammonia synthesis reaction pathway.

Furthermore, we have created “volcano plots” based on the ensembles of energies from the BEEF-vdW functional in order to assess the accuracy of catalytic trends. This reveals that the relative rates have even smaller uncertainty (~1 order of magnitude) due to the covariance of energetic errors across different catalytic materials. We also show that the linear scaling relations between the energies of intermediates are very robust to changes in the exchange-correlation approximation. Ultimately we compute the probability of finding an improved catalyst for ammonia synthesis as a function of the descriptor (N* binding), which represents a new paradigm in computational materials screening.