To address surface reaction network complexity using scaling relations machine learning and DFT calculations

Typical uncertainty for the DFT methods used in this work is ∼0.2-0.3 eV for transition-state formation energies relative to gas-phase species.

“Typical uncertainty for the DFT methods used in this work (estimated with the ensembles in Bayesian error estimation functional with van der Waals correlation (BEEF-vdW)) are ∼0.15 eV for surface species formation energies16, and ∼0.2–0.3 eV for transition-state formation energies (relative to gas-phase species) as indicated in Fig. 2.”

Including additional pathways that are progressively less likely to contain the network rate-limiting step increases the probability that the actual transition state is present.

“Including additional pathways that are progressively less likely to contain the network rate-limiting step increases the probability that the the actual transition state is present, as shown in Fig. 4d.”

At this level of uncertainty, many pathways through the reaction network may be competitive.

“At this level of uncertainty, many pathways through the reaction network may be competitive, as illustrated in Fig. 4.”

The reduced networks constructed at the 50 or 80% confidence level take longer to converge.

“The reduced networks constructed at the 50 or 80% confidence level (that is, the confidence that the final network contains the rate-limiting step at the set of reaction conditions given DFT-level uncertainty) take longer to converge.”

At convergence, energetics have been calculated for only about 40% of the intermediate species in the full reaction network.

“At this point, only 5% of the transition states of the full reaction network have been calculated (all within the final mechanism), and energetics have been calculated for only about 40% of the intermediate species in the full reaction network.”

Typical uncertainty in transition-state energies is 0.1-0.4 eV, as estimated using the BEEF-vdW ensemble function.

“Typical uncertainty in transition-state energies are typically 0.1–0.4 eV, as estimated using the BEEF-vdW ensemble function.”

The approach reduces the number of intermediate calculations by 60% relative to studying the entire network.

“demonstrate reductions of 60% and 95% for the number of intermediate and transition-state calculations, respectively.”

The 50% confidence level converges to the most likely mechanism.

“The 50% confidence level converges to the most likely mechanism, while the 80% confidence level contains additional pathways that cannot be excluded given DFT-level uncertainty.”

The most likely pathway is consistent with experimentally observed selectivity to acetaldehyde.

“The most likely pathway is shown in Fig. 4b and is consistent with experimentally observed selectivity to acetaldehyde14.”

• cites [14] Yang, N. et al. Intrinsic selectivity and structure sensitivity of rhodium catalysts for c2+ oxygenate production. J. Am. Chem. Soc. 138, 3705–3714 (2016). sourceNot checked yet

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The chosen criterion (highest transition-state energy in a pathway) has worked well for determining the rate-limiting step in the networks presented here.

“We have found that the chosen criterion (highest transition-state energy in a pathway) has worked well for determining the rate-limiting step in the networks presented here, likely due to the proximity of the rate-limiting step to the beginning of the pathway.”

The 80% confidence level contains additional pathways that cannot be excluded given DFT-level uncertainty.

“The 50% confidence level converges to the most likely mechanism, while the 80% confidence level contains additional pathways that cannot be excluded given DFT-level uncertainty.”

Typical uncertainty for the DFT methods used in this work is ∼0.15 eV for surface species formation energies.

“Typical uncertainty for the DFT methods used in this work (estimated with the ensembles in Bayesian error estimation functional with van der Waals correlation (BEEF-vdW)) are ∼0.15 eV for surface species formation energies16, and ∼0.2–0.3 eV for transition-state formation energies (relative to gas-phase species) as indicated in Fig. 2.”

• cites [16] Medford, A. J. et al. Assessing the reliability of calculated catalytic ammonia synthesis rates. Science 345, 197–200 (2014). sourceNot checked yet

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Starting from a few DFT calculations and iterating the approach generates the most likely pathway with fewer calculations than would be necessary to study the entire network.

“Starting from a few DFT calculations and iterating this approach generates the most likely pathway with fewer calculations than would be necessary to study the entire network.”

The approach reduces the number of transition-state calculations by 95% relative to studying the entire network.

“demonstrate reductions of 60% and 95% for the number of intermediate and transition-state calculations, respectively.”

At the 90% confidence level, it is impossible to rule out water and methanol as alternate products given DFT-level uncertainty.

“At the 90% confidence level, a desired level of confidence for mechanism reduction, we find that it is impossible to rule out water and methanol as alternate products given DFT-level uncertainty.”

• AssumptionThe authors state this as an assumption: The uncertainty for the linear-scaling relations for transition-state energies is uncorrelated.

At the 80% certainty level, water formation may also be possible.

“At the 80% certainty level, shown in Fig. 4d, water formation may also be possible.”

The methods avoid wasting computational resources on reactions that are part of the final reduced mechanism but not likely to be the rate-limiting step.

“These methods also avoid wasting computational resources on reactions that are part of the final reduced mechanism but not likely to be the rate-limiting step (for example, fast hydrogenation reactions).”

Model uncertainty at the DFT level limits the selection of a mechanism even after all intermediates and transition states have been calculated for a reaction network.

“Model uncertainty at the DFT level limits the selection of a mechanism even after all intermediates and transition states have been calculated for a reaction network.”

• AssumptionThe authors state this as an assumption: The uncertainty for the linear-scaling relations for transition-state energies is uncorrelated.

Casting surface reaction mechanism elucidation in a fully probabilistic framework, starting from a surface with no available mechanism or surface energetics, provides a route to bootstrap to a mechanism of optimal complexity rather than relying on intuition or expensive comprehensive analysis.

“First, we cast the problem of surface reaction mechanism elucidation in a fully probabilistic framework, starting for a surface for which no mechanism or surface energetics are available. This approach provides a route to bootstrap to a mechanism of optimal complexity rather than relying on intuition or expensive comprehensive analysis.”

• AssumptionRests on an assumption: Surface reaction networks involving hydrocarbons exhibit enormous complexity with thousands of species and reactions for all but the very simplest of chemistries.

Propagating uncertainty at every layer of approximation allows for estimates of the residual error in the final reaction mechanism from parts of the reaction network that have not been studied in detail.

“Propagating uncertainty at every layer of approximation allows for estimates on the residual error in the final reaction mechanism from parts of the reaction network that have not been studied in detail.”

Contributions of fragments to the formation energy are not linearly independent quantities.

“Since the contributions of fragments to the formation energy are not linearly independent quantities, as evidenced by the wide applicability of linear scaling relations4”

• cites [4] Nørskov, J. K., Bligaard, T., Rossmeisl, J. & Christensen, C. H. Towards the computational design of solid catalysts. Nat. Chem. 1, 37–46 (2009). sourceNot checked yet

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Uncertainty in the final transition-state energy due to the use of scaling relations was measured and propagated to the model refinement loop.

“Uncertainty in the final transition-state energy due to the use of these scaling relations was also measured and propagated to the model refinement loop.”

• AssumptionThe authors state this as an assumption: The uncertainty for the linear-scaling relations for transition-state energies is uncorrelated.

The presence of alternate products that compose the network at 90% confidence raises questions about the limitations of using DFT to discriminate between competing reaction networks.

“The presence of alternate products that compose the network at 90% confidence raises questions about the limitations of using DFT to discriminate between competing reaction networks.”

Improving the accuracy of surrogate models in this work has a limited benefit in improving the efficiency of network exploration, due to the large separation in pathway energetics between the most and least likely pathways.

“Improving the accuracy of surrogate models in this work has a limited benefit in improving the efficiency of network exploration, due to the large separation in pathway energetics between the most and least likely pathways.”

The kinetic parameters of the rate-limiting step exhibit little sensitivity to the majority of the reaction network.

“The most important properties of these reaction networks, the kinetic parameters of the rate-limiting step, exhibit little sensitivity to the majority of the reaction network.”

• AssumptionRests on an assumption: Surface reaction networks involving hydrocarbons exhibit enormous complexity with thousands of species and reactions for all but the very simplest of chemistries.

Tracking uncertainty at various levels of approximation enables the use of low-accuracy methods for most of the reaction networks.

“Tracking the uncertainty at various levels of approximation enables the use of low accuracy methods for most of the reaction networks and builds on the recent introduction of uncertainty-enabled DFT calculations.”

Using surrogate models as a guide for full-accuracy electronic structure calculations allows for rapid exploration of new reaction networks.

“Using surrogate models as a guide for full-accuracy electronic structure calculations allows for a rapid exploration of new reaction networks.”

The process is robust to the accuracy of the approximations used because any important reactions are studied with full-accuracy DFT calculations and added to model training sets.

“This process is robust to the accuracy of the approximations used since any important reactions are studied with full-accuracy DFT calculations and added to model training sets.”

The overwhelming complexity of reaction networks can be addressed by treating most of the network with less accurate surrogate models because most of the network has little impact on the final results.

“The overwhelming complexity of reaction networks can be addressed with the insight that most of the network has little impact on the final results and can thus be treated with less accurate surrogate models.”

• cites [1] Gutenkunst, R. N. et al. Universally sloppy parameter sensitivities in systems biology models. PLoS Comput. Biol. 3, 1–8 (2007). sourceNot checked yet

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• AssumptionRests on an assumption: Surface reaction networks involving hydrocarbons exhibit enormous complexity with thousands of species and reactions for all but the very simplest of chemistries.