First-principles-based multiscale models are ever more successful in addressing the wide range of length and time scales over which material–function relationships evolve in heterogeneous catalysis. They provide invaluable mechanistic insight and allow screening of vast materials spaces for promising new catalysts — in silico and at predictive quality. Here, we briefly review methodological cornerstones of existing approaches and highlight successes and ongoing developments. The biggest challenge is to overcome presently largely static couplings between the descriptions at the various scales to adequately treat the dynamic and adaptive nature of working catalysts. On the road towards a higher structural, mechanistic and environmental complexity, it is, in particular, the fusion with machine learning methodology that promises rapid advances in the years to come.
This is a preview of subscription content, access via your institution
Open Access articles citing this article.
Topics in Catalysis Open Access 13 January 2022
Nature Communications Open Access 30 October 2020
Topics in Catalysis Open Access 06 October 2020
Subscribe to Nature+
Get immediate online access to the entire Nature family of 50+ journals
Subscribe to Journal
Get full journal access for 1 year
only $9.92 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
Kalz, K. F. et al. Future challenges in heterogeneous catalysis: understanding catalysts under dynamic reaction conditions. ChemCatChem 9, 17–29 (2017).
Nørskov, J. K., Bligaard, T., Rossmeisl, J. & Christensen, C. H. Towards the computational design of solid catalysts. Nat. Chem. 1, 37–46 (2009).
Sutton, J. E. & Vlachos, D. G. Building large microkinetic models with first-principles’ accuracy at reduced computational cost. Chem. Eng. Sci. 121, 190–199 (2015).
Reuter, K. Ab initio thermodynamics and first-principles microkinetics for surface catalysis. Catal. Lett. 146, 541–563 (2016).
Nørskov, J. K., Studt, F., Abild-Pedersen, F. & Bligaard, T. Fundamental Concepts in Heterogeneous Catalysis (Wiley, 2014).
Andersen, M., Panosetti, C. & Reuter, K. A practical guide to surface kinetic monte carlo simulations. Front. Chem. 7, 202 (2019).
Reuter, K., Frenkel, D. & Scheffler, M. The steady state of heterogeneous catalysis, studied by first-principles statistical mechanics. Phys. Rev. Lett. 93, 116105 (2004). One of the first couplings of first-principles calculations with kinetic Monte Carlo models that explored the steady state of CO oxidation on RuO 2 (110) and provided valuable mechanistic insight.
Gokhale, A. A., Dumesic, J. A. & Mavrikakis, M. On the mechanism of low-temperature water gas shift reaction on copper. J. Am. Chem. Soc. 130, 1402–1414 (2008).
Honkala, K. et al. Ammonia synthesis from first-principles calculations. Science 307, 555–558 (2005).
Inderwildi, O. R., Jenkins, S. J. & King, D. A. An unexpected pathway for the catalytic oxidation of methylidyne on Rh(111) as a route to syngas. J. Am. Chem. Soc. 129, 1751–1759 (2007).
Saeys, M., Reyniers, M. F., Neurock, M. & Marin, G. B. Ab initio reaction path analysis of benzene hydrogenation to cyclohexane on Pt(111). J. Phys. Chem. B 109, 2064–2073 (2005).
Filot, I. A. W., Van Santen, R. A. & Hensen, E. J. M. The optimally performing Fischer–Tropsch catalyst. Angew. Chem. Int. Ed. 53, 12746–12750 (2014).
Greeley, J. Theoretical heterogeneous catalysis : scaling relationships and computational catalyst design. Annu. Rev. Chem. Biomol. Eng. 7, 605–635 (2016).
Vlachos, D. G. Multiscale integration hybrid algorithms for homogeneous–heterogeneous reactors. AIChE J. 43, 3031–3041 (1997).
Deutschmann, O. (ed.) Modeling and Simulation of Heterogeneous Catalytic Reactions (Wiley, 2012).
Maestri, M. & Cuoci, A. Coupling CFD with detailed microkinetic modeling in heterogeneous catalysis. Chem. Eng. Sci. 96, 106–117 (2013).
Matera, S. & Reuter, K. First-principles approach to heat and mass transfer effects in model catalyst studies. Catal. Lett. 133, 156–159 (2009).
Matera, S. & Reuter, K. Transport limitations and bistability for in situ CO oxidation at RuO2(110): First-principles based multiscale modeling. Phys. Rev. B Condens. Matter Mater. Phys. 82, 085446 (2010).
Matera, S., Maestri, M., Cuoci, A. & Reuter, K. Predictive-quality surface reaction chemistry in real reactor models: Integrating first-principles kinetic Monte Carlo simulations into computational fluid dynamics. ACS Catal. 4, 4081–4092 (2014).
Matera, S. et al. Evidence for the active phase of heterogeneous catalysts through in situ reaction product imaging and multiscale modelling. ACS Catal. 5, 4514–4518 (2015). Multiscale modelling of an operating reactor coupled first-principle-based microkinetic models with computational fluid dynamics, allowing the identification of the active phase of a transition metal catalyst.
Grajciar, L. et al. Towards operando computational modeling in heterogeneous catalysis. Chem. Soc. Rev. 47, 8307–8348 (2018).
Sabbe, M. K., Reyniers, M.-F. & Reuter, K. First-principles kinetic modeling in heterogeneous catalysis: an industrial perspective on best-practice, gaps and needs. Catal. Sci. Technol. 2, 2010–2024 (2012).
Reuter, K. Modeling Heterogeneous Catalytic Reactions: From the Molecular Process to the Technical System (ed. Deutschmann, O.) 71–111 (Wiley, 2011).
Stamatakis, M. Kinetic modelling of heterogeneous catalytic systems. J. Phys. Condens. Matter 27, 013001 (2015).
Voter, A. F. in Radiation Effects in Solids (eds Sickafus, K. E., Kotomin, E. A. & Uberuaga, B. P.) 1–23 (Springer Netherlands, 2007).
Schlögl, R., Strasser, P., Reier, T., Nong, H. N. & Teschner, D. Electrocatalytic oxygen evolution reaction in acidic environments — reaction mechanisms and catalysts. Adv. Energy Mater. 7, 1601275 (2016).
Ulissi, Z. W., Medford, A. J., Bligaard, T. & Nørskov, J. K. To address surface reaction network complexity using scaling relations machine learning and DFT calculations. Nat. Commun. 8, 14621 (2017).
Li, Q., García-Muelas, R. & López, N. Microkinetics of alcohol reforming for H2 production from a FAIR density functional theory database. Nat. Commun. 9, 526 (2018). An extensive first-principles-based microkinetic study of alcohol reforming on various transition metals exploring complex reaction networks and generating a valuable open, accessible, interoperable and reusable (FAIR) database.
Goldsmith, C. F. & West, R. H. Automatic generation of microkinetic mechanisms for heterogeneous catalysis. J. Phys. Chem. C 121, 9970–9981 (2017).
Margraf, J. T. & Reuter, K. Systematic enumeration of elementary reaction steps in surface catalysis. ACS Omega 4, 3370–3379 (2019). A method was developed to systematically enumerate all possible elementary reaction steps for a given number of atoms, enabling the automatic generation of complete reaction networks.
Oberhofer, H. in Handbook of Materials Modeling 1–33 (Springer International Publishing, 2018).
Voter, A. F., Montalenti, F. & Germann, T. C. Extending the time scale in atomistic simulation of materials. Annu. Rev. Mater. Res. 32, 321–346 (2002).
Foppa, L., Iannuzzi, M., Copéret, C. & Comas-Vives, A. Adlayer dynamics drives CO activation in Ru-catalyzed Fischer–Tropsch synthesis. ACS Catal. 8, 6983–6992 (2018). Meta-dynamics simulations were used to sample the activation mechanisms of CO oxidation in Ru-catalysed Fischer–Tropsch synthesis, revealing the key role of step-edges and surface hydrogen.
Kiss, J., Frenzel, J., Nair, N. N., Meyer, B. & Marx, D. Methanol synthesis on ZnO(0001). III. Free energy landscapes, reaction pathways, and mechanistic insights. J. Chem. Phys. 134, 064710 (2011).
Henkelman, G. & Jónsson, H. Long time scale kinetic Monte Carlo simulations without lattice approximation and predefined event table. J. Chem. Phys. 115, 9657–9666 (2001).
Chill, S. T. & Henkelman, G. Molecular dynamics saddle search adaptive kinetic Monte Carlo. J. Chem. Phys. 140, 214110 (2014).
Xu, L., Mei, D. & Henkelman, G. Adaptive kinetic Monte Carlo simulation of methanol decomposition on Cu(100). J. Chem. Phys. 131, 244520 (2009).
Rupp, M., von Lilienfeld, O. A. & Burke, K. Guest editorial: special topic on data-enabled theoretical chemistry. J. Chem. Phys. 148, 241401 (2018).
Behler, J. Perspective: machine learning potentials for atomistic simulations. J. Chem. Phys. 145, 170901 (2016).
Kitchin, J. R. Machine learning in catalysis. Nat. Catal. 1, 230–232 (2018).
Medford, A. J., Kunz, M. R., Ewing, S. M., Borders, T. & Fushimi, R. Extracting knowledge from data through catalysis informatics. ACS Catal. 8, 7403–7429 (2018).
Wilkinson, M. D. et al. The FAIR guiding principles for scientific data management and stewardship. Sci. Data 3, 160018 (2016).
Bo, C., Maseras, F. & López, N. The role of computational results databases in accelerating the discovery of catalysts. Nat. Catal. 1, 809–810 (2018).
Winther, K. T. et al. Catalysis-Hub.org, an open electronic structure database for surface reactions. Sci. Data 6, 75 (2019).
Zhang, Y. & Ling, C. A strategy to apply machine learning to small datasets in materials science. npj Comput. Mater. 4, 25 (2018).
Chen, J., Li, Y. F., Sit, P. & Selloni, A. Chemical dynamics of the first proton-coupled electron transfer of water oxidation on TiO2 anatase. J. Am. Chem. Soc. 135, 18774–18777 (2013).
Quaranta, V., Hellström, M. & Behler, J. Proton-transfer mechanisms at the water-ZnO interface: the role of presolvation. J. Phys. Chem. Lett. 8, 1476–1483 (2017).
Stecher, T., Reuter, K. & Oberhofer, H. First-principles free-energy barriers for photoelectrochemical surface reactions: proton abstraction at TiO2(110). Phys. Rev. Lett. 117, 1–6 (2016).
Kristoffersen, H. H., Vegge, T. & Hansen, H. A. OH formation and H2 adsorption at the liquid water–Pt(111) interface. Chem. Sci. 9, 6912–6921 (2018).
Sprowl, L. H., Campbell, C. T. & Árnadóttir, L. Hindered translator and hindered rotor models for adsorbates: partition functions and entropies. J. Phys. Chem. C 120, 9719–9731 (2016).
Campbell, C. T., Sprowl, L. H. & Árnadóttir, L. Equilibrium constants and rate constants for adsorbates: two-dimensional (2D) ideal gas, 2D ideal lattice gas, and ideal hindered translator models. J. Phys. Chem. C 120, 10283–10297 (2016).
Piccini, G. & Sauer, J. Effect of anharmonicity on adsorption thermodynamics. J. Chem. Theory Comput. 10, 2479–2487 (2014).
Piccini, G., Alessio, M. & Sauer, J. Ab-initio calculation of rate constants for molecule-surface reactions with chemical accuracy. Angew. Chem. Int. Ed. 55, 5235–5237 (2016).
Groβ, A. in Handbook of Materials Modeling 1–34 (Springer International Publishing, 2018).
Pinto, L. M. C., Quaino, P., Arce, M. D., Santos, E. & Schmickler, W. Electrochemical adsorption of OH on Pt(111) in alkaline solutions: combining DFT and molecular dynamics. ChemPhysChem 15, 2003–2009 (2014).
Ribeiro, R. F., Marenich, A. V., Cramer, C. J. & Truhlar, D. G. Use of solution-phase vibrational frequencies in continuum models for the free energy of solvation. J. Phys. Chem. B 115, 14556–14562 (2011).
Hoffmann, M. J., Medford, A. J. & Bligaard, T. Framework for scalable adsorbate-adsorbate interaction models. J. Phys. Chem. C 120, 13087–13094 (2016).
Wu, C., Schmidt, D. J., Wolverton, C. & Schneider, W. F. Accurate coverage-dependence incorporated into first-principles kinetic models: catalytic NO oxidation on Pt (1 1 1). J. Catal. 286, 88–94 (2012).
Christensen, R., Hansen, H. A. & Vegge, T. Identifying systematic DFT errors in catalytic reactions. Catal. Sci. Technol. 5, 4946–4949 (2015).
Reichenbach, T. et al. Ab initio study of CO2 hydrogenation mechanisms on inverse ZnO/Cu catalysts. J. Catal. 360, 168–174 (2018).
Capdevila-Cortada, M., Łodziana, Z. & López, N. Performance of DFT+U approaches in the study of catalytic materials. ACS Catal. 6, 8370–8379 (2016).
Sun, H. et al. Comparing quasiparticle H2O level alignment on anatase and rutile TiO2. ACS Catal. 5, 4242–4254 (2015).
Sutton, J. E., Guo, W., Katsoulakis, M. A. & Vlachos, D. G. Effects of correlated parameters and uncertainty in electronic-structure-based chemical kinetic modelling. Nat. Chem. 8, 331–337 (2016).
Campbell, C. T. The degree of rate control: a powerful tool for catalysis research. ACS Catal. 7, 2770–2779 (2017).
Döpking, S. et al. Addressing global uncertainty and sensitivity in first-principles based microkinetic models by an adaptive sparse grid approach. J. Chem. Phys. 148, 034102 (2018).
Reuter, K., Plaisance, C. P., Oberhofer, H. & Andersen, M. Perspective: on the active site model in computational catalyst screening. J. Chem. Phys. 146, 040901 (2017).
Stamatakis, M., Chen, Y. & Vlachos, D. G. First-principles-based kinetic Monte Carlo simulation of the structure sensitivity of the water–gas shift reaction on platinum surfaces. J. Phys. Chem. C 115, 24750–24762 (2011).
Fang, Y. & Liu, Z. Mechanism and tafel lines of electro-oxidation of water to oxygen on RuO2(110). J. Am. Chem. Soc. 2, 18214–18222 (2010).
Ma, X., Li, Z., Achenie, L. E. K. & Xin, H. Machine-learning-augmented chemisorption model for CO2 electroreduction catalyst screening. J. Phys. Chem. Lett. 6, 3528–3533 (2015).
Jinnouchi, R. & Asahi, R. Predicting catalytic activity of nanoparticles by a DFT-aided machine-learning algorithm. J. Phys. Chem. Lett. 8, 4279–4283 (2017).
Li, Z., Wang, S., Chin, W. S., Achenie, L. E. & Xin, H. High-throughput screening of bimetallic catalysts enabled by machine learning. J. Mater. Chem. A 5, 24131–24138 (2017).
Ulissi, Z. W. et al. Machine-learning methods enable exhaustive searches for active Bimetallic facets and reveal active site motifs for CO2 reduction. ACS Catal. 7, 6600–6608 (2017).
Gasper, R., Shi, H. & Ramasubramaniam, A. Adsorption of CO on low-energy, low-symmetry Pt nanoparticles: energy decomposition analysis and prediction via machine-learning models. J. Phys. Chem. C 121, 5612–5619 (2017).
Mathew, K. et al. Atomate: a high-level interface to generate, execute, and analyze computational materials science workflows. Comput. Mater. Sci. 139, 140–152 (2017).
Andersen, M., Levchenko, S. V., Scheffler, M. & Reuter, K. Beyond scaling relations for the description of catalytic materials. ACS Catal. 9, 2752–2759 (2019). A compressed sensing model was trained to predict adsorption energies, improving the accuracy of linear scaling relations and allowing screening for active bimetallic alloys at low computational cost.
Tran, K. & Ulissi, Z. W. Active learning across intermetallics to guide discovery of electrocatalysts for CO2 reduction and H2 evolution. Nat. Catal. 1, 696–703 (2018).
Jørgensen, M. & Grönbeck, H. The site-assembly determines catalytic activity of nanoparticles. Angew. Chem. Int. Ed. 57, 5086–5089 (2018). Constructing kinetic Monte Carlo models on metal nanoparticles allowed addressing structural complexity of metal catalysts and revealed synergistic effects between assemblies of active sites.
Jørgensen, M. & Grönbeck, H. Scaling relations and kinetic Monte Carlo simulations to bridge the materials gap in heterogeneous catalysis. ACS Catal. 7, 5054–5061 (2017).
Foppa, L. et al. Contrasting the role of Ni/Al2O3 interfaces in water–gas shift and dry reforming of methane. J. Am. Chem. Soc. 139, 17128–17139 (2017).
Kunz, L., Kuhn, F. M. & Deutschmann, O. Kinetic Monte Carlo simulations of surface reactions on supported nanoparticles: a novel approach and computer code. J. Chem. Phys. 143, 044108 (2015).
Silaghi, M.-C., Comas-Vives, A. & Copéret, C. CO2 Activation on Ni/γ–Al2O3 catalysts by first-principles calculations: from ideal surfaces to supported nanoparticles. ACS Catal. 6, 4501–4505 (2016).
Calle-Vallejo, F., Loffreda, D., Koper, M. T. M. & Sautet, P. Introducing structural sensitivity into adsorption–energy scaling relations by means of coordination numbers. Nat. Chem. 7, 403–410 (2015).
Newton, M. A. Dynamic adsorbate/reaction induced structural change of supported metal nanoparticles: heterogeneous catalysis and beyond. Chem. Soc. Rev. 37, 2644 (2008).
Schlögl, R. Heterogeneous catalysis. Angew. Chem. Int. Ed. 54, 3465–3520 (2015).
Wang, Y.-G., Yoon, Y., Glezakou, V.-A., Li, J. & Rousseau, R. The role of reducible oxide–metal cluster charge transfer in catalytic processes: new insights on the catalytic mechanism of CO oxidation on Au/TiO2 from ab initio molecular dynamics. J. Am. Chem. Soc. 135, 10673–10683 (2013).
Helveg, S. et al. Visualization of oscillatory behaviour of Pt nanoparticles catalysing CO oxidation. Nat. Mater. 13, 884–890 (2014).
Zugic, B. et al. Dynamic restructuring drives catalytic activity on nanoporous gold–silver alloy catalysts. Nat. Mater. 16, 558–564 (2016).
Hansen, P. L. et al. Atom-resolved imaging of dynamic shape changes in supported copper nanocrystals. Science 295, 2053–2055 (2002).
Grønborg, S. S. et al. Visualizing hydrogen-induced reshaping and edge activation in MoS2 and Co-promoted MoS2 catalyst clusters. Nat. Commun. 9, 2211 (2018).
Tauster, S. J., Fung, S. C. & Garten, R. L. Strong metal-support interactions. Group 8 noble metals supported on titanium dioxide. J. Am. Chem. Soc. 100, 170–175 (1978).
Tauster, S. J. Strong metal-support interactions. Acc. Chem. Res. 20, 389–394 (1987).
Campbell, C. T., Parker, S. C. & Starr, D. E. The effect of size-dependent nanoparticle energetics on catalyst sintering. Science 298, 811–814 (2002).
Campbell, C. T. The energetics of supported metal nanoparticles: relationships to sintering rates and catalytic activity. Acc. Chem. Res. 46, 1712–1719 (2013).
Bonnet, N. & Marzari, N. First-principles prediction of the equilibrium shape of nanoparticles under realistic electrochemical conditions. Phys. Rev. Lett. 110, 086104 (2013).
Ouyang, R., Liu, J. X. & Li, W. X. Atomistic theory of ostwald ripening and disintegration of supported metal particles under reaction conditions. J. Am. Chem. Soc. 135, 1760–1771 (2013).
Wang, T., Jelic, J., Rosenthal, D. & Reuter, K. Exploring pretreatment-morphology relationships: ab initio wulff construction for RuO2 nanoparticles under oxidising conditions. ChemCatChem 5, 3398–3403 (2013).
García-Mota, M., Rieger, M. & Reuter, K. Ab initio prediction of the equilibrium shape of supported Ag nanoparticles on α-Al2O3(0001). J. Catal. 321, 1–6 (2015).
Wang, Y. G., Mei, D., Glezakou, V. A., Li, J. & Rousseau, R. Dynamic formation of single-atom catalytic active sites on ceria-supported gold nanoparticles. Nat. Commun. 6, 6511 (2015). Ab initio molecular dynamics were used to simulate the structural distortions of oxide -supported Au catalysts under reaction conditions, revealing the dynamic formation of highly active single-atom sites.
Meyer, J. & Reuter, K. Modeling heat dissipation at the nanoscale: An embedding approach for chemical reaction dynamics on metal surfaces. Angew. Chem. Int. Ed. 53, 4721–4724 (2014).
Rittmeyer, S. P., Bukas, V. J. & Reuter, K. Energy dissipation at metal surfaces. Adv. Phys. X 3, 1381574 (2018).
Zhai, H. & Alexandrova, A. N. Local fluxionality of surface-deposited cluster catalysts: the case of Pt7 on Al2O3. J. Phys. Chem. Lett. 9, 1696–1702 (2018).
Zhai, H. & Alexandrova, A. N. Ensemble-average representation of Pt clusters in conditions of catalysis accessed through GPU accelerated deep neural network fitting global optimization. J. Chem. Theory Comput. 12, 6213–6226 (2016).
Baxter, E. T., Ha, M. A., Cass, A. C., Alexandrova, A. N. & Anderson, S. L. Ethylene dehydrogenation on Pt4,7,8 clusters on Al2O3: strong cluster size dependence linked to preferred catalyst morphologies. ACS Catal. 7, 3322–3335 (2017).
Willinger, E., Massué, C., Schlögl, R. & Willinger, M. G. Identifying key structural features of IrOx water splitting catalysts. J. Am. Chem. Soc. 139, 12093–12101 (2017).
Hoffmann, M. J., Scheffler, M. & Reuter, K. Multi-lattice kinetic Monte Carlo simulations from first principles: reduction of the Pd(100) surface oxide by CO. ACS Catal. 5, 1199–1209 (2015).
Lian, X., Xiao, P., Liu, R. & Henkelman, G. Calculations of oxygen adsorption-induced surface reconstruction and oxide formation on Cu(100). Chem. Mater. 29, 1472–1484 (2017).
Frenken, J. W. M. & Groot, I. M. N. Operando Research in Heterogeneous Catalysis (Springer International Publishing, 2017).
Merte, L. R. et al. Structure of the SnO2(110)-(4×1) surface. Phys. Rev. Lett. 119, 096102 (2017).
Van Den Bossche, M., Grönbeck, H. & Hammer, B. Tight-binding approximation-enhanced global optimization. J. Chem. Theory Comput. 14, 2797–2807 (2018).
Bartók, A. P., Payne, M. C., Kondor, R. & Csányi, G. Gaussian approximation potentials: the accuracy of quantum mechanics, without the electrons. Phys. Rev. Lett. 104, 136403 (2010).
Keil, F. J. Molecular modelling for reactor design. Annu. Rev. Chem. Biomol. Eng. 9, 201–227 (2018).
Andersson, M., Yuan, J. & Sundén, B. Review on modeling development for multiscale chemical reactions coupled transport phenomena in solid oxide fuel cells. Appl. Energy 87, 1461–1476 (2010).
Salmeron, M. & Schlögl, R. Ambient pressure photoelectron spectroscopy: a new tool for surface science and nanotechnology. Surf. Sci. Rep. 63, 169–199 (2008).
Favaro, M. et al. Unravelling the electrochemical double layer by direct probing of the solid/liquid interface. Nat. Commun. 7, 12695 (2016).
Meskine, H., Matera, S., Scheffler, M., Reuter, K. & Metiu, H. Examination of the concept of degree of rate control by first-principles kinetic Monte Carlo simulations. Surf. Sci. 603, 1724–1730 (2009).
Medford, A. J. et al. Assessing the reliability of calculated catalytic ammonia synthesis rates. Science 345, 197–200 (2014).
A.B. and J.T.M. acknowledge support from the Alexander von Humboldt foundation. We further acknowledge support from the Solar Technologies Go Hybrid initiative of the State of Bavaria.
The authors declare no competing interests.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Bruix, A., Margraf, J.T., Andersen, M. et al. First-principles-based multiscale modelling of heterogeneous catalysis. Nat Catal 2, 659–670 (2019). https://doi.org/10.1038/s41929-019-0298-3
Human- and machine-centred designs of molecules and materials for sustainability and decarbonization
Nature Reviews Materials (2022)
Predicting binding motifs of complex adsorbates using machine learning with a physics-inspired graph representation
Nature Computational Science (2022)
Achievements and Expectations in the Field of Computational Heterogeneous Catalysis in an Innovation Context
Topics in Catalysis (2022)
Topics in Catalysis (2022)
Nature Energy (2021)