Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Effects of correlated parameters and uncertainty in electronic-structure-based chemical kinetic modelling

Nature Chemistry volume 8, pages 331–337 (2016)Cite this article

Subjects

Abstract

Kinetic models based on first principles are becoming common place in heterogeneous catalysis because of their ability to interpret experimental data, identify the rate-controlling step, guide experiments and predict novel materials. To overcome the tremendous computational cost of estimating parameters of complex networks on metal catalysts, approximate quantum mechanical calculations are employed that render models potentially inaccurate. Here, by introducing correlative global sensitivity analysis and uncertainty quantification, we show that neglecting correlations in the energies of species and reactions can lead to an incorrect identification of influential parameters and key reaction intermediates and reactions. We rationalize why models often underpredict reaction rates and show that, despite the uncertainty being large, the method can, in conjunction with experimental data, identify influential missing reaction pathways and provide insights into the catalyst active site and the kinetic reliability of a model. The method is demonstrated in ethanol steam reforming for hydrogen production for fuel cells.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Correlations in parametric uncertainty and their effect on global SA predictions.
Figure 2: Quantification of the uncertainty in conversion, selectivity, rates, ethanol reaction order and apparent activation energy.
Figure 3: SRPA of the initial dehydrogenation steps and uncertainty distributions for fractional consumption and net rates.

Similar content being viewed by others

References

  1. Bligaard, T. et al. Electronic-structure-based design of ordered alloys. MRS Bull. 31, 986–990 (2006).

    Article  CAS  Google Scholar 

  2. Greeley, J., Jaramillo, T. F., Bonde, J., Chorkendorff, I. B. & Nørskov, J. K. Computational high-throughput screening of electrocatalytic materials for hydrogen evolution. Nature Mater. 5, 909–913 (2006).

    Article  CAS  Google Scholar 

  3. Greeley, J. & Mavrikakis, M. Alloy catalysts designed from first principles. Nature Mater. 3, 810–815 (2004).

    Article  CAS  Google Scholar 

  4. Greeley, J. & Norskov, J. Combinatorial density functional theory-based screening of surface alloys for the oxygen reduction reaction. J. Phys. Chem. C 113, 4932–4939 (2009).

    Article  CAS  Google Scholar 

  5. Norskov, J., Bligaard, T., Rossmeisl, J. & Christensen, C. Towards the computational design of solid catalysts. Nature Chem. 1, 37–46 (2009).

    Article  CAS  Google Scholar 

  6. Hansgen, D. A., Vlachos, D. G. & Chen, J. G. Using first principles to predict bimetallic catalysts for the ammonia decomposition reaction. Nature Chem. 2, 484–489 (2010).

    Article  CAS  Google Scholar 

  7. Norskov, J. K., Abild-Pedersen, F., Studt, F. & Bligaard, T. Density functional theory in surface chemistry and catalysis. Proc. Natl Acad. Sci. USA 108, 937–943 (2011).

    Article  CAS  Google Scholar 

  8. Wellendorff, J. et al. Density functionals for surface science: exchange-correlation model development with Bayesian error estimation. Phys. Rev. B 85 ( 2012).

  9. Klimes, J. & Michaelides, A. Perspective: advances and challenges in treating van der Waals dispersion forces in density functional theory. J. Chem. Phys. 137, 120901 (2012).

    Article  Google Scholar 

  10. Medford, A. J. et al. Assessing the reliability of calculated catalytic ammonia synthesis rates. Science 345, 197–200 (2014).

    Article  CAS  Google Scholar 

  11. Salciccioli, M., Stamatakis, M., Caratzoulas, S. & Vlachos, D. G. A review of multiscale modeling of metal-catalyzed reactions: mechanism development for complexity and emergent behavior. Chem. Eng. Sci. 66, 4319–4355 (2011).

    Article  CAS  Google Scholar 

  12. Campbell, C. T. Finding the rate-determining step in a mechanism: comparing DeDonder relations with the ‘degree of rate control’. J. Catal. 204, 520–524 (2001).

    Article  CAS  Google Scholar 

  13. Stegelmann, C., Andreasen, A. & Campbell, C. T. Degree of rate control: how much the energies of intermediates and transition states control rates. J. Am. Chem. Soc. 131, 8077–8082 (2009).

    Article  CAS  Google Scholar 

  14. Norskov, J., Bligaard, T. & Kleis, J. Rate control and reaction engineering. Science 324, 1655–1656 (2009).

    Article  CAS  Google Scholar 

  15. Sutton, J. E., Panagiotopoulou, P., Verykios, X. E. & Vlachos, D. G. Combined DFT, microkinetic, and experimental study of ethanol steam reforming on Pt. J. Phys. Chem. C 117, 4691–4706 (2013).

    Article  CAS  Google Scholar 

  16. 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).

    Article  CAS  Google Scholar 

  17. Gokhale, A. A., Kandoi, S., Greeley, J. P., Mavrikakis, M. & Dumesic, J. A. Molecular-level descriptions of surface chemistry in kinetic models using density functional theory. Chem. Eng. Sci. 59, 4679–4691 (2004).

    Article  CAS  Google Scholar 

  18. Phatak, A. A. et al. Kinetics of the water–gas shift reaction on Pt catalysts supported on alumina and ceria. Catal. Today 123, 224–234 (2007).

    Article  CAS  Google Scholar 

  19. Panagiotopoulou, P. & Kondarides, D. I. A comparative study of the water–gas shift activity of Pt catalysts supported on single (MOx) and composite (MOx/Al2O3, MOx/TiO2) metal oxide carriers. Catal. Today 127, 319–329 (2007).

    Article  CAS  Google Scholar 

  20. Calle-Vallejo, F., Loffreda, D., KoperMarc, T. M. & Sautet, P. Introducing structural sensitivity into adsorption–energy scaling relations by means of coordination numbers. Nature Chem. 7, 403–410 (2015).

    Article  CAS  Google Scholar 

  21. Nørskov, J. K. et al. Universality in heterogeneous catalysis. J. Catal. 209, 275–278 (2002).

    Article  Google Scholar 

  22. Christensen, C. H. & Nørskov, J. K. A molecular view of heterogeneous catalysis. J. Chem. Phys. 128, 182503 (2008).

    Article  Google Scholar 

  23. Kourtelesis, M., Panagiotopoulou, P. & Verykios, X. E. Influence of structural parameters on the reaction of low temperature ethanol steam reforming over Pt/Al2O3 catalysts. Catal. Today 258, 247–255 (2015).

    Article  CAS  Google Scholar 

  24. Panagiotopoulou, P. & Verykios, X. E. Mechanistic aspects of the low temperature steam reforming of ethanol over supported Pt catalysts. Int. J. Hydrogen Energy 37, 16333–16345 (2012).

    Article  CAS  Google Scholar 

  25. Sexton, B. A., Rendulic, K. D. & Hughes, A. E. Decomposition pathways of C1–C4 alcohols adsorbed on platinum (111). Surf. Sci. 121, 181–198 (1982).

    Article  CAS  Google Scholar 

  26. Skoplyak, O., Barteau, M. A. & Chen, J. G. Ethanol and ethylene glycol on Ni/Pt(111) bimetallic surfaces: a DFT and HREELS study. Surf. Sci. 602, 3578–3587 (2008).

    Article  CAS  Google Scholar 

  27. Alcala, R., Mavrikakis, M. & Dumesic, J. DFT studies for cleavage of C–C and C–O bonds in surface species derived from ethanol on Pt(111). J. Catal. 218, 178–190 (2003).

    Article  CAS  Google Scholar 

  28. Alcala, R., Shabaker, J., Huber, G., Sanchez-Castillo, M. & Dumesic, J. Experimental and DFT studies of the conversion of ethanol and acetic acid on PtSn-based catalysts. J. Phys. Chem. B 109, 2074–2085 (2005).

    Article  CAS  Google Scholar 

  29. Wang, H. & Liu, Z. Comprehensive mechanism and structure-sensitivity of ethanol oxidation on platinum: new transition-state searching method for resolving the complex reaction network. J. Am. Chem. Soc. 130, 10996–11004 (2008).

    Article  CAS  Google Scholar 

  30. Wang, J.-H., Lee, C. S. & Lin, M. C. Mechanism of ethanol reforming: theoretical foundations. J. Phys. Chem. C 113, 6681–6688 (2009).

    Article  CAS  Google Scholar 

  31. Guo, W. & Vlachos, D. G. On factors controlling activity of submonolayer bimetallic catalysts: nitrogen desorption. J. Chem. Phys. 140, 014703 (2014).

    Article  Google Scholar 

  32. 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).

    Article  CAS  Google Scholar 

  33. Dahl, S. et al. Role of steps in N2 activation on Ru(0001). Phys. Rev. Lett. 83, 1814–1817 (1999).

    Article  Google Scholar 

  34. Bahn, S. R. & Jacobsen, K. W. An object-oriented scripting interface to a legacy electronic structure code. Comp. Sci. Eng. 4, 56–66 (2002).

    Article  CAS  Google Scholar 

  35. Mortensen, J. J., Hansen, L. B. & Jacobsen, K. W. Real-space grid implementation of the projector augmented wave method. Phys. Rev. B 71, 035109 (2005).

    Article  Google Scholar 

  36. Enkovaara, J. et al. Electronic structure calculations with GPAW: a real-space implementation of the projector augmented-wave method. J. Phys.-Cond. Matter 22, 253202 (2010).

    Article  CAS  Google Scholar 

  37. Larsen, A. H., Vanin, M., Mortensen, J. J., Thygesen, K. S. & Jacobsen, K. W. Localized atomic basis set in the projector augmented wave method. Phys. Rev. B 80, 195112 (2009).

    Article  Google Scholar 

  38. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    Article  CAS  Google Scholar 

  39. Kucherenko, S., Rodriguez-Fernandez, M., Pantelides, C. & Shah, N. Monte Carlo evaluation of derivative-based global sensitivity measures. Reliab. Eng. Syst. Safety 94, 1135–1148 (2009).

    Article  Google Scholar 

Download references

Acknowledgements

The ethanol mechanism and the DFT calculations were supported by the Catalysis Center for Energy Innovation, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under award number DE-SC0001004. The uncertainty analysis formulation was supported by the US Department of Energy, Office of Basic Energy Sciences, under Contract No. DE-AC02-98CH10886 and Contract No. DE-SC0010723 and the sensitivity of model ensembles by grants R115-1342R1 and W911NF-15-2-0122 from the Defense Advanced Research Projects Agency. The DFT calculations were carried out at the TeraGrid provided by the Texas Advanced Computing Center of the University of Texas at Austin. The CGSA calculations were carried out on the clusters at the Center for Functional Nanomaterials at Brookhaven National Laboratory and the National Energy Research Scientific Computing Center.

Author information

Authors and Affiliations

  1. Department of Chemical and Biomolecular Engineering, Catalysis Center for Energy Innovation and Center for Catalytic Science and Technology, University of Delaware, Newark, 19716, Delaware, USA

    Jonathan E. Sutton, Wei Guo & Dionisios G. Vlachos

  2. Beijing Institute of Technology, School of Physics, 100081, Beijing, China

    Wei Guo

  3. Department of Mathematics and Statistics, University of Massachusetts at Amherst, Amherst, 01003, Massachusetts, USA

    Markos A. Katsoulakis

Authors
  1. Jonathan E. Sutton
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wei Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Markos A. Katsoulakis
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dionisios G. Vlachos
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

J.E.S. implemented the correlative SA, performed the calculations and analysed the results. W.G. performed the GPAW calculations. D.G.V. conceived the problem, M.A.K. formulated the mathematical foundations of the correlative SA and both supervised J.E.S. and W.G. All the authors contributed to writing the paper.

Corresponding author

Correspondence to Dionisios G. Vlachos.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 2989 kb)

Supplementary information

Supplementary Data 1 (XLSX 386 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sutton, J., Guo, W., Katsoulakis, M. et al. Effects of correlated parameters and uncertainty in electronic-structure-based chemical kinetic modelling. Nature Chem 8, 331–337 (2016). https://doi.org/10.1038/nchem.2454

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nchem.2454

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing