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.

  • Letter
  • Published:

Accurate surface and adsorption energies from many-body perturbation theory

Abstract

Kohn–Sham density functional theory is the workhorse computational method in materials and surface science1. Unfortunately, most semilocal density functionals predict surfaces to be more stable than they are experimentally. Naively, we would expect that consequently adsorption energies on surfaces are too small as well, but the contrary is often found: chemisorption energies are usually overestimated2. Modifying the functional improves either the adsorption energy or the surface energy but always worsens the other aspect. This suggests that semilocal density functionals possess a fundamental flaw that is difficult to cure, and alternative methods are urgently needed. Here we show that a computationally fairly efficient many-electron approach, the random phase approximation3 to the correlation energy, resolves this dilemma and yields at the same time excellent lattice constants, surface energies and adsorption energies for carbon monoxide and benzene on transition-metal surfaces.

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

Access options

Buy this article

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

Figure 1: Atop CO adsorption and surface energies for Pt(111) and Rh(111).
Figure 2: Electronic DOS for CO adsorbed atop a Pt atom on Pt(111).
Figure 3: Surface energies, lattice constants and adsorption energies.

Similar content being viewed by others

References

  1. Kohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133–A1138 (1965).

    Article  Google Scholar 

  2. Hammer, B., Hansen, L. B. & Nørskov, J. K. Improved adsorption energetics within density-functional theory using revised Perdew–Burke–Ernzerhof functionals. Phys. Rev. B 59, 7413–7421 (1999).

    Article  Google Scholar 

  3. Nozières, P. & Pines, D. Correlation energy of a free electron gas. Phys. Rev. 111, 442–454 (1958).

    Article  Google Scholar 

  4. Feibelman, P. J. et al. The CO/Pt(111) puzzle. J. Phys. Chem. B 105, 4018–2025 (2001).

    Article  CAS  Google Scholar 

  5. Gil, A. et al. Site preference of CO chemisorbed on Pt(111) from density functional calculations. Surf. Sci. 530, 71–86 (2003).

    Article  CAS  Google Scholar 

  6. Mason, S. E., Grinberg, I. & Rappe, A. M. First-principles extrapolation method for accurate CO adsorption energies on metal surfaces. Phys. Rev. B 69, 161401 (2004).

    Article  Google Scholar 

  7. Wang, Y., de Gironcoli, S., Hush, N. S. & Reimers, J. R. Successful a priori modeling of CO adsorption on Pt(111) using periodic hybrid density functional theory. J. Am. Chem. Soc. 129, 10402–10407 (2007).

    Article  CAS  Google Scholar 

  8. Stroppa, A. & Kresse, G. The shortcomings of semi-local and hybrid functionals: What we can learn from surface science studies. New J. Phys. 10, 063020 (2008).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  10. Diaz, C. et al. Chemically accurate simulation of a prototypical surface reaction: H2 dissociation on Cu(111). Science 326, 832–834 (2009).

    Article  CAS  Google Scholar 

  11. Armiento, R. & Mattsson, A. E. Functional designed to include effects in self-consistent density functional theory. Phys. Rev. B 72, 085108 (2005).

    Article  Google Scholar 

  12. Perdew, J. P. et al. Restoring the density-gradient expansion for exchange in solids and surfaces. Phys. Rev. Lett. 100, 136406 (2008).

    Article  Google Scholar 

  13. Lee, C., Yang, W. & Parr, R. Development of the Colle–Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 37, 785–789 (1988).

    Article  CAS  Google Scholar 

  14. Hedin, L. New method for calculating the one-particle Green’s function with application to the electron-gas problem. Phys. Rev. 139, A796–A823 (1965).

    Article  Google Scholar 

  15. Blyholder, G. J. Molecular orbital view of chemisorbed carbon monoxide. J. Phys. Chem. 68, 2772–2777 (1964).

    Article  CAS  Google Scholar 

  16. Hammer, B., Morikawa, Y. & Nørskov, J. K. CO chemisorption at metal surfaces and overlayers. Phys. Rev. Lett. 76, 2141–2144 (1996).

    Article  CAS  Google Scholar 

  17. Van Santen, R. A. Molecular Heterogeneous Catalysis: A Conceptual and Computational Approach (Wiley-VCH, 2006).

    Book  Google Scholar 

  18. Krukau, A. V., Vydrov, O. A., Izmaylov, A. F. & Scuseria, G. E. Influence of the exchange screening parameter on the performance of screened hybrid functionals. J. Chem. Phys. 125, 224106 (2006).

    Article  Google Scholar 

  19. Anazawa, T., Kinoshita, I. & Matsumoto, Y. Two-photon photoemission study of CO/Pt(111). J. Electron Spectrosc. Relat. Phenom. 88, 585–590 (1998).

    Article  Google Scholar 

  20. Tsilimis, G., Kutzner, J. & Zacharias, H. Photoemission study of clean and c(4×2)-2CO-covered Pt(111) using high-harmonic radiation. Appl. Phys. A 76, 743–749 (2003).

    Article  CAS  Google Scholar 

  21. Hu, Q-M., Reuter, K. & Scheffler, M. Towards an exact treatment of exchange and correlation in materials: Application to the CO adsorption puzzle and other systems. Phys. Rev. Lett. 98, 176103 (2007).

    Article  Google Scholar 

  22. Ren, X., Rinke, P. & Scheffler, M. Exploring the random phase approximation: Application to CO adsorbed on Cu(111). Phys. Rev. B 80, 045402 (2009).

    Article  Google Scholar 

  23. Harl, J. & Kresse, G. Accurate bulk properties from approximate many-body techniques. Phys. Rev. Lett. 103, 056401 (2009).

    Article  Google Scholar 

  24. Tyson, W. R. & Miller, W. A. Surface free energies of solid metals: Estimation from liquid surface tension measurements. Surf. Sci. 62, 267–276 (1977).

    Article  CAS  Google Scholar 

  25. Vitos, L., Ruban, A. V., Skriver, H. L. & Kollàr, J. The surface energy of metals. Surf. Sci. 411, 186–202 (1998).

    Article  CAS  Google Scholar 

  26. Abild-Pedersen, F. & Andersson, M. P. CO adsorption energies on metals with correction for high coordination adsorption sites —a density functional study. Surf. Sci. 601, 1747–1753 (2007).

    Article  CAS  Google Scholar 

  27. Rohlfing, M. & Bredow, T. Binding energy of adsorbates on a noble-metal surface: Exchange and correlation effects. Phys. Rev. Lett. 101, 266106 (2008).

    Article  Google Scholar 

  28. Jenkins, S. J. Aromatic adsorption on metals via first-principles density functional theory. Proc. R. Soc. A 465, 2949–2976 (2009).

    Article  CAS  Google Scholar 

  29. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).

    Article  Google Scholar 

  30. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).

    Article  CAS  Google Scholar 

  31. Shishkin, M., Marsman, M. & Kresse, G. Accurate quasiparticle spectra from self-consistent GW calculations with vertex corrections. Phys. Rev. Lett. 99, 246403 (2007).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

This work was supported by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung (FWF).

Author information

Authors and Affiliations

Authors

Contributions

L.S., J.H., A.S., F.M. and G.K. carried out the calculations. J.H., A.G., M.M. and G.K. contributed to the implementation of hybrid functionals and RPA. G.K. prepared the manuscript initially. All authors contributed to the discussions and revisions of the manuscript.

Corresponding authors

Correspondence to L. Schimka or A. Stroppa.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schimka, L., Harl, J., Stroppa, A. et al. Accurate surface and adsorption energies from many-body perturbation theory. Nature Mater 9, 741–744 (2010). https://doi.org/10.1038/nmat2806

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nmat2806

This article is cited by

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