Hong Jiang ( 蒋 鸿） College of Chemistry, Peking University

1. Shenzhen, Dec 20, 2012 Towards Rational Design of Solar Materials: Electronic Band Structures from the GW Perspective Hong Jiang (蒋 鸿） College of Chemistry, Peking University Email: h.jiang@pku.edu.cn Homepage: www.chem.pku.edu.cn/jianghgroup

2. Outline • Challenges in materials for solar energy conversion • Electronic band structure from first-principles • GW for solar energy conversion materials • Conclusions

3. Materials for solar energy conversion:grand challenges R. M. Navarro Yerga et al. (2009)

4. Solar energy: the power for the future Particulate photocatalysts Photoelectrochemical cells Direct exploitation of solar energy • Solar electricity (photovoltaic cell) • Solar fuels (photo-catalysis) N. S. Lewis, Nature (2001)

5. Grand challenges for materials • right band gap • right band edge positions • easy electron-hole separation • efficient charge transfer in bulk and across the solid/solution interface • chemical stability • • • • • • • Maeda and Domen JPCC (2007)

6. Routes towards new solar materials • sensitization of TiO2 • Doping of TiO2 • Organic materials • New inorganic materials • Nanostructured materials • • • • • • • P. V. Kamat JPCC (2007) infinite possibilities  rational design!!! Maeda and Domen (2007)

7. Fundamental scientific issues • Electronic band structures of complicated materials • Excited states (e.g. e/h-phonon coupling) of extended systems • electron/hole transfer in bulk (effects of defects) • e/h transfer at solid/solution interface • Catalysis on solid/solution interface • • • • • • • R. J. D. Miller and R. Memming (2008)

8. What can first-principles modeling do now? • Detailed structural and energetic properties (e.g. TiO2 surface, defects) • Electronic band structures (e.g. Egap) • Band edge position (w.r.t. vacuum) • Level alignment at solid/molecule interface • Basic band parameters • electron/hole semi-classical dynamics • quantum size effects • • • • • •

9. GW method : the first-principles approach for electronic band structure

10. - - hv Electronic band structure: Experiment vacuum hv - - hv + I - + Eg - - - - - - - - - PES IPS absorption Yu and Cardona, Fundamentals of Semiconductors (2003)

11. NiO Mean field approaches

12. DFT band gap problem • KS HOMO-LUMO Gap  Egap even with exact Exc • But for all explicit density functionals, e.g. LDA/GGA, xc=0 Perdew & Levy (1983); Godby & Sham (1988) Cohen, Mori-Sanchez, Yang, Chem. Rev. 112, 289 (2012)

13. Band Gap from hybrid-functionals • Hybrid-functionals approachgeneralized Kohn-Sham (GKS) approach Cohen, Mori-Sanzhez, and Yang (2008) M. Marsman et al. (2008) Garcia-Lastra et al. Phys. Rev. B 80, 245427 (2009)

14. Electronic band structure: quasi-particle theory Quasi-particle equation (courtesy of Dr. R. I. Gomez-Abal）‏ H. Jiang, Acta Phys.-Chim. Sin.26, 1017(2010)

15. G0W0 and GW0 approximation “best G best W”G0W0, partial SCGW0 Implementation: FHI-gap(Green-functions with Augmented Planewaves) • Based on full-potential linearized augmented planewaves (FP-LAPW) • Currently interfaced with WIEN2k (P. Blaha et al. (2001)) • G0W0, GW0@LDA/GGA(+U) • Spin-polarization  magnetic systems • Further developments  FP (FHI-PKU)-GAP H. Jiang，R. I. Gomez-Abal, et al. submitted to Comput. Phys. Comm. (2012)

16. GW: the state of the art H. Jiang et al. PRL 102, 126403(2009) H. Jiang, Acta Phys.-Chim. Sin.26, 1017(2010)

17. Transition metal dichalcogenides (TMDC) Jiang, H., J. Chem. Phys , 134, 204705(2011) Jiang, H., J. Phys. Chem. C 116, 7664 (2012).

18. GW for SEC materials: ATaO3 H. Wang, F. Wuand H. Jiang, J. Phys. Chem. C 115, 16180 (2011)

19. ATaO3 (A=Li, Na, K) • All have photocatalytic activity for pure water-splitting under UV radiation • strongly influenced by excess alkali and NiO cocatalyst • La-doped NaTaO3+NiO: QE=56%, pure water, UV light (the current record) Using data from Kata and Kudo, JPCB (2001) Hu et al. APL (2009)

20. ATaO3：Band Gaps Pbnm Pm-3m c-ATaO3 o-NaTaO3 r-LiTaO3 R3ch H. Wang, F. Wuand H. Jiang, J. Phys. Chem. C, 115, 16180, (2011)

21. The ionic model for the band gap Pbnm R3ch P. A. Cox, The Electronic Structure and Chemistry of Solids (1987)

22. Cubic LiTaO3: Change of volume

23. Change of crystal structures: Pm-3m  R3c Pm-3m x = 0.0 1.0 R3ch

24. First-principles determination of absolute band positions CB I VB

25. crucial for interface properties: • band offsets in semiconductor hetero-junctions • Photo-catalytic reaction: suitable alignment between the VB/CB edges with the redox potentials of relevant reactions Why absolute band positions important? CB I VB Graetzel, Nature (2001)

26. IP of extended systems from first-principles • IP from KS orbital energies: • exact Kohn-Sham  • LDA/GGA  - HOMO very poor approximation !!! CB I VB

27. GW correction: GW-VBM scheme Vvac

28. TMDC: absolute band positions Jiang, H., J. Phys. Chem. C 116, 7664 (2012).

29. Summary • electronic band structure extremely important for solar-energy conversion materials; • GW : the method of choice for electronic band structures, promising for solar energy conversion • ATaO3: accurate for A=Na and K, but overestimates for A=Li new physics; crystal structures have significant influences on electronic band structures in LiTaO3, mainly via Madelung potentials and band widths; Internal distortion of TaO6 stronger influences on Egap than inter-TaO6 distortion • Absolute band positions from first-principles: quasi-particle corrections necessary, but may not be enough for some materials

30. Acknowledgements Coworkers: Huihui Wang, Feng Wu, Yuchen Shen Funding: NSFC Thank You for Your Attention！