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

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 Direct exploitation of solar energy Solar electricity (photovoltaic cell) Solar fuels (photo-catalysis) N. S. Lewis, Nature (2001) Particulate photocatalysts Photoelectrochemical cells

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 TiO 2 Doping of TiO 2 Organic materials New inorganic materials Nanostructured materials infinite possibilities  rational design!!! P. V. Kamat JPCC (2007) 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. TiO 2 surface, defects) Electronic band structures (e.g. E gap ) 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. Electronic band structure: Experiment Yu and Cardona, Fundamentals of Semiconductors (2003) + - hv - -- - - - -- - - - -- + PESIPSabsorption vacuum I EgEg

11. Mean field approaches NiO

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

13. Band Gap from hybrid-functionals M. Marsman et al. (2008) Hybrid-functionals approach  generalized Kohn-Sham (GKS) approach Cohen, Mori-Sanzhez, and Yang (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. G 0 W 0 and GW 0 approximation “best G best W”  G 0 W 0, partial SC  GW 0 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))  G 0 W 0, GW 0 @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, Acta Phys.-Chim. Sin. 26, 1017(2010) H. Jiang et al. PRL 102, 126403(2009)

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: ATaO 3 H. Wang, F. Wu and H. Jiang, J. Phys. Chem. C 115, 16180 (2011)

19. ATaO 3 (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 NaTaO 3 +NiO: QE=56%, pure water, UV light (the current record) Using data from Kata and Kudo, JPCB (2001) Hu et al. APL (2009)

20. ATaO 3 ： Band Gaps Pm-3m Pbnm R3ch H. Wang, F. Wu and H. Jiang, J. Phys. Chem. C, 115, 16180, (2011) c-ATaO 3 o-NaTaO 3 r-LiTaO 3

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

22. Cubic LiTaO 3 : Change of volume

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

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

25. Why absolute band positions important? 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 CB VB I 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 VB I

27. GW correction: GW-VBM scheme V vac

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

29.  electronic band structure extremely important for solar-energy conversion materials;  GW : the method of choice for electronic band structures, promising for solar energy conversion  ATaO 3 : accurate for A=Na and K, but overestimates for A=Li  new physics; crystal structures have significant influences on electronic band structures in LiTaO 3, mainly via Madelung potentials and band widths; Internal distortion of TaO 6 stronger influences on E gap than inter-TaO 6 distortion  Absolute band positions from first-principles: quasi-particle corrections necessary, but may not be enough for some materials Summary

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