1. A method to rapidly predict the injection rate in Dye Sensitized Solar Cells Daniel R. Jones and Alessandro Troisi PG Symposium 2009

2. Outline 1. Introduction What is a dye sensitized solar cell? How can theory help? 2. Theory How do we compute the rate of electron transfer? 3. Results The rate of injection by this method. 4. Continuations Where do we go from here?

3. Dye Sensitized Solar Cell Load Voltage Conductive Glass Electrode 3 I − Dye Coated Nanocrystalline TiO 2 Counter Electrode I3− I3−

4. Dye Sensitized Solar Cell +Attractive “third-generation” solar technology offering up to 11% IPCE +Cheap material and processing costs mean that it may compete with fossil fuels in terms of W/$ −Ideally needs to be more efficient to increase uptake. −Liquid electrolyte is not ideal

5. How can theory help? Designing the optimum chromophore is still an active area of research Screen candidate molecules for their potential Minimize efficiency losses Better understanding of the electron transfer reaction mechanisms Aspire to a multiscale model of the functioning cell

6. Goal To provide a method to screen candidate molecules for their potential in dye sensitized solar cells (DSSC) which is: – computationally inexpensive – not reliant on experimental parameterization Compute the rate of electron transfer from the photoexcited chromophore into the conduction band of the TiO 2

7. For example… Li et al investigated Anthraquinone dyes 1 Found they produced cells with efficiency worse than that of naked TiO 2 Chemical intuition does not always work Can we do better by computational screening? 1 Li et al. Solar Energy Materials and Solar Cells 2007, 91, 1863-1871.

8. Outline 1. Introduction What is a dye sensitized solar cell? How can theory help? 2. Theory How do we compute the rate of electron transfer? 3. Results The rate of injection by this method. 4. Continuations Where do we go from here?

9. The Method 1) 2) 3) Chromophore dye system modelled by separating into 3 subsystems

10. The Method It can be shown that the effective Hamiltonian for the state can be written The self energy, Σ, is complex, and can be separated into real and imaginary components The imaginary part of self energy, Γ s, can be calculated using

11. The Method To compute the coupling terms, V sl, the states on the semiconductor and the states on the chromophore are recast in an atomic basis set The energy dependent density matrix ρ kk ’. The self energy on the molecule in an atomic basis set The self energy on the first excited state

12. The Method 1) 2) 3) Chromophore dye system modelled by separating into 3 subsystems C sm, E V mk ρ kk’ Γ mn

13. Coupling - V sm Rutile (110) surface Ti-O(mol) 2.07 Å Ti-Ti-O(mol) 80˚ Anatase (101) surface Ti-O(mol) 2.16 Å Ti-Ti-O(mol) 70˚

14. Computing ρ kk’ Electronic structure computed using B3LYP/6-31G*. Clusters embedded in a volume of point charges to model bulk electrostatics.

15. Chromophore Chromophore’s electronic structure and geometry computed using B3LYP/6-31G* c sm comes from the DFT output The energy of injection, E, can be approximated in one of 2 ways. 1.Using the energy of the LUMO 2.Take the difference between the energy of the 1 st excited state from TD-DFT and the energy of the cation.

16. Outline 1. Introduction What is a dye sensitized solar cell? How can theory help? 2. Theory How do we compute the rate of electron transfer? 3. Results The rate of injection by this method. 4. Continuations Where do we go from here?

17. Variation of rate with injection energy E in this range

18. Real Chromophores – realistic rates? Dyerutile (110)/ fsanatase(101) / fs a2.831.43 b56.753.9 c2.250.18 d1.815.96 e3.586.20 f9.994.09 a) b) c) d) e) f)

19. Molecular Engineering? Perylene derivatives Substitution at the 2 position means the LUMO is less localised on the carboxylic acid group. Rutile (110) lifetimes 7.99 fs 12.3 fs 27.3 fs

20. Importance of injection energy Rapid variation of injection rate with changing energy. Energy of injection computed using the LUMO energy of the neutral chromophore compared to that computed using E TDDFT −E Cation differ by ~1.5 eV Computed rate using E LUMO and E TDDFT −E Cation Qualitatively different, the more sophisticated computation matches much better with experimental evidence 2.83 fs 2260 fs 56.5 fs 195 fs

21. Conclusions and closing remarks We have developed a method to rapidly compute the rate of electron transfer from chromophore to semi- conductor in DSSC We note the importance of choosing the correct injection energy Our method may be improved by aligning the energy levels with experiment This method is modular, so may be improved relatively easily if more accurate computations for any of the subsystems are available

22. Outlook All chromophores considered so far have been connected by a carboxylic bridge, consider other anchoring groups Compute the rate of recombination, where an electron in the conduction band neutralises the chromophore +, more difficult to guess qualitatively Try to find “better ways” to treat the semiconductor surface Write a thesis…

23. Acknowledgements Alessandro Troisi His group, past and present: Dave Cheung, Natalia Martsinovich, Arijit Bhattacharyay, Sara Fortuna, Dave McMahon, Jack Sleigh, Konrad Diwold EPSRC and University of Warwick for funding. … and you for your attention