A method to rapidly predict the injection rate in Dye Sensitized Solar Cells

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

3. Dye Coated Nanocrystalline TiO2 Conductive Glass Electrode Counter Electrode Load Voltage 3 I− I3− Dye Sensitized Solar Cell

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 TiO2

7. For example… • Li et al investigated Anthraquinone dyes1 • Found they produced cells with efficiency worse than that of naked TiO2 • 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 • Introduction • What is a dye sensitized solar cell? • How can theory help? • Theory • How do we compute the rate of electron transfer? • Results • The rate of injection by this method. • 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, Γs, can be calculated using

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

12. The Method 1) Csm, E 2) Γmn Vmk 3) ρkk’ Chromophore dye system modelled by separating into 3 subsystems

13. Coupling - Vsm 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 ρkk’ • 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* • csm comes from the DFT output • The energy of injection, E, can be approximated in one of 2 ways. • Using the energy of the LUMO • Take the difference between the energy of the 1st excited state from TD-DFT and the energy of the cation.

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

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

18. Real Chromophores – realistic rates? b) a) d) c) f) e)

19. Molecular Engineering? • Perylene derivatives • Substitution at the 2 position means the LUMO is less localised on the carboxylic acid group. • Rutile (110) lifetimes 27.3 fs 12.3 fs 7.99 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 ETDDFT−ECation differ by ~1.5 eV 2.83 fs • Computed rate using ELUMO and ETDDFT−ECation • Qualitatively different, the more sophisticated computation matches much better with experimental evidence 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