th International Workshop on Computational Physics and Materials Science: Total Energy and Force Methods January 2011

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2220-4 15th International Workshop on Computational Physics and Materials Science: Total Energy and Force Methods 13-15 January 2011 Computational study of optical and structural properties of an organic dye sensitized solar cell Ralph Gebauer ICTP Trieste Italy

15th International Workshop on Computational Physics and Materials Science: Total Energy and Force Methods January 13-15, 2011 Computational study of optical and structural properties of an organic dye sensitized solar cell Ralph Gebauer Thursday, January 13 th, 2011

Overview Nanostructured photovoltaic devices (Grätzel cells) Application of TDDFT to such systems computational approach dry system including (explicit) solvent averaging over MD in presence of solvent Dye adsorption/desorption in presence of explicit solvent

Sensitized semiconductor surfaces as photovoltaic devices Idea (Graetzel solar cells):

Functioning of a Grätzel cell Source: M. Grätzel, Nature 414, 338 (2001)

Various dyes Squaraine dye Source: M. Grätzel, Prog. Photovolt. Res. Appl. 8, 171-185 (2000)

Our system: Squaraine on TiO 2 slab Slab geometry: 1x4 TiO2 anatase slab, Exposing (101) surface PBE functional, PW basis set (Quantum-ESPRESSO code) Shown here: minimum energy configuration

TiO2 slab with squaraine dye

TDDFT treatment of model system Adiabatic PBE functional Recursive Lanczos algorithm for TDDFT: Ideally suited for large systems broad spectral region, large basis set

Linear response formalism in TDDFT: Now define the following linear combinations: c c

With the following definitions:

Consider an observable A: Its Fourier transform is:

Recall: Therefore: Thus in order to calculate the spectrum, we need to calculate one given matrix element of.

Use a recursion to represent L as a tridiagonal matrix: And the response can be written as a continued fraction!

Convergence of the TDDFPT spectrum Isolated squaraine molecule

Charge response at main absorption peak:

Main features: Recursive Lanczos technique allows to compute TDDFT spectra: Rather fast (even in large systems) Over broad spectral region No virtual KS states required Allows to analyze particular features of a spectrum (use of this "turbotddft" code will be part of next week's hands-on tutorial)

Experimental and TDDFT absorption spectra Experiment Computation

Analyzing the various transitions

A more realistic system: Including the solvent

TDDFT calculation of optical spectra and related quantities Various challenges: System is large (429 atoms, 1.666 electrons, 181.581 PWs, resp. 717.690 PWs) Broad spectral region of interest Many excited states in spectral region Computational tool: Recursive Lanczos algorithm for TDDFT

TDDFT optical spectrum: dry system Energy [ev]

TDDFT optical spectrum including solvent Energy [ev]

Including the solvent in MD and TDDFT computations Solvent is treated at the same level of theory as molecule and surface slab Solvent changes electrostatic conditions (dielectric constant ) Solvent participates actively: - in formation surface dipoles, etc. - hydrogen bonding networks - is essential for geometry of solute

Energy level fluctuations and electron injection driving force

Dye desorption steps:

Conclusions TD-DFT study of squaraine dye adsorbed on TiO 2 slab Fair agreement with experiment in absence of solvent in computation Including the solvent explicitly Improvement of computed spectrum, but important features are not reproduced (shoulders, etc.) Molecular dynamics of dye sensitized slab with explicit solvent Averaging of optical properties over many configurations leads to a description of optical properties in good agreement with experiment Very efficient implementation of TD-DFT for large systems/basis sets Recursive Lanczos TDDFT based on time-dependent DFPT for a system composed of 429 atoms and described by! 200,000 PWs

Filippo De Angelis (Perugia) Thanks to: Stefano Baroni (SISSA & DEMOCRITOS, Trieste) Brent Walker (University College, London) Dario Rocca (UC Davis) O. Baris Malcioglu (Univ. Liège) Quantum ESPRESSO and its community To know more: Phys. Rev. Lett. 96, 113001 (2006) J. Chem. Phys. 127, 164106 (2007) J. Chem. Phys. 128, 154105 (2008) Chem. Phys. Lett. 475, 49 (2009)

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