1. Using a tight-binding approximation to compute the electronic structure of sensitizer molecules adsorbed onto TiO 2 surfaces. Daniel R. Jones & Alessandro Troisi, Department of Chemistry, University of Warwick, UK. E-mail: d.r.jones.1@warwick.ac.uk www.warwick.ac.uk/go/troisigroup 3. Theory The local density of states, ρ, on the surface can be computed using, Where C is the matrix of orbital coefficients on the surface, and δ is the Dirac delta function, the index, l, runs across all “crystal orbitals.” The imaginary component of the self-energy, Γ, can then be computed by. Where, V i,k1 is the coupling between a basis function, i on the molecule and k1 on the crystal 2. Computing the Local Density of States on TiO 2 Using a tight-binding Hamiltonian, with parameters computed using DFT treatment of clusters of TiO2 embedded in a volume of point charges (as shown in figure 1) the local density of states, ρ, is computed. 1. Introduction The rate of electron transfer between an adsorbed molecule and a TiO 2 surface is essential when determining the effectiveness of a particular molecule as a chromophore in a DSSC. In order to compute this rate two key components are needed; the electronic interaction between the molecule and the surface and the reorganisation energy. This work focuses on computing the electronic interaction between the adsorbed chromophore and the surface. The computation of the reorganisation energy is relatively straightforward, so we should be able to provide theoretical rates of electron transfer using this method. One key idea of the methodology described is that it is modular. The electronic structure of the molecule and the surface are computed separately, then a third computation is performed on the interface between the molecule and the surface. This enables a large number of potential chromophores to be studied for relatively small computational cost, which will allow us to theoretically scan many molecules for their potential as chromophores in a DSSC. Abstract: The development and systematic improvement of dye sensitised solar cell (DSSC) has been hampered somewhat by the lack of a consistent theoretical framework that can guide improvements to the efficiency of a DSSC. We attempt to remedy this problem using theories developed for the study of molecular electronics. Using a tight-binding approximation based on the DFT treatment of TiO 2 clusters, the energy dependant density matrix, ρ, of “crystal like” TiO 2 surfaces are computed. This allows us to compute the interaction between the electrons in the solid state and the molecular orbitals of the chromophore. From this, we will be able to predict and compare rates of the elementary charge separation, charge neutralisation and charge recombination steps. We report the initial results of this investigation and draw some early conclusions. 5. Outlook This method shows promise for computing the electronic interaction between a TiO 2 surface and an adsorbed molecule with modest computational cost. This will enable the scanning of multiple chromophore molecules, and to recommend candidates for new chromophores to use in DSSCs. A very similar procedure should allow us to also study the various loss mechanisms in the DSSC and make efforts to predict what needs to be done to minimise loss of efficiency. We plan to compute the rate of electron transfer for some typical chromophores, shown in figure 4, to the TiO 2 surface. We also plan to perform similar computations using the anatase (101) surface. This computation, combined with a computation of the electronic coupling between a small molecule, e.g. ethanoic acid, and a few TiO 2 atoms, using Gaussian03, allows us to compute an approximate self-energy of the small molecule adsorbed on the surface. In this system, the self-energy represents the broadening and shifting of energy levels on the adsorbed molecule due to the interaction with the continuum of electronic states on the TiO 2 surface, alternatively it represents the lifetime for electrons to reside on the molecule. We plan to use this self-energy and the reorganisation energy computed separately to compute the rate of electron transfer across the interface between a chromophore and a TiO 2 surface. Figure 1: A (Ti 32 O 62 ) 4+ cluster embedded in a volume of point charges. White, Ti atom; red, O atom; green, 2+ point charge; blue, 1- point charge. 4. Computing the Self-Energy The density of electronic states of a 94 atom cluster of TiO 2 using a tight binding Hamiltonian with only nearest neighbour interactions based on B3LYP computations with a 3-21G basis set on the O atoms and a LANL2MB basis set and pseudopotential on the Ti atoms is shown in figure 2. Using this electronic structure, ρ, can be computed with equation (1). The electronic coupling is computed using Gaussian03 software. When computing the electronic coupling, a small molecule containing the connecting group and a very small cluster of TiO 2 are considered. For example, the system used to study the interaction between a carboxylic acid group and the rutile (110) surface is shown in figure 3 this computation in combination with the computation of ρ is used to compute the self- energy, Γ, using equation (2). We assume the chromophores in DSSCs interact primarily through connecting groups, e.g. carboxylic acid, phosphoric acid, 1,2-benzenediol, and consider other interactions to be negligible, we can therefore use the self-energy of the small molecules as the approximate self-energy for the chromophores, which we can then use to compute the rate of electron transfer from the chromophore to the surface. Figure 2: Density of states for (Ti 32 O 62 ) 4+ red; energy levels of ethanoic acid, blue. Figure 3: Adsorbed ethanoic acid molecule, green, Ti; red, O; blue, C; white, H. Figure 4: We plan to apply this method to the study of N3 dye, alizarin, porphyrins and other potential chromophores. (1) (2)