Quantum Chemical Investigation of Cluster Models for TiO 2 Nanoparticles with Water-Derived Ligand Passivation: Studies of Excess Electron States and Implications for Charge Transport in the Gratzel Cell Vladimir Blagojevic, † Yiing-Rei Chen, ‡ Michael Steigerwald, Louis Brus,* and Richard A. Friesner Department of Chemistry, Columbia UniVersity, New York, New York 10025 ReceiVed: June 6, 2009; ReVised Manuscript ReceiVed: September 9, 2009 We present hybrid DFT calculations for large TiO 2 cluster models in the gas phase and in solution. Two clusters are investigated, one derived from the anatase bulk structure and the second from rutile. The surfaces are passivated with hydroxyl and water ligands, and continuum solvation is used to model bulk solvent in a subset of calculations. The geometrically optimized bonding patterns, structures, and electronic properties are similar in the two clusters. The distinction between anatase and rutile is minor at this small size. The HOMO and LUMO of the clusters are delocalized, and qualitatively resemble those observed in bulk for both the anatase and rutile derived species. When an additional electron is added, the wave function is again delocalized and there is little change in geometry, and hence minimal polaronic self-trapping. Removal of a surface ligand, creating a defect in that location, does lead to localization of the wave function, but it is unclear whether this actually occurs in real nanocrystalline TiO 2 systems. Our results suggest that modeling of electron transport in TiO 2 nanocrystal photovoltaic cells may require the presence of electrolyte ions to stabilize localized trapping states. I. Introduction Titanium dioxide is an important material widely used in science and technology. 1,2 Its nanoparticles are proving to be very suitable for photochemical applications 3-5 and interfacing with organic molecules 6 and DNA. 7 Although, macroscopically, the rutile phase is more thermo- dynamically stable than the anatase phase at ambient pressure and room temperature, 8 anatase has been found to be easy to synthesize at the nanoscale. Banfield 2,9,10 found that the synthesis of nanocrystalline TiO 2 consistently resulted in anatase nano- particles, which transformed to rutile upon reaching a particular size (<14 nm). Transformation from anatase to rutile has been observed under varying experimental conditions, 11,12 like tem- perature and particle size. Barnard and Zapol conducted an extensive theoretical study of TiO 2 nanostructures. They used a thermodynamic model 13 based on the free energy of nano- crystals as a function of size and shape to determine the minimum energy morphology of anatase and rutile phases at the nanoscale and to examine the phase stability of faceted TiO 2 nanocrystals 14 as a function of surface hydrogenation. 15 They predicted that the minimum energy morphology of anatase is a bifrustum Wulff construction 16 and that of rutile is a bitetragonal bipyramidal Wulff construction, which became more oblate as the hydrogenation level increased. They used these results to study the relative phase stability of nanoscale anatase and rutile in water 17 and their surfaces with adsorbates representative of acidic and basic conditions. 18 They looked at the (001), (100), and (101) surfaces of anatase and the (100), (011), and (110) surfaces of rutile, as these are the most common crystalline planes in bulk crystals and nanoparticles alike. In recent years, TiO 2 has attracted attention as a material for dye-sensitized solar cells. 19-21 It was found that the use of TiO 2 nanocrystals improves solar cell efficiency. There has been extensive investigation in the process of electron injection into the nanoparticles by the light-absorbing dye. 22 Potential existence of defects on the nanocrystal surface, like oxygen vacancies, represents an additional dimension to this problem. Experimental studies have shown that oxygen vacancies in rutile can act as active sites for water dissociation 23 and bonding sites for molecules and metal clusters. 24 Our principal focus in the present paper is on understanding key electronic states (e.g., anionic states containing an excess electron) of TiO 2 nanoparticles, via density functional theory (DFT) calculations, in the condensed phase environment characteristic of photovoltaic devices such as the Gratzel cell. The preparation of the nanoparticles invariably involves some exposure to water, and it is believed that this results in passivation of the surface by water-derived ligands, e.g., water itself or hydroxyl. The remainder of the solution phase environ- ment is modeled via dielectric continuum theory, using standard quantum chemical self-consistent reaction field techniques. The deployment of this environment and the focus on the electronic structure of the anion and possible trapping states for the excess electron differentiate the present paper from previous DFT calculations on TiO 2 nanoparticles. 31-33 We begin by constructing passivated cluster models for both anatase and rutile derived nanocrystals. We find that the anatase and rutile model clusters show quite similar surface structure, which in fact is different than either the anatase or rutile bulk structures. However, even in our small model clusters of 21-23 titanium atoms, the delocalized lowest unoccupied molecular orbitals (LUMOs) are very similar to those of the bulk anatase and rutile band structures, respectively. The oxygen centered highest occupied molecular orbital (HOMO) is delocalized in † Present address: Chemistry Department, University of Waterloo, Waterloo, Ontario, Canada. ‡ Present address: Physics Department, National Taiwan Normal Uni- versity, Taipei 11677, Taiwan. J. Phys. Chem. C 2009, 113, 19806–19811 19806 10.1021/jp905332z CCC: $40.75  2009 American Chemical Society Published on Web 10/26/2009