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Structural and Electronic Properties of Photoexcited TiO2 Nanoparticles from First Principles Francesca Nunzi, Saurabh Agrawal, Annabella Selloni, and Filippo De Angelis J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/ct500815x • Publication Date (Web): 14 Jan 2015 Downloaded from http://pubs.acs.org on January 20, 2015
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Journal of Chemical Theory and Computation
Structural and Electronic Properties of Photoexcited TiO2Nanoparticles from First Principles Francesca Nunzi,a,b*Saurabh Agrawal,aAnnabella Selloni,cFilippo De Angelisa*
a
Computational Laboratory of Hybrid/Organic Photovoltaics (CLHYO), CNR-ISTM, via Elce di Sotto 8, I-06123 Perugia, Italy.
b
Dipartimento di Chimica,Biologia e Biotecnologie, Università degli Studi di Perugia, via Elce di Sotto 8, I-06123 Perugia, Italy. c
Department of Chemistry, Princeton University, Princeton, NJ-08544, USA.
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KEYWORDS: DFT – POLARON – CHARGE CARRIERS – ELECTRON TRANSPORT – PHOTOVOLTAICS – TRAPPING
Abstract The structure and energetics of excitons and individual electron and hole polarons in a model anatase TiO2 nanoparticle (NP) are investigated by means of Density Functional Theory (DFT) and Time Dependent (TD)-DFT calculations. The effect of the Hartree-Fock exchange (HF-exc) contribution in the description of TiO2 NPs with unpaired electrons is examined by comparing the results from semi-local and hybrid DFT functionals with different HF-exc percentages, including a long-range corrected hybrid functional. The performances of TD-DFT and ground state (SCF) DFT approaches in the description of the photoexcited polaron states in TiO2 NPs are also analyzed. Our results confirm that the HF-exc contribution is essential to properly describe the self-trapping of the charge carriers as well as suggest that long-range corrected functionals are needed to properly describe excited state relaxation in TiO2 NPs. TD-DFT geometry optimization of the lowest excited singlet and triplet states deliver photoluminescence values in close agreement with the experimental data.
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Journal of Chemical Theory and Computation
1. Introduction The properties of photoexcited carriers are critical to the efficiency of TiO2 in photocatalysis1 and photovoltaics2. Upon photoexcitation by UV light absorption, valence band (VB) electrons of TiO2 are promoted into unoccupied conduction band (CB) states, while correspondingly positively charged holes are created in the VB. The electron and hole charge carriers can diffuse to the surface and react with adsorbed molecules, or become trapped at defect sites, or again travel through the TiO2 crystal to a collecting electrode. Electron-hole recombination usually represents a major competing process, so that higher quantum efficiency for the photocatalytic and photovoltaic processes can be attained by promoting charge separation and inhibiting subsequent recombination. Fundamental characterization of charge transport phenomena in TiO2 is thus important for the development of models and the definition of strategies to control and reduce recombination rates. In this context, nanocrystalline anatase TiO2 is usually preferred over rutile because it shows higher photocatalytic activity3 and electron mobility,4 thus allowing longer diffusion pathways of photogenerated carriers and increased quantum efficiencies. Photogenerated charges in TiO2 have been observed by electron paramagnetic resonance (EPR),5 photoluminescence (PL)6 and O2 photodesorption.7 PL measurements show a broad band centered at ∼ 2.3 eV attributed to radiative recombination of self-trapped excitons.6e, 8 The picture of the photoexcited electrons and holes is based on the polaron model,9 in which the charge carriers become localized on just a few atoms, inducing a lattice distortion that stabilizes (traps) the localized state. The electrons are preferentially trapped at Ti sites to form Ti3+ions, while holes are trapped by oxygen atoms to form O- species, and both charge carriers can move from site to site through thermal hopping. The accurate theoretical modeling of polaron states in TiO2 has proven quite challenging. The self-interaction error of local and semi-local Density Functional Theory (DFT) functionals10 results in an artificial bias towards delocalization of partially occupied states which reduces the 3 ACS Paragon Plus Environment
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Coulomb repulsion.10 To mitigate the delocalization error and improve the description of the polaronic nature of excess electrons and holes in TiO2, DFT+U methods9, 11 or hybrid functionals containing a fraction of exact Hartree-Fock exchange (HF-exc)10b, 12 are generally used. Among the latter, the Becke 3-parameter Lee-Yang-Parr (B3LYP) functional, originally fitted to reproduce molecular properties, has been shown to overcome many of the DFT deficiencies in the description of wide band gap semiconductors.10a, 13 For bulk anatase TiO2, in particular, B3LYP calculations have predicted a self-trapping energy (∆Etrap) of 0.58 eV for the triplet exciton, and ∆Etrap values of 0.23 and 0.74 eV for separated electron and hole polarons, respectively.12 Due to the prominent role of nanocrystalline TiO2 in photocatalysis and photovoltaics, it is interesting to extend the investigation of polaron states toTiO2 NPs. In this work, we characterize the structure and energetics of excitons and single electron and hole polarons in anatase TiO2 NPs by means of hybrid DFT and Time Dependent (TD)-DFT calculations. TD-DFT offers a rigorous approach to the description of excited states and related optical transitions of fairly large systems, as the TiO2 NPs studied here, and essentially represents the best compromise between accuracy and computational overhead. We focus on the effect of the HF-exc in the description of exciton and electron and hole polaron states by comparing the results of pure GGA and hybrid DFT functionals with different percentages of HF-exc. We also consider the range-separated exchange-correlation CAM-B3LYP functional,14 which has proven successful in the TD-DFT scheme, especially for the description of excited states with a strong charge transfer character. Recent TD-DFT studies of the excited states of (TiO2)n (n
