This journal is © the Owner Societies 2018 Phys. Chem. Chem. Phys., 2018, 20, 18907--18911 | 18907 Cite this: Phys. Chem. Chem. Phys., 2018, 20, 18907 Reliable and computationally affordable prediction of the energy gap of (TiO 2 ) n (10 r n r 563) nanoparticles from density functional theory† A ´ngel Morales-Garcı ´ a, * Rosendo Valero and Francesc Illas * The optical gap (O gap ) of a set of (TiO 2 ) n nanoclusters and nanoparticles with n = 10–563 and different morphologies such as spherical, octahedral, lamellar, or tubular finite structures is investigated based on a relativistic all-electron description along with a numerical atomic centered orbital basis set. Two different functionals are used, PBE and PBEx, the former corresponds to a standard implementation of the generalized gradient approximation (GGA) and the latter to a hybrid functional with 12.5% of Fock exchange which reproduces the band gap of bulk TiO 2 anatase and rutile. It is shown that the inclusion of exchange Fock in the PBE functional promotes a systematic energy gap opening of 1.25 eV relative to the PBE values. Remarkably, a linear correlation is found between PBEx and PBE O gap calculated values with concomitant similar correlations for the HOMO and LUMO orbital energies. However, it appears that PBEx induces a larger downshift on the HOMO orbital than the upshift observed on the LUMO one. The fact that the PBEx hybrid functional was shown to reproduce the experimental energy gaps of stoichio- metric and reduced TiO 2 bulk phases leads to a suitable and practical way to successfully estimate O gap of TiO 2 nanoparticles containing up to thousands of atoms with PBEx precision from computationally affordable PBE calculations. The water splitting breakthrough reported by Fujishima and Honda is one of the main discoveries that promoted the development of photocatalysis across a broad range of research areas, including especially environmental and energy-related fields. 1–3 The photo- catalytic properties of certain materials have been used with the ultimate goal of converting solar energy into chemical energy used either to oxidize or to reduce compounds, to obtain useful products including hydrogen and hydrocarbons, and to remove pollutants and bacteria from wall surfaces, either in air or in water environments. 4–7 Among different photocatalysts investigated, titanium dioxide (TiO 2 ) is a fascinating material exhibiting unique photocatalytic properties which are exploited in many technological applications due to its strong oxidizing abilities for the decomposition of organic pollutants, chemical stability, long durability, nontoxicity and low cost. 2,8 The possibility to use sunlight for photocatalytic processes carries the promise to an almost inexhaustible and sustainable energy source and TiO 2 , in its many forms, is by far the most studied compound. However, the exceedingly large energy gap of TiO 2 implies that an earnest effort has to be put into understanding the electronic structure of TiO 2 nanoparticles to provide arguments for a rational design of photocatalysts with reduced band gaps. Many TiO 2 nanostructures with different morphologies such as spheres, nanorods, fibers, tubes, sheets, and interconnected architectures have been recently fabricated. 9–13 Not surprisingly, the morphology and the size of the system are two aspects to control when aiming at optimizing its photocatalytic activity. 14 Unfortunately, because of many technical problems, it is very difficult to rely on experiments to correlate the effect of size and shape to the electronic properties of TiO 2 nanosystems. On the other hand, computational modeling provides a reliable and unbiased approach to analyze the influence of these factors on the structural and electronic properties. However, the modeliza- tion of different morphologies (for a fixed composition) or compositions (for a fixed morphology) requires appropriate systems containing perhaps thousands of atoms. Recent works based on bottom-up 15–17 and top-down 18 models of TiO 2 nano- particles have been reported showing that it is nowadays possi- ble to approach the properties of large systems by means of first principles density functional theory (DFT) based calculations. These works have shown how electronic properties of TiO 2 finite systems, such as the optical gap (O gap ), corresponding to the lowest singlet to singlet excitation, and electronic gap (E gap ), defined as the difference between the vertical ionization potential and the electron affinity, evolve with the morphology of the material. 15,18 The largest variations are, not surprisingly, observed in the quite small (TiO 2 ) n nanoclusters with n o 30. 15 These fluctuations result from quantum confinement and atomic environments which are far enough away from the bulk atomic connections. Departament de Cie `ncia de Materials i Quı ´mica Fı ´sica & Institut de Quı ´mica Teo`rica i Computacional (IQTCUB), Universitat de Barcelona. c/Martı ´ i Franque `s 1, 08028 Barcelona, Spain. E-mail: francesc.illas@ub.edu, angel.morales@ub.edu † Electronic supplementary information (ESI) available. See DOI: 10.1039/c8cp03582b Received 6th June 2018, Accepted 25th June 2018 DOI: 10.1039/c8cp03582b rsc.li/pccp PCCP COMMUNICATION