On the Use of DFT+U to Describe the Electronic Structure of TiO2 Nanoparticles: (TiO2)35 as a Case Study

One of the main drawbacks in the density functional theory (DFT) formalism is the underestimation of the energy gaps in semiconducting materials. The combination of DFT with an explicit treatment of electronic correlation with a Hubbard-like model, known as DFT+U method, has been extensively applied to open up the energy gap in materials. Here, we introduce a systematic study where the selection of U parameter is analyzed considering two different basis sets: plane-waves (PWs) and numerical atomic orbitals (NAOs), together with different implementations for including U, to investigate the structural and electronic properties of a well-defined bipyramidal (TiO₂)₃₅ nanoparticle (NP). This study reveals, as expected, that a certain U value can reproduce the experimental value for the energy gap. However, there is a high dependence on the choice of basis set and, and on the +U parameter employed. The present study shows that the linear combination of the NAO basis functions, as implemented in FHI-aims, requires a lower U value than the simplified rotationally invariant approaches as implemented in VASP. Therefore, the transferability of U values between codes is unfeasible and not recommended, demanding initial benchmark studies for the property of interest as a reference to determine the appropriate value of U.