Ab-Initio Investigation of Finite Size Effects in Rutile Titania Nanoparticles with Semilocal and Nonlocal Density Functionals

In this work, we employ hybrid and generalized gradient approximation (GGA) level density functional theory (DFT) calculations to investigate the convergence of surface properties and the electronic gap of rutile titania (TiO2) nanoparticles with particle size. The surface energies and electronic gaps are calculated for cuboidal particles with minimum dimension ranging from 3.7 Å (24 atoms) to 10.3 Å (384 atoms) using a highly parallel real-space DFT code to enable hybrid-level DFT calculations of larger nanoparticles than are typically practical. We deconvolute the geometric and electronic finite size effects in surface energy and evaluate the influence of defects on the electronic gap and density of states (DOS). The electronic finite size effects in surface energy vanish when the minimum length scale of the nanoparticles becomes greater than 10 Å. We show that this length scale is consistent with a computationally efficient numerical analysis of the characteristic length scale of electronic interactions. The surface energy of nanoparticles having a minimum dimension beyond this characteristic length can be approximated using slab calculations that account for the geometric defects. In contrast, the finite size effects on the electronic gap and DOS are highly dependent on the shape and size of these particles. The DOS for cuboidal particles and more realistic particles constructed using the Wulff algorithm reveal that defect states within the electronic gap play a key role in determining the eigenvalue distribution of nanoparticles and the electronic gap does not converge to the bulk limit for the particle sizes investigated.