Ab-initio investigation of finite size effects in rutile titania nanoparticles with semilocal and nonlocal density functionals

TL;DR

This study uses advanced DFT calculations to analyze how finite size effects influence the surface properties and electronic structure of rutile titania nanoparticles, revealing size-dependent convergence behaviors and defect impacts.

Contribution

It provides a detailed ab-initio analysis of size-dependent surface and electronic properties of TiO₂ nanoparticles, including the effects of shape, defects, and computational methods.

Findings

Electronic surface energy effects vanish beyond 10 Å size

Defect states significantly influence bandgap and DOS

Finite size effects on band structure depend on particle shape

Abstract

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 band structure of rutile titania (TiO$_2$) nanoparticles with particle size. The surface energies and band structures are calculated for cuboidal particles with minimum dimension ranging from 3.7 \r{A} (24 atoms) to 10.3 \r{A} (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 band structure 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 \r{A}. 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 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 band structure is 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 bandgap play a key role in determining the band structure of nanoparticles and the bandgap does not converge to the bulk limit for the particle sizes investigated.