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

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 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 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 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 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.

References in corpus (10)

• Optimized norm-conserving Vanderbilt pseudopotentials
• Optimization Algorithm for the Generation of ONCV Pseudopotentials
• Nearsightedness of Electronic Matter
• Extracting convergent surface energies from slab calculations
• SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Extended systems
• SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Isolated clusters
• SQDFT: Spectral Quadrature method for large-scale parallel $\mathcal{O}(N)$ Kohn-Sham calculations at high temperature
• Modelling Realistic TiO2 Nanospheres: a Benchmark Study of SCC-DFTB against Hybrid DFT
• Ab-initio Electronic and Structural Properties of Rutile Titanium Dioxide
• On nearsightedness in metallic systems for $\mathcal{O}(N)$ Density Functional Theory calculations: A case study on Aluminum

Cited by in corpus (1)

• GPU acceleration of local and semilocal density functional calculations in the SPARC electronic structure code