Effects of exchange, correlation, and numerical approximations on the computed properties of the rutileTiO2(100) surface

Abstract

We present fully converged, all-electron, ab initio calculations of the structural relaxation at the TiO 2 (100)-(1ϫ1) surface. The effects of electron exchange, correlation, and various numerical approximations are isolated and quantified. We find that the predicted relaxations are insensitive to the treatment of exchange and correlation, but do depend on numerical approximations. The results of previous ab initio calculations are discussed in the light of these findings. ͓S0163-1829͑99͒05003-1͔

First-principles study of potassium adsorption onTiO2surfaces

“…The largest displacements at the clean surface are along the ͓010͔ direction with the surface O, Ti, and subsurface O ions moving by Ϫ0.3 Å, 0.1 Å, and Ϫ0.15 Å, respectively. 37 Displacements along ͓100͔ are no more than 0.05 Å. K adsorption induces larger displacements of the surface O ions along ͓010͔ and ͓100͔. The adsorption also reduces the symmetry of the surface allowing the O ions to move along the ͓001͔ direction by 0.08 Å towards the Ti (4) ion, and thus away from the Ti (3) ion, as illustrated in Fig.…”

“…This is sufficient to converge the surface structure to within 0.01 Å. 37 Other approximations are introduced as a consequence of the use of local basis functions. In CRYSTAL the convergence of the direct space summations of the Coulomb and exchange contributions to the Fock matrix are controlled by five overlap criteria.…”

“…12,16 It has been shown in previous studies that a slab thickness of nine atomic layers ͑three TiO 2 formula units͒ is adequate to model the structure and energetics of this surface accurately. 37 The surface unit cell of the c(2ϫ2) structure is shown in Fig. 2.…”

“…42 The resultant DVSC basis set has been thoroughly tested in other bulk and surface investigations of TiO 2 and is found to yield structural parameters converged to within 0.02 Å of those extrapolated to the infinite basis set limit. 37 For the purpose of comparison, the calculation of small energy differences and for the calculation of the electronic structure we have used a more sophisticated triple valence all-electron ͑TVAE͒ basis set for Ti, O, 39,38 and K. 40,39 The structural model for the ͑100͒ surface of TiO 2 is a two dimensional slab periodic in the ͓010͔ and ͓001͔ directions but finite in the ͓100͔ as illustrated in Figs. 1 and 2.…”

Water adsorption on rutile TiO2(110) for applications in solar hydrogen production: A systematic hybrid-exchange density functional study

“…These basis sets were developed in previous studies of the bulk and surface phases of titania in which a systematic hierarchy of all-electron basis sets was used to quantify the effects of using a finite BS. 70,71 The hydrogen atom is described by two s and one p shells, corresponding to a 6-31G** contraction 72 ; the quality of the oxygen and the hydrogen BS in describing the water molecule is assessed in Appendix A.…”