Semiempirical calculations of TiO₂ (rutile) clusters

Abstract

The densities of states for small (TiO&clusters, x = 1 , 3 , 6 , 9 , and 14, have been calculated by means of the INDO method. The shape of the valence bands' density of states (DOS) are discussed in terms of the distribution of coordination numbers. A one-slab cluster with uniform distribution of the coordination numbers was used to compare our calculations with experimental spectra. The photoelectric DOS and DOS for a cluster with an oxygen vacancy are in very good agreement with experimental findings for the TiOz (001) surface. 0 1 s core level shifts between a surfacelike and a bulklike oxygen atom have been estimated. It is concluded that the observed surface-bulk shift for the Ti02 (001) surface contains a substantial relaxation contribution.

Energy levels of small titanium oxide clusters obtained from SCF calculations

“…In such a case, the above localized molecular orbital mechanism (as an alternative to the current quantum confinement explanation) could not be ignored in discussing the observed band-gap increase for the small cluster sizes. In our opinion, the transfer of this argument to real systems is justified, since the effect on the energy levels results to a large extent from changes in the Ti-0 bond length, which, in turn, depends on the atomic coordination numbers [9]. Thus, since the relaxation of the crystal at or near the surface is likely to lead to changes in the atomic coordination numbers, this will lead to the above effect on the oxygen-centered orbitals.…”

“…Full convergence was never reached with this method, but the "best" geometry was used as an input for another optimization, now with Newton-Raphson steps in the Berny optimization. To obtain convergence, it was necessary to calculate the analytic Hartree-Fock force constants at every point, which probably is related to the fact that these types of clusters have potential minima with several very soft vibrational modes [9].…”

N 1s x-ray absorption study of the bonding interaction of bi-isonicotinic acid adsorbed on rutile TiO2(110)

“…12 ZINDO has also been used to study clusters and model surfaces containing transition metal atoms, 13,14 including TiO 2 . 15 The XAS spectrum of isolated bi-isonicotinic acid was calculated for the cis and trans conformers, as well as for a 90°twisted bi-isonicotinic acid molecule. No significant differences were found, and only the results for the cis conformer are shown.…”

Connection between slab and cluster models for crystalline surfaces

“…As examples of MC model applications to surface studies using some of the above mentioned rules there may be considered calculations of MgO, TiO 2 (rutile, anatase structures), and Cr 2 O 3 (corundum structure) surfaces and adsorption of small molecules on them [23][24][25][28][29][30][31][32][33][34][35][36][37]. But it is also possible to find examples in the literature where these rules have not been applied [38,39] and in part unphysical results were obtained.…”

“…In order to study the effect of the distribution of saturation atoms on calculated properties of crystalline surfaces, we have selected the rutile (110) surface for new MSINDO calculations. A large number of theoretical studies have been performed using the MC model for the simulation of this surface [28,[30][31][32][34][35][36][37][38][39]. We used the semi-empirical SCF MO method MSINDO [40], the successor of the SINDO1 method that was successfully applied in studies of metal oxide surfaces [23][24][25]28,29].…”