Exact expressions for finite-volume Kirkwood–Buff (KB) integrals are derived for hyperspheres in one, two, and three dimensions. These integrals scale linearly with inverse system size. From this, accurate estimates of KB integrals for infinite systems are obtained, and it is shown that they converge much better than the traditional expressions. We show that this approach is very suitable for the computation of KB integrals from molecular dynamics simulations, as we obtain KB integrals for open systems by simulating closed systems.

The charge distribution of the defect states at the reduced ${\mathrm{TiO}}_2(110)$ surface is studied via a new method, the resonant photoelectron diffraction. The diffraction pattern from the defect state, excited at the $\mathrm{Ti}\mathrm{\text{−}}2p\mathrm{\text{−}}3d$ resonance, is analyzed in the forward scattering approach and on the basis of multiple scattering calculations. The defect charge is found to be shared by several surface and subsurface Ti sites with the dominant contribution on a specific subsurface site in agreement with density functional theory calculations.

We report a theoretical study on x-ray absorption spectroscopy at the Ti-L2,3-edge of rutile and anatase TiO2 as well as SrTiO3. Using the first-principles multichannel multiple-scattering method, we obtain good agreement with experiment in all cases. We show that both multiplet-type electron correlation effects and the long-range band structure strongly influence the spectra. The differences in line shape between the three compounds are essentially a long-range effect which reflects the different crystal structures on a length scale of 1 nm.