2.2 Chemical bonding analysis

The density of states and its projection onto the atomic orbitals have been calculated through the periodic LCAO approach, using the CRYSTAL-06 code ¹⁵³ and the same DFT functional ⁴³ as used in all calculations described here. Oxygen atoms were described by an 8-411+d all electron basis set ¹⁵⁴ and Xe atoms by a cc-pVTZ basis set ¹⁵⁵, specifically devised for the fully-relativistic ECP28MDF pseudopotential, with 26 electrons per Xe kept active. In order to avoid problems of numerical catastrophes ¹⁵³ , the original cc-pVTZ(12s11p9d1f)/[5s4p3d1f] basis set ¹⁵⁵ was slightly modified by removing the outermost s, p and d Gaussians and the f polarization function to yield a final (11s10p8d)/[5s4p3d] contracted basis set. The Kohn-Sham matrix was diagonalized on an isotropic 8 8 8 k-mesh and the same mesh was used in the Fermi energy calculation and density matrix reconstruction. Bader’s charges and atomic quadrupole moment tensors were evaluated from the periodic LCAO electron density and using the TOPOND package ¹⁵⁶ interfaced to the CRYSTAL code. TOPOND determines the boundaries of the atomic basins and the integrated properties within these basins using fully analytical and on-the-fly evaluations of the electron densities and its derivatives (up to the 4th order), i.e. no use is made of electron densities on a grid or of numerical approximations of electron density gradients ¹⁵⁷. Basin boundaries are determined through the PROMEGA algorithm ¹⁵⁸, while the basin integration is performed in spherical coordinates, using Gaussian quadrature formulas. The resulting atomic charges were very close to those obtained from the PAW wavefunction and the numerical algorithm described in ¹³⁷. Band gaps were recalculated within GW approximation as implemented in the VASP code ¹⁵⁹.