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The existence of an off-centre distortion for impurities in cubic oxides is explored by Density Functional Theory calculations. We find that models based on ionic radii are inadequate to explain the off-centre instability. By contrast, increase of the nominal impurity charge or decrease of the host lattice constant act against the off-centre distortion. This explains why the motion of just the Ni 2+ impurity can happen in SrO, in agreement with experimental data, while not for smaller Cr 3+ or Ti 4+ ions in the same lattice. Moreover, the different electronic structure and coupling to the host lattice are shown to be behind a small but positive force constant for Na + and Mn 2+ in SrO. Our results indicate that an off-centre motion in MgO:Ni 2+ is rather unlikely and that the local contributions to the instability in pure BaTiO 3 are not enough to induce ferroelectricity if just the movement of Ti 4+ ion is considered. [ABSTRACT FROM AUTHOR]

The vibronic coupling Hamiltonian is a standard model used to describe the potential energy surfaces of systems in which non-adiabatic coupling is a key feature. This includes Jahn–Teller and Renner–Teller systems. The model approximates diabatic potential energy functions as polynomials expanded about a point of high symmetry. One must ensure the model Hamiltonian belongs to the totally symmetric irreducible representation of this point group. Here, a simple approach is presented to generate functions that form a basis for totally symmetric irreducible representations of non-Abelian groups and apply it to D ∞ h (2D) and O (3D). For the O group, the use of a well known basis-generating operator is also required. The functions generated for D ∞ h are then used to construct a ten state, four coordinate model of acetylene. The calculated absorption spectrum is compared to the experimental spectrum to serve as a validation of the approach. [ABSTRACT FROM AUTHOR]

Abstract: The sequence of phases of CeAlO3, which experimentally have been found by lowering the temperature: , can be characterized by cooperative pseudo Jahn–Teller effects due to interaction of the ground state (4f)1 with the excited state (5d)1 from the Ce3+-ion. The three phases, a tetragonal one, an orthorhombic one and a rhombohedral phase which are found from low temperature, successively to higher temperature, can be described by distortions from respectively a single T 2u -component, a linear combination of two T 2u -components and a linear combination of three T 2u -components. Since in CeAlO3 the distortions are at the Ce3+-center, it is practical to name the distortion mode: T 2u at the R-point (with respect to the center with a 12-environment of anions). The four short bonds around each Ce3+-ion in the tetragonal phase point to covalent bonding. This bonding is in the tetragonal structure stronger than in the rhombohedral phase. This can explain the observation that the rhombohedral phase, with three short bonds, occurs at higher temperature, and is stabilized by entropy. [Copyright &y& Elsevier]