Effects of a quantum-mechanical lattice on the electronic structure and d–d spectrum of the (MnF6)4− cluster in Mn2+ :KZnF3

Abstract

The electronic structure of the Mn2+ :KZnF3 impurity system has been computed by means of a Hartree–Fock–Roothaan cluster model. First, the Mn2+ center has been simulated by the (MnF6 )4− unit in vacuo. Then, the effects of the KZnF3 lattice have been included in the cluster calculation using three different lattice models. The well-known point–charge approximation has been compared with two rigorous quantum–lattice models derived from the ideas of the theory of electronic separability. In these two models the lattice ions are represented by an effective lattice potential and a lattice projection operator that enforces the cluster–lattice orthogonality. In the Coulomb or Hartree model the cluster–lattice exchange interactions are neglected. The ab initio model potential (MP) lattice model makes use of model potentials for representing the lattice ions and includes an accurate nonlocal exchange operator. According to the present results, the point–charge lattice model destroys the acceptable picture of the electronic ground state of the (MnF6 )4− unit obtained at the cluster-in vacuo stage, giving a continuously repulsive nuclear potential. The quantum–lattice models restore the bound ground state and give an equilibrium geometry qualitatively correct and quantitatively reasonable. The seven d–d electronic transitions observed in this system are computed within a quarter of eV after correcting the Hartree–Fock description with a configuration interaction limited to the octahedral configurations of the d5 problem and a semiempirical correlation-energy correction. Lattice effects on vertical transition energies turn out to be small. However, important indirect lattice effects are encountered in the theoretical spectrum as a consequence of the lattice-induced modification of the equilibrium geometry of the ground state.

Ga + , In+, and Tl+ impurities in alkali halide crystals: Distortion trends

“…This procedure has to be improved in order to obtain a realistic description of the lattice distortions around the impurity. [9][10][11][12]15,18,21,24,26,27,31,33 Model potentials have been developed to represent the effects of the environment on the active cluster, that include attractive and repulsive quantum-mechanical terms aside from the classical Madelung term. 34 (b) An active cluster size that is too small.…”

Investigations of the g ‐factors and local phase‐transition behavior for Ni3+ ion in the tetragonal phase of RbCaF3 crystal

“…From the optical spectra of K 3 NiF 6 crystal, Allen and Warren [17] found that B ≈ 703 cm −1 (so ƒ γ ≈ 0.588), |D q | ≈ 1620 cm −1 and suggested that the ground orbital state of (NiF 6 ) 3-clusters is the low spin 2 E. This point is supported by the TanabeSugano diagram [18,19], in which for 3d 7 ions in octahedra, if |D q /B| > 2.2, the ground orbital state is the low-spin 2 E state. Since for 3d n clusters, the parameter Dq µ R 0 −n (where 3.5 6.5 n ≈ - [20,21]), and the Racah parameter B or C increases slightly with the increasing average impurity-ligand distance R 0 [22,23]. Thus, from the distances R 0 ≈ 1.90 Å and 2.02 Å for (NiF 6 ) 3− clusters in K 3 NiF 3 and RbCaF 3 crystals (note: in the pure crystals, the distance R 0 is close to the sum of ionic radii [16] C ≈ 2885 cm…”

Pressure-induced changes inCr3+-doped elpasolites andLiCaAlF6: Interpretation of macroscopic data

“…24 Along this line, it should be noticed that according to Kohn, the localization of electrons is the fingerprint of every insulating material. 25,26 Bearing in mind these considerations, it turns out that 10Dq for an octahedral MX 6 c-6a complex microscopically depends on the M-X distance, R. The law describing the R dependence of 10Dq derived from theoretical calculations is found to be [24][25][26][27][28] …”