M. Bermejo

Evaluation of the rotation matrices in the basis of real spherical harmonics

Abstract Rotation matrices (or Wigner D functions) are the matrix representations of the rotation operators in the basis of spherical harmonics. They are the key entities in the generation of symmetry-adapted functions by means of projection operators. Although their expression in terms of ordinary (complex) spherical harmonics and Euler rotation angles is well known, an alternative representation using real spherical harmonics is desirable. The aim of this contribution is to obtain a general algorithm to compute the representation matrix of any point-group symmetry operation in the basis of the real spherical harmonics, paying attention to the use of recurrence relationships that allow the treatment of functions with high angular momenta.

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

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...

Quantum mechanical cluster calculations of ionic materials: the ab initio perturbed ion (version 7) program

Abstract We describe the computational implementation of the ab initio perturbed ion method, a self-consistent calculation of the electronic structure and energy of a system under the assumption that the total wave function can be written as an antisymmetric product of local ionic (or atomic) wave functions. Large bases of Slater-type orbitals are supported on every center. Very large, realistic, models of ionic materials can be efficiently solved. The program is provided with an easy-to-use and easy-to-learn interface, with special orders for three-dimensional solids, either pure and defective, and for isolated clusters.

Systematic interpretation of experimentally measured and theoretically calculated spectra of transition-metal compounds by an optimized, linearized crystal field fitting procedure

Abstract Linearized, least-squares fitting of experimental and theoretical spectra of transition-metal clusters by the crystal field (CF) model yields not only the usual systematically optimized CF orbital splitting and Racah parameters but also a convenient and direct measure of the sensitivity of the transition energies to those various quantities. Specifically considered are the transitions observed for Cr3+ and Ni2+ ions in octahedral fluoride clusters. The quality of the fit is less influenced by the Racah C B ratio than by the scaling of the metal d orbitals (i.e., the nephelauxetic effect). Consistent fittings of observed and SCF-MO-calculated spectra of NiF64− and CrF63− show very close agreement in values of, and sensitivities to, the CF parameter 10 Dq, the nephelauxetic factor, and the effective orbital population, the last being a direct measure of breakdown of the orbital approximation to the wavefunction. In comparing Racah parameters for free and complexed ions it is essential to choose values such that the same degree of electron correlation is encompassed in both cases.

Quantum Mechanical Cluster Calculations of Solids: The ab initio Perturbed Ion Method

There has been, in the last few years, a significant interest in the application of molecular quantum mechanical methods to describe the bulk and surface electronic structure of solids [1–5]. We are justified to take this route due to the existence of clusters, i.e. electronic groups in the solid that correlate only slightly with its environs. Even so, the interaction energy between the cluster and the rest of the crystal is decisive for many cluster properties and cannot be ignored in the calculation. The accurate representation of the embedding of the cluster is precisely the largest difference between methods derived to treat isolated molecules and those needed for solid state systems.

Electronic structure of closed-shell hexafluorides

Abstract The electronic structures of four closed-shell hexafluorides have been obtained by Hartree-Fock-Roothaan calculations on the MF(6) clusters (M = Li(+), Na(+), Mg(2+), and Zn(2+)). Bound ground state nuclear potentials are obtained when the metallic basis sets are augmented with diffuse and polarization functions. Fluoride bandwidths and metal-fluoride bandgaps obtained from these calculations are in good agreement with observed data. The charge transfer associated with the formation of the metal-fluoride bond is discussed in the light of electron deformation density maps.

Ab Initio Perturbed Ion Calculations on Oxo- and Fluoroperovskites

The electronic structure of KMgF3, KZnF3, RbCaF3, and SrTiO3 has been calculated by means of the ab initio Perturbed Ion method at several values of the cell size. The study includes (a) analysis of core and valence energies and their variation with the crystal geometry; (b) obtaining of local ionic densities consistent with the lattice interactions; (c) calculation of crystal properties like lattice energy, equilibrium cell parameter, and bulk modulus, and (d) determination of separate ionic contributions to the chemical bonding. Particular attention is paid to the small but highly significant non-classical energy terms appearing in the formalism, as well as to the effects of the electron correlation in the computed properties. The global results show that the aiPI method gives as good a performance as that found for simpler crystals like alkali halides and MgO.

Theoretical calculation of bulk properties of ionic crystals from the cluster approach: Application to NaF

Abstract The Theory of Electronic Separability is applied to the calculation of the ground state total energy and related bulk properties of simple ionic crystals. The work is based on a general equation of this theory that gives the total energy of the crystal in terms of additive energies of conjugate clusters. The cluster additive energy is deducible from standard cluster-in-the-lattice calculations once the effective energy of the cluster is partitioned into net (cluster- in vacuo ) energy and cluster-lattice interaction energy. In this way, the cluster approach becomes a rigorous theoretical tool to compute crystalline bulk properties. Taking the NaF as an example, this approach is discussed for two different cluster sizes: single-ion cluster and octahedral species like NaF 5− 6 and FNa 5+ 6 . Given the relevance of the interaction energy, several approaches to this quantity are analyzed in detail, from the unphysical stage of its total neglect (cluster- in vacuo calculations) to rigorous formulations involving lattice models which are consistent with the Theory of Electronic Separability. The properties of the NaF crystal analyzed in this work include equilibrium geometry, cohesive energy, elastic constants, and external pressure effects on these quantities.

Simulation of transition metal ions in ionic crystals

Abstract This is a review of our last developments concerning the theoretical calculation of transition metal ions within ionic crystals. The attention is focused towards the embedding procedure, understood as the requirement of physical and mathematical consistency between the descriptions of the cluster and the rest of the lattice. The Theory of Electronic Sparability (TES) provides an efficient way to gain such consistency. Several models built on the TES basic equations are presented, and their relative merits and weaknesses are discussed.