The electronic properties and stereochemistry of mono-nuclear complexes of the copper(II) ion

Publisher Summary The limitations of applying an ab initio linear combination of atomic orbitals (LCAO) methods to complex molecules and solids are the size of the basis sets and the number of multicenter integrals or equivalent Hartree-Fock matrix elements In the self-consistent field (SCF)-Xα scattered-wave model that is also a first-principle technique, there is no basis-set problem because Schrodinger's equation for an Xα potential is numerically integrated There are no multicenter integrals and the model is practicable in both spin-restricted and spin-unrestricted forms for polyatomic systems of considerable stereochemical complexity The SCF-Xα scattered-wave technique uses only a small fraction of the computer time required by an ab initio Hartree–Fock LCAO method The applications of the scattered-wave method to polyatomic molecules and crystals are concerned with the generation of one-electron energy and wave functions While an SCF-Xα one-electron analysis leads to an accurate quantitative description of many chemical and physical properties, it is also very important to determine the total many-electron energy As the present method leads to a rapidly convergent numerical representation of the orbital wave functions, the accuracy of the theoretical model can easily be improved via perturbation theory, when necessary Finally, the original theoretical formalism can be extended to more general forms of superposed-atom Xα potentials by means of the generalized scattered-wave theory

Scattered-Wave Theory of the Chemical Bond

A theoretical overview of the cooperative Jahn-Teller effect in the insulating phase is given. We obtain an effective Hamiltonian of an interaction between the orbital states of the Jahn-Teller ions through a canonical transformation, which associates each electronic state with a local lattice distortion, and by use of the mean field approximation. The effective Hamiltonian yields a simple unified picture of cooperative distortions of various types. The competing effect of the spin-orbit coupling is discussed also. Electron itinerancy is briefly discussed at the end.

Crystal Distortion in Magnetic Compounds

The polarized absorption spectra of Ni2+ and Co2+ in crystals of ZnO, ZnS, and CdS; Ni2+ in crystals of Cs2ZnCl4 and Cs2ZnBr4; and Cu2+ in ZnO have been measured at 4°K, 77°K, and room temperature. The spectra have been interpreted by the use of crystal field theory for the states of the (3d)n configuration acted on by a potential of predominately Td symmetry. Certain details of the spectra are accounted for by smaller contributions from fields of lower symmetry, notably a C3v potential contribution for the transition metal ions in ZnO. Crystal field, electrostatic repulsion, and spin‐orbit parameters have been obtained for all these cases. An empirical correlation between the electrostatic repulsion parameter, B, for the ions in the crystals and the ligand polarizibility has been obtained. Although the configuration mixing between the states of the configurations (3d)n and (3d)n—1 (4p) has been found to give a negligible contribution to the calculated relative energies of the levels, it does partially ex...

Optical Spectra of Ni2+, Co2+, and Cu2+ in Tetrahedral Sites in Crystals

Density-functional calculations using the linearized-augmented-plane-wave method were carried out for the scheelite materials ${\mathrm{CaMoO}}_{4},$ ${\mathrm{CaWO}}_{4},$ ${\mathrm{PbMoO}}_{4},$ and ${\mathrm{PbWO}}_{4}$ in order to determine their ground-state electronic properties. The results indicate that ${\mathrm{CaMoO}}_{4}$ and ${\mathrm{CaWO}}_{4}$ have direct band gaps at the center of the Brillouin zone, while ${\mathrm{PbMoO}}_{4}$ and ${\mathrm{PbWO}}_{4}$ have band extrema at wave vectors away from the zone center with possibly indirect band gaps. The magnitudes of the band gaps increase in the order ${\mathrm{PbMoO}}_{4}{l\mathrm{PbWO}}_{4}{l\mathrm{CaMoO}}_{4}{l\mathrm{CaWO}}_{4}.$ The valence and conduction bands near the band gap are dominated by molecular orbitals associated with the ${\mathrm{MoO}}_{4}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\alpha}}}$ and ${\mathrm{WO}}_{4}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\alpha}}}$ ions, where $\ensuremath{\alpha}\ensuremath{\approx}2.$ The valence-band widths are 5 and 5.5 eV for the Ca and Pb materials, respectively. In the Pb materials, the Pb $6s$ states form narrow bands 1 eV below the bottom of the valence bands, and also hybridize with states throughout the valence bands, while the Pb $6p$ states hybridize with states throughout the conduction bands. In the Ca materials, the Ca $3d$ states contribute to a high density of states 3--4 eV above the bottom of the conduction bands.

Electronic band structures of the scheelite materials CaMoO 4 , CaWO 4 , PbMoO 4 , and PbWO 4

Complete theory of Ni(II) and V(III) in cubic crystalline fields

Intensities in inorganic complexes: Part II. Tetrahedral complexes

Inherent configurational instability of octahedral inorganic complexes in Eg electronic states

The method, previously developed by the authors, for calculating the intensity of d n electronic transitions in inorganic complexes is extended to include electronic systems which exhibit configuration interaction. The oscillator strengths of both the spin-allowed and spin-forbidden spectral transitions of divalent nickel and trivalent vanadium complex salts are computed and compared with experiment. Fair agreement is found. Some critical comments concerning the relative merit of such calculations are presented. The envelope of the Ni(II) red band is elucidated in terms of the spin-orbit fine structure of the 3T1g electronic state.

Andrew D. Liehr

Papers

Complete theory of Ni(II) and V(III) in cubic crystalline fields

Intensities in inorganic complexes: Part II. Tetrahedral complexes

Inherent configurational instability of octahedral inorganic complexes in Eg electronic states

Intensities in inorganic complexes

Semiempirical Theory of Vibronic Interactions in Some Simple Conjugated Hydrocarbons