Electronic structure of the octachlorodimolybdenum(II) anion using X-ray emission and X-ray photoelectron spectroscopies

X-ray emission (Mo Lβ_{2, 15} and Cl Kβ_{1, 3}) and X-ray photoelectron spectra from K₄ [Mo₂ Cl₈] have been combined to give a detailed picture of the electronic structure of the octachlorodimolybdenum(II) anion. Chlorine 3p orbitals form a relatively narrow band which has the same range of ionization energies as the more tightly bound orbitals with molybdenum 4d character. The molecular orbitals of the MoMo quadruple bond can be identified as well as those involved in MoCl bond formation and Cl non-bonding orbitals.     

The orbital characters and kz dispersions of bands in iron-pnictide NaFeAs

The electronic structure and orbital characters of iron-pnictide NaFeAs have been studied by polarization dependent angle-resolved photoemission spectroscopy. Some of the bands are mixed with the orbitals of opposite symmetries, which could be interpreted by the hybridization among the bands. According to the photon energy dependent experiment, the k_z dispersions of the bands that cross the Fermi energy are weak in both paramagnetic and spin density wave states. However, a band well below the Fermi level shows a k_z dispersion of 41 meV, which mainly contains the d_z² orbital.     

Theory of the angular distribution of molecular orbitalK x rays seen in heavy-ion-atom collisions

Dynamical calculations of angular distributions and intensities of two-collision 1s σ molecular orbital x rays in 12–90-MeV Ni + Ni collisions are reported. The Coriolis and spin-orbit coupling between 2pσ and 2pπ and the 3pσ and 3pπ molecular orbitals is included. Due to Coriolis coupling, the molecular wavefunctions and therefore the transition dipoles do not follow the rotation of the internuclear axis in collisions with small impact parameters, but remain approximately fixed in direction. Consequently one can predict the symmetry relations between the laboratoryx, y, andz components of the molecular orbital intensity and therefore the anisotropy of the radiation seen at energies near the united atomK α x-ray line. These relations are used to predict anisotropies of molecular orbital radiation in encounters with large united atom atomic numbers,Z ₁ +Z ₂>137. For Ni + Ni encounters, a lower population of the 2pπ and 3pπ orbitals than the 2pσ and 3pσ orbitals is needed to reproduce the observed anisotropies.     

Progressive changes in atomic structure and gap states on Si(0 0 1) by Bi adsorption

From ab initio studies employing the pseudopotential method and the density functional scheme, we report on progressive changes in geometry, electronic states, and atomic orbitals on Si(0 0 1) by adsorption of different amounts of Bi coverage. For the 1/4 ML coverage, uncovered Si dimers retain the characteristic asymmetric (tilted) geometry of the clean Si(0 0 1) surface and the Si dimers underneath the Bi dimer have become symmetric (untilted) and elongated. For this geometry, occupied as well as unoccupied surface states are found to lie in the silicon band gap, both sets originating mainly from the uncovered and tilted silicon dimers. For the 1/2 ML coverage, there are still both occupied and unoccupied surface states in the band gap. The highest occupied state originates from an elaborate mixture of the p_z orbital at the Si and Bi dimer atoms, and the lowest unoccupied state has a ppσ* antibonding character derived from the Bi dimer atoms. For 1 ML coverage, there are no surface states in the fundamental bulk band gap. The highest occupied and the lowest unoccupied states, lying close to band edges, show a linear combination of the p_z orbitals and ppσ* antibonding orbital characters, respectively, derived from the Bi dimer atoms.     

Anion height as a controlling parameter for the superconductivity in iron pnictides and cuprates

Both families of high T_c superconductors, iron pnictides and cuprates, exhibit material dependence of superconductivity. Here, we study its origin within the spin fluctuation pairing theory based on multiorbital models that take into account realistic band structures. For pnictides, we show that the presence and absence of Fermi surface pockets is sensitive to the pnictogen height measured from the iron plane due to the multiorbital nature of the system, which is reflected to the nodeless/nodal form of the superconducting gap and T_c. Surprisingly, even for the cuprates, which is conventionally modeled by a single orbital model, the multiorbital band structure is shown to play a crucial role in the material dependence of superconductivity. In fact, by adopting a two orbital model that considers the d_z² orbital on top of the d_x²−y² orbital, we can resolve a long standing puzzle of why the single layered Hg cuprate have much higher T_c than the La cuprate. Interestingly, here again the apical oxygen height measured from the CuO₂ plane plays an important role in determining the relative energy difference between d_x²−y² and d_z² orbitals, thereby strongly affecting the superconductivity.     

Electronic structure of TiH2

The electronic structure of TiH₂ has been studied using the augmented-plane-wave method and the LCAO interpolation. The density of states and its orbital components show that the conduction band is Ti d-like and that the valence band is largely derived from the hydrogen orbitals with small Ti 3d hybridization. The electronic charges on the hydrogen atom are ～ 1.5 as compared to 1.6–1.7 of the rare-earth metal hydrides.     

New family of Dirac and Weyl semimetals in XAuTe (X = Na,K, Rb) ternary honeycomb compounds

We propose a new family of 3D Dirac semimetals based on XAuTe(X = K, Na, Rb) ternary honeycomb compounds, determined based on first-principles calculations, which are shown to be topological Dirac semimetals in which the Dirac points are induced by band inversion. Dirac points with four-fold degeneracy that are protected by C3 rotation symmetry and located on the Γ-A high-symmetry path are found. Through spatial-inversion symmetry breaking, a K(Au0.5 Hg0.5)(Te0.5As0.5) superlattice structure composed of KHgAs and KAuTe compounds is proven to be a Weyl semimetal with type-II Weyl points, which connect electronand hole-like bands. In this superlattice structure, the six pairs of Weyl nodes are distributed along the K-Γ high-symmetry path on the kz = 0 plane. Our research expands the family of topological Dirac and type-II Weyl semimetals.     

A study of some potassium hexachlorometallate complexes using electron spectroscopy

X-ray photoelectron (ESCA) spectra of the core (Cl 2p K 2p and metal 4f, if present) and valence orbitals are reported for K₂ReCl₆, K₂OsCl₆, K₂IrCl₆· 3 H₂O, K₂PtCl₆, K₃MoCl₆, and K₂SnCl₆. The K 2p_{$\text{3}\text{2}$} binding energy was found to be nearly constant (292.7 eV) and that of Cl to increase very slightly with increasing atomic number for the third row transition metals. The chemical shifts of Re(IV), Os(IV), Ir(IV), and Pt(IV) relative to the metals were in qualitative agreement with atomic calculations utilizing configurations obtained from extended Hückel calculations. The valence spectra of the transition metal complexes exhibit a three-band structure. On the basis of MO results and intensity considerations the high binding energy band is assigned as a composite of the a_1g, e_g, 1t_2g MO's. The middle band represents the t_2u, 2t_1g MO's; and the low binding energy band the 2t_2g MO. Calculated nd orbital photoionization cross sections correlate reasonably well with the relative intensifies of the valence manifolds. Comparison of band separations and charge-transfer transition energies suggests that interelectronic repulsion and MO energy separation contribute about equally to the overall charge-transfer energy.     

The adsorption of methylcyclopentane on Pt(1 1 1)

The adsorption of methylcyclopentane (MCP) on Pt(1 1 1) has been studied using the atom superposition and electron delocalization (ASED-MO) molecular orbital method. Results show a weak interaction with the metallic surface. The adsorption energy is rather independent of the adsorption site coordination number. We find that Pt 6s, 6p_z and 5d_z² orbitals are involved in the bonding with MCP. There is no bonding between the carbon ring and the Pt surface and the interaction comes from the hydrogen atoms to the surface.     

Unrestricted Dirac-Fock theory: Relativistic determination of core polarization hyperfine interactions

The unrestricted Dirac-Fock (UDF) method is developed for determining relativistic contributions to the hyperfine interaction, notably that due to core polarization. Radial core-polarization of the one-electron (jj-coupled) spin orbitals is obtained by relaxing the restraint in restricted Dirac-Fock (RDF) theory that the radial part be independent of the magnetic quantum number, the projection m_j of j. Relativistic effects on the core polarization are obtained by comparison with results obtained from the non-relativistic spin polarized Hartree-Fock (m_s unrestricted) and spin plus orbital polarized Hartree- Fock (m_s plus m_j unrestricted) calculations. For the 5d transition series ions, the relativistic core polarization enhancement factor, S_s(z), is determined to be about a factor of two and so is much smaller than the isomer shift charge density enhancement factor (≈6) found earlier for these same ions. Comparison is made with limited experimental data available to date; for the case of atomic Re, excellent agreement is obtained with experiment.     

Emergent nesting of the Fermi surface from local-moment description of iron-pnictide high-T<Subscript>c</Subscript> superconductors

We uncover the low-energy spectrum of a t-J model for electrons on a square lattice of spin-1 iron atoms with 3d _xz and 3d _yz orbital character by applying Schwinger-boson-slave-fermion mean-field theory and by exact diagonalization of one hole roaming over a 4 × 4 × 2 lattice. Hopping matrix elements are set to produce hole bands centered at zero two-dimensional (2D) momentum in the free-electron limit. Holes can propagate coherently in the t-J model below a threshold Hund coupling when long-range antiferromagnetic order across the d + = 3d _{(x + iy)z} and d ? = 3d _{(x ? iy)z} orbitals is established by magnetic frustration that is off-diagonal in the orbital indices. This leads to two hole-pocket Fermi surfaces centered at zero 2D momentum. Proximity to a commensurate spin-density wave (cSDW) that exists above the threshold Hund coupling results in emergent Fermi surface pockets about cSDW momenta at a quantum critical point (QCP). This motivates the introduction of a new Gutzwiller wavefunction for a cSDW metal state. Study of the spin-fluctuation spectrum at cSDW momenta indicates that the dispersion of the nested band of one-particle states that emerges is electron-type. Increasing Hund coupling past the QCP can push the hole-pocket Fermi surfaces centered at zero 2D momentum below the Fermi energy level, in agreement with recent determinations of the electronic structure of mono-layer iron-selenide superconductors.     

Band structure for some Nb3X compounds

The tight binding method is used to calculate band structure for a number of Nb₃X compounds. The 4d band of the niobium, as well as the s-p bands of the X-atoms, are considered. The transfer and overlap integrals are calculated using tabulated atomic orbitals. The crystal field parameters (CFP) are estimated more carefully, taking into account deviations from a muffin-tin potential. We employ here the independent band approximation in which no interband interaction is considered. This approximation has been proved successful for the V₃Ga case, and it is estimated here that interband interaction may shift some levels up or down by 50 mRy or so, but the overall band-structure does not change. The Fermi level is found to lie in the neighbourhood of three peaks; one belongs to the δ₂(d_xy) band and the two others belong to the π(d_xz, d_yz) band.     

First-principles study on the electronic and magnetic properties of InN nanosheets doped with 2p elements

The electronic structure of InN nanosheets doped by light elements (Be, B, C, and O) is studied based on spin-polarized density functional theory within the generalized gradient approximation. The results show that the Be and C dopants in InN nanosheets induce spin polarized states in the band gap, or near the valence band, which generates local magnetic moments of 1.0 µ_B with one dopant atom. Due to the exchange spin-splitting, the three 2p electrons of Be atom are all in p_x and p_y orbitals (↑↑↓). So Be will coordinate with host atoms by σ coordination bond. The long-range ferromagnetic order above room temperature is attributed to p–p coupling. For C atom, the configuration of the five 2p electrons is (↑↑↑↓↓), and the unpaired electron is in p_z(↑) orbital. So the π bond will be formed between C atom and other atoms. Due the weak π bond cannot support long-range coupling, no stable magnetism is sustained if two C dopants are separated by longer than 3.58 Å.     

The photoelectron spectra of gaseous silver halides

Ionization potentials have been determined for gaseous AgCl, AgBr and AgI using He(I) photoelectron spectroscopy. The solids were vaporized directly into the photon beam from a heated substrate. Molecular orbitals were assigned to observed spectral bands based upon simple molecular orbital arguments, band intensity relationships and observed spin—orbital splitting. The spectra of the gaseous silver halides are more complex than those of other diatomic halides as a result of Ag(d)-X(π) interactions which occur in these molecules.     

Observation of p- and d-like surface states on CuCl(100) by angle-resolved photoemission

In the course of a systematic ultraviolet photoemission study of the electronic band structure of CuCl, we have identified two occupied surface states on CuCl(100), situated at 0.25 and 3.0 eV below valence band maximum in normal emission spectra. They essentially show pure p- and d-like orbital symmetry, respectively. We interpret them as a chlorine p_x,y-like occupied antibonding resonance and a copper Γ₁₂-derived state split off from the bulk orbitals by the surface potential. We also present critical point energies along Γ-X and Γ-L.     

Calculated electronic structure of the sandwichd 1 metals LaI2 and CeI2: Application of new LMTO techniques

The electronic structures of the cubic layeredd ¹ metals LaI₂ and CeI₂ were calculated using local density-functional theory and the linear muffin-tin orbital method. Special care was taken in the sphere packing used for the atomic spheres approximation. the band structure and the bonding were analysed in terms of projections of the bands onto orthogonal orbitals. The conduction-band structure could be calculated with a down-folded two-orbital basis which then served for the construction of an analytical 2×2 orthogonal, two-center tight-binding Hamiltonian. The conduction band has almost pure Ln-Ln 5d e _g character. Thex ²–y ²contribution dominates and is two-dimensional and short ranged. Strong hybridization with the 3z ²–1 orbital occurs near the saddle point, which is thereby lowered in energy and bifurcated due to thek _z -dispersion provided by the 3z ²–1 orbital. This strengthens the metal-metal bonds and prevents the nesting instability of the Fermi surface of the half filledx ²–y ²band. Within the limited accuracy of the LDA, the band structure of CeI₂ was found to be identical to that of LaI₂. The conduction-band 4f hybridizationV _{d f} ² (0) was analysed and found to be several times smaller than in fcc -Ce, in qualitative agreement with recent photoemission results [1]. Of importance for this reduction seems to be that the conduction band is formed by essentially only one orbital, ,that the number of Ce nearest-neighbors is small, and that the Ce–Ce distance is relatively large.     

Spontaneous spin polarization in rubrene studied by density functional theory calculations

We theoretically studied the spontaneous spin polarization properties of organic molecule rubrene by using density functional theory calculations. Our investigations show that normally nonmagnetic molecule rubrene could be spin polarized by spinless-hole injection. Magnetic moment of the molecule increases linearly with the extra hole charge amount only when the injected hole charges reach a certain value. The spin density resides predominantly on the carbon atoms in the tetracene backbone of rubrene molecule and also the bond lengths change differently due to the injected charge. Spontaneous spin polarization can be explained as the preferably filling of the spin-splitted carbon p_z orbitals near the Fermi energy for the injected charge.     

Spin-Hamiltonian theory of orbital near-degenerate state in tetragonal field

In this paper, a Spin-Hamiltonian theory of orbital near-degenerate state in tetragonal field is presented. For orbital doublet ²E, which is an orbital degenerate state in the cubic field and is a near-degenerate state in the tetragonal field, we obtain the cubic invariant form and the tetragonal invariant form of the Spin-Hamiltonian. In case of near-degeneracy (tetragonal splitting is very small) two additional g-factors are introduced to investigate Zeeman-splitting for tetragonal field. The two additional g-factors g_2z and g_2xy describe the magnetic interest between A_1g and B_1g states for a parallel magnetic field with z-axis and a perpendicular magnetic field with z-axis, respectively. The theory is based on the time-reversal invariant and the point-group symmetry invariant. The theoretical method can also be used for other orbital degenerate states ^2S+1Γ including and Γ=T₁ or T₂ and can be used for other point-group symmetry.     

CNDO calculations of nickel atom clusters

CNDO molecular orbital calculations for nickel atom clusters containing from one to thirteen atoms in various geometric arrangements are presented. The parameters were selected so that an octahedral Ni₆ cluster had an equilibrium inter-nuclear distance, d band occupancy, binding energy, Fermi level, and d band width approximating those of bulk nickel. For clusters with a given number of atoms the stability always increased in the order linear < planar < three-dimensional cluster. The general assumption that the binding energy per atom in metal clusters is proportional to the number of nearest neighbours is supported by these CNDO calculations although this relation is certainly not exact for small clusters. Examination of the calculated orbitals does not indicate a separation of the d band into one part made up from atomic t_2g orbitals and another from e_g orbitals. Overall the CNDO method appears to present a reasonable approach to calculating properties of small metal clusters.