Generalising localisation schemes of orthogonal orbitals to the localisation of non-orthogonal orbitals

ABSTRACT

When a set of orthogonal orbitals is localised using orthogonal transformations, the orbital metric is conserved as the unit matrix during the localisation. In this paper we describe how non-orthogonal orbitals may be localised by requiring that the orbital metric is conserved. In particular, we demonstrate how exponential mappings may be used to parametrise orbital transformations such that the orbital metric is conserved. Using this parametrisation, the localisation of non-orthogonal orbitals becomes a generalisation of the localisation for orthogonal orbitals, where the conservation of a unit metric is replaced by the conservation of a non-unit metric. As a result, standard orbital localisation functions and optimisation algorithms that have been used for localising orthogonal orbitals may also be used to localise non-orthogonal orbitals. Numerical illustrations show that the thickness of the orbital tails may be reduced when a set of non-orthogonal orbitals is localised compared to the orthogonal counterpart, and further that the physical interpretation of occupied orbitals for representing chemical bonds is preserved.     

Angular distribution of the photoelectron spectra for ethylene,propylene, butene and butadiene

The photoelectron spectra using the He I resonance line (21.22 eV) were measured for ethylene, propylene, 1-butene, cis-butene, trans-butene and 1,3-butadiene as a function of angle between the direction of the incoming photons and outgoing photoelectrons. From these data the angular parameter, β, is obtained for each photoelectron peak in each spectrum. The β value is a function of the energy of the photoelectron and the nature of the molecular orbital from which the photoelectron is ejected. A qualitative comparison is made between the experimentally derived β values and the molecular orbital assignments. In particular, it is noted that the photoelectron peak corresponding to the CC double bond π orbital yields a relatively high value of β. This has led in the case of butadiene to a confirmation that the first two photoelectron peaks both result from ionization in π orbitals.     

Unraveling the nature of charge excitations in La₂CuO₄ with momentum-resolved Cu K-edge resonant inelastic x-ray scattering

The results of model calculations using exact diagonalization reveal the orbital character of states associated with different Raman loss peaks in Cu K-edge resonant inelastic x-ray scattering (RIXS) from La?CuO?. The model includes electronic orbitals necessary to highlight the nonlocal Zhang-Rice singlet, charge transfer, and d-d excitations, as well as states with apical oxygen 2p(z) character. The dispersion of these excitations is discussed with prospects for resonant final state wave-function mapping. A good agreement with experiments emphasizes the substantial multiorbital character of RIXS profiles in the energy transfer range 1-6 eV.     

Angular dependence of auger electron emission from Cu (111) and (100) surfaces

Experimental angular emission profiles of the M_2,3M_4,5M_4,562 eV Cu Auger electrons from clean copper (100) and (111) surfaces in several azimuths are presented. A simple single scattering theory to account for elastic scattering of the Auger electrons by other ion cores in the solid is presented, and calculations have been performed to assess the importance of this process in contributing to the observed angular dependence. These calculations produce angular structure having a similar magnitude and temperature dependence to that observed experimentally, and some featural similarity in peak positions or shapes. It appears that elastic scattering is an important source of angular dependence, and that studies of adsorbed species on surfaces should provide a very sensitive method of surface structure determination.     

运用R矩阵方法研究低能电子与NO_2分子的散射

基于静电-交换和密耦合两种模型,采用R矩阵方法,研究了低能电子与二氧化氮自由基分子的积分散射截面和动量迁移散射截面,包括弹性散射和从电子基态到电子激发态的非弹性散射.采用aug-cc-pVTZ基组进行靶分子结构优化和散射研究.在密耦合模型中,包含6个电子的最低三个占据轨道1b_2,1a_1,2a_1被冻结,其余17个电子自由运动在活化空间中,并给活化空间增加了2b_1和7a_1两个虚轨道.包含了所有垂直激发能小于20 eV的靶分子电子组态,得到了收敛的散射截面,并与最新理论和实验值进行了比较.当入射能量小于4 eV时,本文结果与实验值符合得更好,校正了以往部分理论结果在极低能量处过高的现象,表明关联效应对于极低能量散射是非常重要的.     

VC(001)弛豫表面构型与电子结构第一性原理研究

用第一性原理方法对VC(001)清洁表面的构型和电子结构进行了详细研究，与TiC(001)面类似，VC(001)面弛豫后形成表面皱褶，其表层V原子和C原子分别朝体相和真空方向移动. 能带计算结果表明，过渡金属碳化物(001)面的能带结构符合刚性带理论模型. 对于VC(001)面，表面态主要处在-30eV附近，其主要成分为表层C原子的2pz轨道. 此外，以表层V原子的3d轨道成分为主的表面态出现在费米能级附近，由于这些表面态以表面法线方向的轨道(3d２z和3dxz/dyz)为主要成分，因此在表面反应中将起到重要作用，从而体现出与TiC(001)面不同的反应性质. 关键词： 过渡金属碳化物 表面态 能带结构     

Angular resolved ups of surface states on GaAs(1̄1̄1̄) prepared by molecular beam epitaxy

The As-rich (2 × 2), a newly found (√3 × √3) and the (√19 × √19) surfaces of GaAs(1̄1̄1̄) are studied by angular resolved UPS (ARUPS). The (2 × 2) surface is prepared by molecular beam epitaxy and the others by mild annealing. For the (2 × 2) surface emission from surface states is observed, which shows dispersion periodic within the (2 × 2) surface Brillouin zone. Using s-polarized light and the known symmetry selection rules the uppermost surface bands between 1 and 2 eV below the valence band maximum are assigned to the As dangling bond orbital. The bands near 4 and 7 eV assigned to the backbonds. From the strong decrease of emission intensity of the As-derived surface states between the (2 × 2) and the annealed surfaces it is concluded that the character of the As dangling bond orbital must have been changed from sp³-hybridic to s-like. This gives further evidence for our recently proposed model for the (√19 × √19) surface, which is particularly applicable for the (√3 × √3) surface.     

Angle-resolved photoelectron spectra of ethylene as a function of photon energy using synchrotron radiation

As a test of the applicability of multiple-scattering theory to an unsaturated organic system, angle-resolved photoelectron spectra of the first four bands of ethylene have been measured from 1.5 eV above threshold to a photon energy of 28 eV. The results are compared to the multiple-scattering theory calculations of Grimm. The comparisons are excellent except for the 1 b_3u orbital below 14 eV, and the disagreement is attributed to the occurrence of autoionization. It is found that the π orbital has a much higher β value than the σ orbitals, but the β value for the π orbital varies more rapidly than that for the σ orbitals from threshold to ～0.5 Rydberg (～7 eV).     

Proton Orbital [541]1/2 and Backbending in 178W

The microscopic mechanism of nine experimentally observed bands in ¹⁷⁸W is investigated using the particle-number conserving method of the cranked shell model with monopole and quadrupole paring interactions. The experimental results, including the moments of inertia and angular momentum alignments of nine bands in ¹⁷⁸W, are reproduced well by the particle-number conserving calculations, in which no free parameter is involved. Calculations demonstrate that occurrence of sharp backbending comes mainly from the contribution of high-j intruder orbitals νi13/2 or πh11/2 and their interference effect with orbitals near the Fermi surface. The ω variation of the occupation probability of each cranked orbital and the contribution to moment of inertia from each cranked orbital are analyzed.     

Surface structure from angular dependence of auger electron emission

Auger electrons emitted from atoms in the vicinity of a solid surface can show strong angular dependence in their emission due to elastic scattering from the surrounding ion cores of the solid. Model calculations for the emission of Auger electrons from sulphur adsorbed on a Ni (100) surface show that these angular features are very sensitive to the adsorption site of the emitting atoms, and that a study of these effects should produce a method of surface structure analysis for the location of preferred surface adsorption sites. This approach would appear to be an improvement over LEED because of its high sensitivity to structural changes and because it does not require long range order in the adsorbate layer.     

Angular resolved photoemission from palladium single crystals

Photoelectron spectra emitted normal to Pd(001), (011) and (111) faces are presented for He I (21.2 eV) and for Ne I (16.8 eV) radiation. The spectra are different from each other, and in each case the Ne I spectra show a distinct narrowing compared to the He I spectra. Most of the features in all these spectra can be accounted for in terms of initial states only, if different cross-sections are assumed for bands derived from particular d orbitals. This analysis is consistent only for d orbitals related to surface rather than bulk co-ordinates. Spectral features which do not fit this analysis are found to be very sensitive to surface adsorption. An example of the variation in emission away from the surface normal is given.     

非共面双对称几何条件下电子离化He的（e,2e）反应

运用修正后的BBK理论计算了入射能为27.6 eV,29.6 eV和34.6 eV,非共面双对称几何条件下,电子入射离化氦原子的三重微分截面,计算结果与实验结果进行比较发现两者符合的较好,验证了低入射能时修正后的BBK模型同样适用于非共面双对称条件下的(e,2e)过程,从碰撞的微观机理上分析了影响出射电子角分布的原因.     

Orbital ordering in frustrated Jahn-Teller systems with 90 degrees exchange

We show that superexchange interactions in frustrated Jahn-Teller systems with transition metal ions connected by the 90 degrees metal-oxygen-metal bonds (e.g., NaNiO2, LiNiO2, and ZnMn2O4) are much different from those in materials with the 180 degrees bonds. In the 90 degrees -exchange systems spins and orbitals are decoupled: the spin exchange is much weaker than the orbital one and it is ferromagnetic for all orbital states. Though the mean-field orbital ground state is strongly degenerate, quantum orbital fluctuations select particular ferro-orbital states. We explain the orbital and magnetic ordering observed in NaNiO2 and show that LiNiO2 is not a spin-orbital liquid.     

Effects of Breaking Waves on Composite Backscattering from Ship-Ocean Scene

The existence of the sea surface is bound to affect the electromagnetic(EM) scattering from marine targets. When dealing with the composite scattering from targets over a sea surface by applying high-frequency EM theories,the total scattering field can be decomposed into three parts in low sea states, namely, the direct scattering from the sea surface, the direct scattering from targets and the coupling scattering between the sea surface and targets. With regard to high sea states, breaking waves make the direct scattering from the sea surface and the coupling scattering more complicated. To solve this issue, a scattering model is proposed to analyze the composite scattering from a ship over a rough sea surface under high sea states. To consider the effect of breaking waves,a three dimensional geometric model is adopted together with Ufimtsev's theory of edge waves for the scattering from a breaker. In addition, the coupling scattering between targets and breaking waves is taken into account by considering all possible scattering paths. The simulated results indicate that the influence of breaking waves on the scattering field from the sea surface and on the coupling field is non-negligible, and the numerical results also show the effectiveness of the proposed scattering model.     

Die Winkelabhängigkeit der Resonanzstreuung niederenergetischer Elektronen an He,Ne, Ar und N2

The energy dependence of the elastic resonance scattering of low energy electrons from He, Ne, Ar, and N₂ has been measured in the angular range from 8° to 110°. From the measurements are derived the total angular momenta and hence the configurations of the quasistationary negative ion states. The line shapes depend very strongly on the phase shifts for the potential scattering and on the interference of different partial waves. In the cases of He and Ne phase shifts are determined. The resonance structure in the elastic scattering from N₂ in the energy range from 1.75 eV to about 3,5 eV seems to be due to the formation of the N ₂ ^? -ion in its electronic ground state with a²Π configuration. The separations of its first few vibrational states are 237±10 meV, the natural half-width of these states being approximately 150 meV.     

Xe(4d~(10))(e,2e)反应三重微分截面的理论研究

采用修正后的扭曲波玻恩近似理论,计算了共面不对称几何条件下Xe(4d~(10))(e,2e)反应的三重微分截面.散射电子能量为1000 eV,敲出电子能量为20 eV,散射电子角度分别固定在2°,4°和7.5°.理论计算与Avaldi等人的实验结果和扭曲波玻恩近似理论计算进行了比较,发现出射电子之间的后碰撞相互作用较弱,极化效应在反应过程中起着重要作用.     

Spectroscopic states of PTCDA negative ions and their relation to the maxima of unoccupied state density in the conduction band

Electron attachment spectroscopy is employed to demonstrate that the scattering of slow (0–15 eV) electrons from perylenetetracarboxilic dianhydride (PTCDA) molecules in the gas phase leads to the resonant formation of molecular and fragment negative ions detected in the mass-spectrometric experiment. Depending on the electron energy, currents of anions have clearly manifested peaks at 0.14, 1.9, 3.0, 4.8, and 5.7 eV. In addition, resonant states are also detected at thermal energy (0 eV) of scattered electrons, as well as at 0.4 and 1.0 eV, as shoulders on experimental curves. The spectroscopic states of PTCDA anions at energies exceeding 0 eV are interpreted in terms of the formation of shape resonances on the basis of calculated values of energies of π*-type unoccupied molecular orbitals. It is found that the positions of unoccupied orbitals of an isolated PTCDA molecule correspond to the peaks in the density of states of the conduction band of PTCDA films provided that the energies of the orbitals are shifted by 1.4 eV. The latter value can be interpreted as the binding energy of a molecule in the film due to the polarization interaction with the surroundings.     

Angle resolved UV photoemission spectra from a Bi(0001) surface

Angle resolved photoemission spectra taken from a Bi(0001) surface for hv = 16.9 and 21.2 eV exhibit (1) broad features which appear to be associated with one dimensional density of states, rather than band like features, and (2) a weak dependence upon the direction of incident light These effects can be explained by a large number of nondegenerate final state bands available for optical emission and by a uniform mixing of atomic orbitals in the initial states.     

Angular correlation function of wave scattering by a random rough surface and discrete scatterers and its application in the detection of a buried object

Abstract

The scattering of waves by a buried object is often obscured by the clutter around it. Such clutter can be attributed to the scattering by random rough surfaces and random discrete scatterers. Recent studies show that, because of the memory effect, the angular correlation function can suppress the effects of clutter and make the scattering by the buried object more conspicuous. In this paper, we study the angular correlation function of wave scattering by a buried object underneath a layer of random discrete scatterers and a non-Gaussian random rough surface. Such problems are common when the target is buried below a rough surface that is underneath a layer of vegetation. Numerical results are illustrated for various parameters of rough surfaces and discrete scatterers. The angular correlation function is calculated by frequency and angular averaging. It is shown that the use of the angular correlation function can enhance target detection in the presence of clutter.     

Atmospheric turbulence and orbital angular momentum of single photons for optical communication

The effects of propagation through random aberrations on coherence for single-photon communication systems based on orbital angular momentum states are quantified. A rotational coherence function is derived which leads to scattering equations for azimuthal modes of different orbital angular momentum states. The effect on a single-photon communication system is quantified using the channel capacity. The work shows that the decoherence effect of atmospheric turbulence on such systems is important even for weak turbulence.