Effective One-particle Potential Research Articles

Single-Pole Polarization Models: Rapid Evaluation of Electron Affinities of Solvated-Electron and Superatomic Molecular Anionic States.

We propose a single-parameter effective one-particle potential, termed the single-pole exchange-correlation (1p-XC), to rapidly evaluate electron affinities (EAs) of nonvalence electronic states of molecular clusters and nanoassemblies. The model combines exact-exchange and the random phase approximation (RPA) correlation potential with a single-pole approximation to model the frequency-dependent polarization function. It captures long-range static and dynamic-frequency effects in the correlation potential, with mean absolute errors of 0.06 eV for EAs of hydrated- and ammoniated-electron clusters with EA values in the range 0.24-1.77 eV. The 1p-XC approximation enables EA estimation with a computational wall-time similar to that of hybrid functionals. The model also provides a compressed-basis, which significantly reduces the rank of higher-level parameter-free one-particle Hamiltonians and further simplifies the computation of EAs. The compressed-basis approach is used to model the hybridization of superatomic molecular states of (C60)2- and (C60)3-, thereby verifying previous model Hamiltonian studies.

回折法と X 線吸収分光(XAFS)法を用いた地球惑星物質の精密構造解析

Advantage of mineralogical approach in clarifying peculiar physical properties for materials is introduc in the review. Precise structure analyses of the diffraction and X?ray absorption fine structure (XAFS) spectroscopy methods provide the important information on the Earth and planetary materials. The information from both long-range-order structure by diffraction method and local structure by XAFS method is important for the understanding of the correlation between structures and physical properties of minerals. High pressure and high temperature in-situ diffraction and XAFS experiments were performed using a multi-anvil high-pressure device and synchrotron radiation. Both experiments are also useful as a probe of vibration dynamics and disordered structure. The pressure-dependent anharmonic effective potentials and characteristic values can be investigated using the diffraction and XAFS Debye-Waller factors. The ionic conduction mechanism has been proposed based on the effective one-particle potential and effective pair potential. Super ionic conduction of the mantle constituents resulting from anharmonic thermal vibration can produce the high electric and the low thermal conductivities in the Earth's lower mantle. Local structures of atoms in melt and glass of tetrahedrally coordinated materials change rapidly to higher coordinated states with pressure as if first-order phase transition. Unique structures are left in the local structures of the trace elements in minerals and tektite-impactite glass. The application of recently innovated techniques to the characterization of materials under extreme conditions contributes to the advancement of fundamental Earth-scientific knowledge.

不規則性をもつ結晶，超イオン導電体，非晶質，ガラス，融体の構造解析―不規則系・ランダム系の結晶学―１．周期系における不規則性の解析 回折法とＸＡＦＳ法を併用した不規則構造解析―α‐ＡｇＩ型構造の超イオン導電機構―

The Debye-Waller factors determined by diffraction and XAFS experiments provide important information about the thermal vibration and disordered structure. The statistical distribution of Ag in α-AgI and supersonic conduction mechanism have been discussed based on the effective one-particle potential, probability density function and effective pair potential. The disordered nature of α-AgI is due to the thermal motion and the probability of finding mobile Ag ions at saddle point is a few percent in α-AgI.

Electron density and electrostatic potential of KMnF3: a phase-transition study.

Three accurate X-ray diffraction experiments (Mo Kalpha, T = 190, 240 and 298 K) were carried out to track the temperature dependence of the electron density in the cubic perovskite potassium manganese trifluoride, KMnF3, from room temperature to just above that of the phase transition to the tetragonal structure (186 K), and to correlate the parameters of the critical points with the phase-transition mechanism. The data obtained were approximated by the Hansen-Coppens multipole model expanded up to hexadecupoles; the anharmonicity of the atomic displacements up to the fourth level was considered. Topological analysis shows only two types of chemical bond at room temperature, Mn-F and K-F. However, at low temperature the K-F bonds blocking the rotation of the MnF6 octahedra are weakened and new Mn-K bonds are formed to keep the crystal structure from disintegrating. The Mn-K bonds become stronger as the temperature approaches 186 K. This rearrangement of chemical bonds can be regarded as a precursor effect, which starts 50-60 degrees above the phase-transition temperature. The effective one-particle potential of the F atom has a single minimum at 298 K and four well separated minima (with a shift of 0.2 A from the equilibrium position towards the structural holes) at 190 K. Parameters of the critical points of the electron density indicate closed-shell type interactions between K-F and Mn-K pairs, whereas the Mn-F bond can be considered as an intermediate type. The topology of the electrostatic potentials is discussed as well.

非調和熱振動の新しい解析法に関する研究

The Maximum Entropy Method (MEM) can provide a high-resolution nuclear density distribution purely from experimental neutron diffraction data. The distribution expresses thermal smearing, which is caused by all kinds of thermal-vibration modes both harmonic and anharmonic. If the effective one-particle potential (OPP) is assumed to describe thermal smearing of nuclei, the potential parameters can be determined by least squares refinement of the nuclear density distribution. It is found that this technique gives sufficiently small correlation between potential parameters than the conventional structure analysis technique and the potential parameters can be precisely determined even in a powder diffraction case.

Ag2Ti2P2S11: A New Layered Thiophosphate. Synthesis, Structure Determination and Temperature Dependence of the Silver Distribution

The new Ag2Ti2P2S11 quaternary phosphosulfide disilver dititanium undecathiodiphosphate is obtained by heating the elements at ca 850 K in an evacuated silica tube. It crystallizes in orthorhombic symmetry, Pnma space group, with a = 8.5222 (11), b = 6.8359 (10), c = 24.142 (4) Å, V = 1406.4 (4) Å3 and Z = 4 at 293 K. The refinement of the room-temperature structure leads to a reliability factor of R = 0.0378 for 1556 independent reflections and 128 variables. Ag2Ti2P2S11 is composed of layers, separated by van der Waals gaps. The layers are composed of [Ti2S9] chains built from [TiS7] units (TiS6 octahedra in which a corner has been replaced by an S2 pair) and linked through regular [PS4] and highly distorted [AgS4] tetrahedra. The formula of the compound can be written as AgI 2TiIV 2PV 2(S2)−IIS−II 9. A Gram–Charlier anharmonic development of the atomic displacement factor for Ag atoms reveals a strong non-harmonic probability density deformation, especially in the direction of two empty neighbouring tetrahedra, away from the Ti and P cations. The temperature dependence of the effective one-particle potential shows that the Ag distribution is primarily static in nature. At high temperature the tetrahedrally coordinated site is the preferential site. At lower temperature the Ag atoms are redistributed over the tetrahedral site and the adjacent triangular site. The disorder could not be resolved due to a phase transition with splitting of spots just below room temperature.

An accurate determination of the thermal vibration of rutile from the nuclear density distribution of the maximum-entropy analysis

The maximum-entropy method (MEM) can provide a high-resolution nuclear density distribution purely from experimental neutron diffraction data. The distribution expresses thermal smearing, which is caused by all kinds of thermal-vibration modes both harmonic and anharmonic. If the effective one-particle potential (OPP) is assumed to describe thermal smearing of nuclei, the potential parameters can be determined by least-squares refinement of the nuclear density distribution. By this method, the OPP parameters of rutile (TiO 2 ) are directly determined from the nuclear density distribution originally derived by Sakata, Uno, Takata & Howard [J. Appl. Cryst. (1993), 26, 159-164]. In the rutile case, the x coordinate of the O atom located at (x,x,0) has to be determined before the OPP parameters are analysed. The atomic position is defined as the position where the first-order moment of the nuclear density becomes zero. The obtained x coordinate is 0.30477, which shows excellent agreement with the previous study of Rietveld analysis by Howard, Sabine & Dickson [Acta Cryst. (1991), B47, 462-468], i.e. 0.30478 (6). The higher-order moments of nuclear density are calculated in order to build an adequate OPP model. Among these values, none of the sixth order is significant and hence the OPP model up to fourth-order anharmonicity is employed. The potential parameters are refined by least-squares analysis using the above OPP model. For the Ti atom, nine OPP parameters (three harmonic and six fourth-order anharmonic) are determined with reliability factor R = 0.73%. For the O atom, twelve OPP parameters (three harmonic, three third- and six fourth-order anharmonic) are determined with R = 3.83%. The nuclear density of the O atom shows substantial skewness in rutile owing to the third-order anharmonicities. It is shown that the present method is a very powerful technique to determine the precise values for both harmonic and anharmonic potential parameters based on the OPP model in comparison with conventional structure analysis.

Thickness Dependence of Electronic Structure of Small Spherical Metal Shells

We investigate the ground-state electronic structure of small spherical metal shells on the basis of a model system which consists of valence electrons and a spherical jellium shell (JS). The electron density distribution and the effective one-particle potential are calculated by using the local-density-functional formalism involving the self-interaction correction (SIC). By varying the electron number and the inner radius of the JS, conserving the charge neutrality of the whole system, we closely examine how the electronic structure evolves from a jellium-sphere system to an electron system sharply localized around a spherical surface. By comparing the results in the SIC scheme with those in the ordinary Kohn-Sham scheme, we explore effects of the SIC especially on energy levels of occupied electron shells and on the total energy.

Characteristics of Electronic Structure of Small Spherical Metal Shells

The ground-state electronic structure of a small spherical metal shell is investigated on the basis of the model system composed of valence electrons and a spherical jellium shell (JS). The electron density distribution and the effective one-particle potential are calculated by means of the density functional theory involving the local density approximation. We follow the evolution of the electronic structure as we vary the electron number and the inside radius of the JS, conserving the charge neutrality as a whole. The results of our calculation highlight the characteristics of the electronic structure of the small spherical metal shell, which can be understood in terms of the transition from the electronic structure of the metal sphere to that of the electron system sharply localized around a spherical surface.

Local-density functional and on-site correlations: The electronic structure of La2CuO4 and LaCuO3.

State-of-the-art electronic-structure calculations based on the local-density approximation (LDA) to the density functional fail to reproduce the insulating antiferromagnetic ground state in the parent compounds of the high-temperature oxide superconductors. Similar problems have been observed earlier in classical transition-metal oxides such as FeO, CoO, and NiO. In this work we present the method which delivers the correct insulating antiferromagnetic ground state in the correlated oxides preserving other properties as well as the efficiency of the standard LDA. The method embeds the relevant (for a given system of electrons) part of the Hubbard Hamiltonian into the Kohn-Sham LDA equation. The resulting Hamiltonian attempts to fix two intrinsic problems of the LDA: the deficiency in forming localized (atomiclike) moments and the lack of discontinuity of the effective one-particle potential when going from occupied to unoccupied states. We present the detailed study of La2CuO4 and LaCuO3. In the case of La2CuO4 the energy gap and the value of the localized magnetic moment in the stable insulating antiferromagnetic solution are in good agreement with experiment. We compare our results with the standard local spin density approximation calculation and multiband Hubbard model calculations, as well as with results of spectroscopy: inverse photoemission, valence photoemission, and x-ray absorption at the K edge of oxygen. In the case of LaCuO3 such an extensive comparison is limited due to the limited data available for this compound. We discuss, however, the electric and magnetic properties and the insulator-metal-insulator transitions upon increase of oxygen deficiency.

Temperature dependence of the silver distribution in Ag2MnP2S6 by single crystal X-ray diffraction

Abstract The Ag distribution in the layered compound Ag2MnP2S6 [non-conventional space group C2/n, a = 6.339(1) Å, b = 10.933(1) Å, c = 13.893(2) Å, β = 108.29(1)°, Z = 4, T = 300 K] is investigated as a function of temperature with the aid of single crystal X-ray data. Ag2MnP2S6 is built of S/(Ag2)1/3Mn1/3(P2)1/3/S sandwiches, in which Mn and P2-pairs are distributed over the octahedral voids in an ordered triangular way; at room temperature the Ag+ cations are located within the two sulfur layers of a sandwich, at the centers of the opposite triangular faces of sulfur octahedra. The Gram-Charlier expansion of the structure factor up to the fourth order is used to analyze the development of the Ag distribution with temperature. Joint probability density function maps calculated from the refined tensor elements of the atomic displacement parameter of Ag indicate that at higher temperatures the neighbouring tetrahedral sites within the gap between the sandwiches also become partly occupied. In addition they also show that the centers of the sulfur octahedra do not become occupied. The temperature dependence of the effective one-particle potential shows that the disorder in the Ag distribution is primarily static in nature. The development of the Ag distribution leads to a strengthening of the inter-sandwich bonding and to stronger distortions in the sulfur sheets. The anharmonic model is also applied to the parent phase Ag2ZnP2S6 with improved result as compared to the split structure model.

Probability density and effective one-particle potential of octahedral Ag in the fast ion conductor Ag 0.39 TiS 2

The structure of Ag 0.39TiS 2 has been determined in the temperature range 300–600 K using single crystal X-ray data. The parameters of the hexagonal unit cell (space group P 3 ml) at 300 K are: a=3.4359 (2) Å, c=3.4151 (6) Å. The structure factor is extended to include fourth order tensor elements for Ag to account for the softening of the vibration potential at higher temperatures. wR F 2 factors range from 0.012 to 0.031. It is shown that the surface of constant displacement probability of Ag is an ellipsoid, displaying the anisotropic nature of the softening of the vibration potential. From the temperature dependence of the harmonic tensor elements and the effective one-particle potential it is deduced that only occupational disorder is present in the Ag distribution, i.e. without accompanying static displacement disorder. Thus, Ag vibrates in a strongly anharmonic vibration potential around only one equilibrium site in the center of a sulfur octahedron.

Quantum tunneling of surface-state electrons.

We have calculated quasi-bound-state energies and lifetimes of surface-state electrons above liquid helium for two single-particle potentials. In the first case, the electric field due to other electrons is taken to be that of a uniform charge sheet. The second is an effective one-particle potential that includes correlation effects in a simple manner. We solved the Schr\"odinger equation numerically to determine the asymptotic amplitude and the phase of the wave function, from which resonances and their widths are obtained. Tunneling rates and thermal activation energies are calculated as a function of correlation-hole radius, electron density, and pressing electric field amplitude. We compare these results with recent experiments.

Crystal structure analyses of the pyrochlore and fluorite-type Zr2Gd2O7 and anti-phase domain structure

The detailed structure investigations of Zr 2 Gd 2 O 7 with pyrochlore- and fluorite-type structures have been carried out by X-ray single crystal method at room temperature. The bond distances between cations and oxide ions versus the site population for cations reasonably support that the fluorite phase is made up of the structure with microdomains of the pyrochlore. Sharp fundamental and diffuse superstructure reflections of the pyrochlore are interpreted assuming that anti-phase domain boundaries lie parallel to the &{211} and that domain sizes are not uniform. It should be proposed that the layers composed of the 48f site oxide ions are anti-phase boundaries. The probability density function maps and effective one-particle potentials of the pyrochlore structure reveal that the magnitudes of anharmonic thermal motions for the 48f site oxide ions are large toward the unoccupied 8b site. Compared to the s -pyrochlore phase (with sharp superstructure reflections), the 48f site oxide ions of the d -pyrochlore (with diffuse superstructure reflections) and fluorite phases have larger temperature factors and gentler potential curves. This is due to that the anti-phase domains are coherent each other and that their electron density distributions are the averages of individual domains.

Local structure of the superionic conducting α-AgI type AgI 1− xBr x solid-solution

The local structures of the α-AgI type AgI 1− x Br x solid-solution (0⩽×⩽0.4) at 573 K have been determined by EXAFS and XANES analyses. The AgI and AgBr distances in the solid-solution remain constant values of 2.76 Å and 2.69 Å, respectively. There are little changes in the Br K and Ag K edge XANES spectra in the solid-solution. It is concluded that only tetrahedral sites are occupied at equilibrium in the solid-solution though the α-AgI type structure has several kinds of sites among interstices of the b.c.c. lattice formed by anions. The AgI distance in α-AgI obtained by EXAFS is significantly shorter than that by diffraction experiments, indicating that the average volume of tetrahedra occupied by Ag ions is smaller than that of unoccupied tetrahedra. The effective one-particle potentials (O.P.P.) and the probability-density functions (P.D.F.) Ag and I atoms in α-AgI are calculated. The potentials along the Ag-I bond do not change appreciably through the βα phase transition. The widespread distribution obtained for both atoms in the P.D.F. maps exhibits that the periodicity is substantially disturbed by the large thermal motion of the atoms. The Ag ion can jump to the neighboring site with appreciable probability by the thermal motion, while the I ion is localized on the b.c.c. lattice. The diffusion path of the Ag ions is determined from the P.D.F. maps. The potential barrier along the diffusion path is evaluated to be 0.07 eV from the O.P.P..

Atomic vibrations in cuprous iodide

The Debye-Waller factors of CuI were measured in a Mossbauer scattering experiment. The parameters in the effective one-particle potential were determined for copper. The results indicate that the potential is lowest in (100) directions, which suggests that in the superionic phase the copper atoms hop in (100) directions.

Symmetry of Terms in the Temperature Factor for Bragg Diffraction of X Rays or Neutrons

Terms in the anharmonic Debye-Waller factor, taken as a perturbation about the harmonic case to second order in the van Hove ordering parameter, are classified according to the point-group symmetry of the vibrating atom. The classification is valid for a fully interacting (many-body) crystal potential. It is pointed out that certain terms, which are symmetry-allowed for such a general crystal potential, are excluded if an effective one-particle potential is employed.

Anharmonic potentials and pseudo potentials in ordered and disordered crystals

An extension of existing structure-factor formalisms for anharmonic thermal motion in crystals and the corresponding one-particle potentials is presented and applied to ordered and disordered structures. A generalized probability density function (joint p.d.f.) is introduced and it is first shown that anharmonic temperature factors ('thermal motion') and split positions ('disorder') are mathematically equivalent in describing electron or nuclear densities. When probability densities are interpreted in terms of an effective one-particle potential, however, ordered and disordered structures show different behaviour. For ordered structures the effective one-particle potentials are found to be almost independent of temperature; for disordered structures one obtains a temperature-dependent pseudo potential. The different temperature dependence can be used to distinguish between order and disorder. Pseudo potentials are calculated for several types of disorder and compared with potentials derived from X-ray or neutron diffraction experiments.

Anharmonic temperature factors of atoms with 4mm and [formula omitted]2m site symmetries

The anharmonic temperature factors of atoms with 4mm and 4 2m site symmetries were formulated following the method of Matsubara, and the formulate were incorporated into a conventional full-matrix least-squares program for structure refinement. In the present treatment, anharmonic terms up to the third order in effective one-particle potentials were taken into account and Boltzmann statistics was employed.

Molecular theory for moderately concentrated polymer solutions in shear flow

A molecular theory for the rheological properties of moderately concentrated polymer solutions is developed on the basis of a model of interacting dumbbells. The interaction is treated in a mean field approximation, leading to an effective one-particle potential and a Gaussian stationary distribution function. Various rheological functions such as birefringence, shear viscosity and first normal-stress coefficient for simple shear flow and the Trouton viscosity for simple extensional flow are calculated. Good qualitative agreement with experimental observations is found, especially at intermediate flow rates. It is predicted, for example, that the birefringence increases approximately linearly with shear rate at intermediate shear rates and that the concentration dependence of the gradient varies asc1/2. The typical non-Newtonian behaviour is obtained for the shear viscosity. For small concentrations the onset of shear rate dependence decreases asc−1/2. At intermediate shear rates an apparent power law is obtained with an exponent between − 0.5 and − 1.0, decreasing with concentration.