Formulation of a phonon band calculation for molecular crystals using a coarse-grained coordinate approach under periodic boundary conditions

A phonon band calculation scheme based on our previously proposed coarse-graining theory under periodic boundary conditions was formulated. Starting with a simple one-dimensional, one-body periodic system, we introduced the basis set of a phase-shift coordinate system that can easily afford the discrete Fourier transformation of vectors and matrices with infinite dimensions. When the unit cell contains two or more bodies, the basis set of the phase-shift coordinate system is represented with tensors. By choosing an appropriate tensor basis set of a coarse-grained space, we can approximately block-diagonalize the dynamical matrix. Then, we can obtain the inertia and stiffness matrices represented by the given coarse-grained coordinate system, upon which the application of the mass-weighted Hessian equation affords a set of angular frequencies (ω) as functions of the wavenumber (k). Thus, the phonon band structure (k–ω plot) is obtained based on the coarse-graining approximation. When this approximation is applied to molecular assemblies comprising hydrogen bonding, the computational error resulting from this scheme is expected to be a maximum of a few cm^?1.

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Ru9Zn7Sb8: a structure with a 2 × 2 × 2 supercell of the half-Heusler phase

The title compound Ru(9)Zn(7)Sb(8) was synthesized via a high-temperature reaction from the elements in a stoichiometric ratio, and its structure was solved by a single-crystal X-ray diffraction method. The structure [cubic, space group Fm3m, Pearson symbol cF96, a = 11.9062(14) ? (293 K), and Z = 4] adopts a unique 2a(hh) × 2a(hh) × 2a(hh) supercell of a normal half-Heusler phase and shows abnormal features of atomic coordination against the Pauling rule. The formation of this superstructure was discussed in light of the valence electron concentration per unit cell. It is a metallic conductor [ρ(300 K) = 16 μΩ·m], and differential scanning calorimetry revealed that Ru(9)Zn(7)Sb(8) undergoes a transformation at 1356(1) K and melts, by all indications, congruently at 1386 K. At room temperature, its thermal conductivity is about 3 W/m·K, which is only one-quarter of that of most normal half-Heusler phases. Ru(9)Zn(7)Sb(8) as well as its analogues of iron-, cobalt-, rhodium-, and iridium-containing compounds are expected to serve as a new structure type for exploring new thermoelectric materials.     

Effect of local pipe bends on pump performance of a small air-lift system in transporting solid particles

The pump performance of a small air-lift system in transporting solid particles is investigated experimentally. Three types of riser pipe were used to examine the effect of local bends of riser pipes on the flow characteristics of a three-phase air–water–solid particles mixture. Two of them were locally S-shaped either below or above a gas injector. The other was vertically straight. Alumina particles of 3 or 5 mm diameter were used as solid particles. It is indicated that the pump performance is appreciably reduced when the pipe bend is above the gas injector. The critical condition under which solid particles are vertically lifted is discussed from a practical viewpoint. In addition, the particle motion in the region of a pipe bend is investigated by photographic observations.     

The Source of “Fairy Rings”: 2‐Azahypoxanthine and its Metabolite Found in a Novel Purine Metabolic Pathway in Plants

Rings or arcs of fungus‐stimulated plant growth occur worldwide; these are commonly referred to as “fairy rings”. In 2010, we discovered 2‐azahypoxanthine (AHX), a compound responsible for the fairy‐ring phenomenon caused by fungus; AHX stimulated the growth of all the plants tested. Herein, we reveal the isolation and structure determination of a common metabolite of AHX in plants, 2‐aza‐8‐oxohypoxanthine (AOH). AHX is chemically synthesized from 5‐aminoimidazole‐4‐carboxamide (AICA), and AHX can be converted into AOH by xanthine oxidase. AICA is one of the members of the purine metabolic pathway in animals, plants, and microorganisms. However, further metabolism of AICA remains elusive. Based on these results and facts, we hypothesized that plants themselves produce AHX and AOH through a pathway similar to the chemical synthesis. Herein, we demonstrate the existence of endogenous AHX and AOH and a novel purine pathway to produce them in plants.     

Facial Reduction Algorithms for Conic Optimization Problems

In the conic optimization problems, it is well-known that a positive duality gap may occur, and that solving such a problem is numerically difficult or unstable. For such a case, we propose a facial reduction algorithm to find a primal–dual pair of conic optimization problems having the zero duality gap and the optimal value equal to one of the original primal or dual problems. The conic expansion approach is also known as a method to find such a primal–dual pair, and in this paper we clarify the relationship between our facial reduction algorithm and the conic expansion approach. Our analysis shows that, although they can be regarded as dual to each other, our facial reduction algorithm has ability to produce a finer sequence of faces of the cone including the feasible region. A simple proof of the convergence of our facial reduction algorithm for the conic optimization is presented. We also observe that our facial reduction algorithm has a practical impact by showing numerical experiments for graph partition problems; our facial reduction algorithm in fact enhances the numerical stability in those problems.     

Homogeneous spaces with invariant projectively flat affine connections

We characterize invariant projectively flat affine connections in terms of affine representations of Lie algebras, and show that a homogeneous space admits an invariant projectively flat affine connection if and only if it has an equivariant centro-affine immersion. We give a correspondence between semi-simple symmetric spaces with invariant projectively flat affine connections and central-simple Jordan algebras.

     

Molecular cluster theory for chemisorption of first row atoms on nickel (100) surfaces

Self-consistent Hartree-Fock-Slater molecular cluster models for the chemisorption of first row atoms on Ni(100) surfaces are presented. Energy levels and ground state charge distributions for XNi_S clusters with the adatom X = H, C, N, O located in C_{4 V} symmetry at a fixed height of h = 2.0 au above the surface are given. The variation of properties with h was studied in detail for the case of oxygen. Theoretical results compare rather well with experimental photoelectron and energy loss data. Local-densities-of-states diagrams are used to clarify the interaction between adsorbate levels and metal conduction bands.