Orbital Method Research Articles

Small unitary representations of the double cover of $\operatorname{SL}(m)$

The irreducible unitary representations of the double cover $\widetilde {\mathrm {SL}(m)}$ of the real group $\mathrm {SL}(m)$, with infinitesimal character $\frac {1}{2}\rho$, which are small in the sense that their annihilator in the universal enveloping algebra is maximal, are expressed as Langlands quotients of generalized principal series. In the case where $m$ is even we show that there are four such representations and in the case where $m$ is odd there is just one. The representations’ smallness allows them to be written as a sum of virtual representations, leading to a character formula for their $K$-types. We investigate the place of these small representations in the orbit method and, in the case of $\widetilde {\mathrm {SL}(2l+1)}$, show that the representation is attached to a nilpotent coadjoint orbit.The $K$-type spectrum for the Langlands quotients is explicitly determined and shown to be multiplicity free.

First principles study of structural and electronic properties of Bex Zn1–xS and Bex Zn1–xTe alloys

AbstractWe present the results of first‐principles study of the structural and electronic properties of Bex Zn1–x S and Bex Zn1–x Te alloys for different concentrations x. The computational method is based on the full‐potential muffin‐tin orbitals method (FP‐LMTO) in the framework of density‐functional theory (DFT). The exchange and correlation energy is described in the local density approximation (LDA) using Perdew–Wang parameterization. We have investigated the effect of composition on the ground‐state properties, band gap and effective mass. We report the results concerning the variation of the gaps and crossover of the direct, indirect bandgap and the bowing. Using the approach of Zunger and coworkers, the microscopic origins of bandgap bowing have been detailed and explained. A reasonable agreement is found from the comparison of our results with other theoretical calculations. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Molecular Recognition and Spectroscopic Properties of Cyclobis(paraquat-p-anthracene)

Cyclobis(paraquat-p-anthracene) is a novel electron-deficient macrocyclic host. One of the most important applications of the host is molecular recognition. The binding energies of the host to several guest molecules like water, ammonia, alcohol, and heterocycles were investigated. The structures of the host-guest complexes were optimized using DFT (density functional theory) at B3LYP/3-21G level. The energies of the complexes were calculated at B3LYP/6-31G(d) level. The binding energies of the complexes were obtained after the correction of basis set superposition error. The 13C and 3He chemical shifts of the complexes were calculated by the gauge-including atomic orbital (GIAO) method at B3LYP/3-21G level. It indicates that the host can bind the guest molecules via hydrogen bonds between the heteroatoms in the guest and hydrogen atoms in the host. The binding energies of the complexes were mainly affected by the number and distance of the hydrogen bonds. The energy gaps for some of the complexes were increased owing to the formation of the hydrogen bonds. At the same time, the chemical shifts of the carbon atoms on the C-H bonds connected with the hydrogen bonds in the complexes relative to those of the same carbon atoms in the host were transferred downfield. The aromaticities of the complexes were relevant to the binding energies and ways. The aromaticity of the host was increased by the weak interaction between the host and guest molecules. The cyclic current of the host was decreased, thus the aromaticity was lowered owing to too strong host-guest interaction and incorporation of the guest molecules inside the cavity of the host.

Vibrational and Quantum Chemical Study of Triphenylantimony(V)-o-salicylate

A complete normal coordinate analysis was performed by two different methods: a classical Wilson G-F matrix method and the semi-empirical molecular orbital PM3 method, for a five coordinate non rigid triphenyl antimony diester SbPh3(O2CR)2,[R=C6H4OH-o], known to be a bioactive molecule. The study of vibrational spectra suggested that the title compound might have secondary bonding interaction between the central antimony atom and the carbonyl oxygen atoms. The atomic charge distribution, geometry optimization and thermochemistry, were also calculated by PM3 method, which help in finding the potential sites of the title compound.

Ab initio electronic band structure calculations of half‐metallic c alcium pnictides

AbstractAb initio electronic structure calculations of hypothetical zinc‐blende CaX (X = P, As, Sb) were performed using tight‐binding linear muffin‐tin orbital method. It was found that, these compounds are ferromagnets exhibiting half‐metallicity. Total energy calculations show that the zinc blende ferromagnetic phase is more stable than the zinc‐blende non‐magnetic phase at equilibrium volume. Ground state properties such as equilibrium lattice constant, bulk modulus and cohesive energy were calculated. The calculated magnetic moment is found to be 1μB per formula unit for all these materials, which agrees well with the other theoretical results. On reducing the cell volume all these compounds are found to undergo a magnetic phase transition from zinc‐blende ferromagnetic phase to zinc‐blende non‐magnetic phase. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Tuning of Energy Band Gaps in Ternary Semiconductors

The first principle investigations on electronic structure of ABC2 (A = Cd; B = Si, Ge, Sn; C= P, As) pnictides using the Tight Binding Linear Muffin Tin Orbital (TB-LMTO) method within the Atomic Sphere Approximation (ASA) is reported. Variation of Eg with pressure reveals the direct and pseudodirect natures of these compounds. CdSiP2 shows a pseudo direct and CdGeP2, CdSnP2, CdSiAs2, CdGeAs2 and CdSnAs2 show direct band gap natures. Semiconductor to metal transition at high pressures is observed. Metallisation volumes (V/Vo) m and pressures (Pm), bulk modulus (Bo) and its pressure derivative (Bo 1) are reported. Correlation connecting Bo and the unit cell volume (Vo) is established.

Polarization of a scalar field vacuum on a manifold conformally equivalent to the manifold R⊗G

In the present paper, vacuum average energy-momentum tensors are calculated on a group manifold for a real scalar field by the method of coadjoint representation orbits. An example is considered for the group SO(3). The energy-momentum tensor is calculated for a conformally equivalent metric with the help of a conformal transformation.

Normal coordinate analysis and quantum chemical study of tris(p-fluorophenyl)antimony di(N-phenylglycinate) [(p-FC6H4)3Sb(O2CCH2NHC6H5)2

A complete normal coordinate analysis was performed by two different methods: a classical Wilson’s G-F matrix method and the semi-empirical molecular orbital PM3 method, for a five coordinate tris(p-fluorophenyl)antimony di(N-phenylglycinate) [(p-FC6H4)3Sb(O2CCH2NHC6H5)2], known to be an in vitro antitumour molecule.

Electronic structures, chemical bonding, and defect formation in mixed cyanoferrates M2Cu[Fe(CN)6] (M = Na, K, Rb, and Cs)

The effect of the alkali metal nature on the electronic structures and chemical bonding in mixed cyanoferrates M2Cu[Fe(CN)6] (M = Na, K, Rb, and Cs) was studied by ab initio tight-binding linear muffin-tin orbital (TB-LMTO) method (in the spin-polarized implementation) and the extended Huckel molecular orbital (EHMO) method. It was found that the X-ray photoelectron spectra of the ferrimagnetic compounds Na2Cu[Fe(CN)6] (I), K2Cu[Fe(CN)6] (II), Rb2Cu[Fe(CN)6] (III), and Cs2Cu[Fe(CN)6] (IV) are similar. The magnetic moments on Cu2+ and iron ions remain virtually constant in compounds I–IV (μ(Cu) = 0.9 μB, μ(Fe) < −0.06 μB). Analyses of the electron density maps and the bond overlap populations showed that the cubic frameworks of cyanoferrates are built from stable fragments ⋯-Fe-C≡N-Cu-⋯. The bond strength in these fragments decreases substantially in the order C-N → Fe-C → Cu-N and only slight in the order IV → III → II → I. The calculated total energies of the cyanoferrates Cs2−x Cu[Fe(CN)6], CsHCu[Fe(CN)6], and NaHCu[Fe(CN)6] for different concentrations and configurations of defects (cesium vacanices and hydrogen substitution defects) suggest mutual repulsion of defects. This repulsion is responsible for the experimentally observed lowering of the ionic conductivity with an increase in the defect concentration in the mixed cyanoferrates.

Influence of Structural Parameters to Engineer the Band Gaps in Ternary Pnictide Semiconductors - Theory as a Tool

The band gap anomaly exhibited by ABC2 : A = Cd; B = Si,Ge,Sn; C = P,As pnictides with respect to their binary analogs GaP, Ga0.5In0.5P, InP, GaAs, Ga0.5In0.5As, InAs is studied using Tight Binding Linear Muffin Tin Orbital (TBLMTO) method as an investigating theoretical tool. The influence of the structural parameters, η and u are analyzed to enable one to tune energy gap to make tailor made compounds.

Structure and superconductivity in the ternary silicide CaAlSi

Using the linear response-linearized Muffin-tin orbital (LR-LMTO) method, we study the electronic band structure, phonon spectra, electron-phonon coupling and superconductivity for c-axis ferromagnetic-like (F-like) and antiferromagnetic-like (AF-like) structures in ternary silicide CaAlSi. The following conclusions are drawn from our calculations. If Al and Si atoms are assumed to arrange along the c axis in an F-like long-range ordering (-Al-Al-Al-and-Si-Si-Si-), one could obtain the ultrasoft B1g phonon mode and thus very strong electron-phonon coupling in CaAlSi. However, the appearance of imaginary frequency phonon modes indicates the instability of such a structure. For Al and Si atoms arranging along the c axis in an AF-like long-range ordering (-Al-Si-Al-), the calculated electron-phonon coupling constant is equal to 0.8 and the logarithmically averaged frequency is 146.8 K. This calculated result can correctly yield the superconducting transition temperature of CaAlSi by the standard BCS theory in the moderate electron-phonon coupling strength. We propose that an AF-like superlattice model for Al (or Si) atoms along the c direction may mediate the inconsistency estimated from theory and experiment, and explain the anomalous superconductivity in CaAlSi.

Electronic structure calculations of europium chalcogenides EuS and EuSe

AbstractWe have performed ab‐initio self‐consistent calculations on the full‐potential linear muffin‐tin orbital method with the local‐density approximation and local spin‐density approximation to investigate the structural and electronic properties of EuS and EuSe in its stable (NaCl‐B1) and high‐pressure phases. The magnetic phase stability was determined from the total energy calculations for both the nonmagnetic (NM) and magnetic (M) phases. These theoretical calculations clearly indicate that both at ambient and high pressures, the magnetic phase is more stable than the nonmagnetic phase. The transition pressure at which these compounds undergo the structural phase transition from NaCl‐B1 to CsCl‐B2 phase is calculated. The elastic constants at equilibrium in both NaCl‐B1 and CsCl‐B2 structures are also determined. (© 2007 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

A Theoretical Study of the Interaction Between Cytosine and BX3 (X = F, Cl) Systems

The B3LYP method of DFT and HF theories of ab initio with 6-311+G** basis sets were used to predict the geometries of the cytosine-BX3 (X,=F, Cl) complex systems. Four conformers were obtained with no imaginary frequencies, respectively. The binding energies, enthalpies and Gibbs energies of cytosine-BX3 have been obtained. The analyses of the combinations between cytosine and BX3 using the natural bond orbital (NBO) method and thermodynamics indicate that the complexes (a) and (e), which depend on the proton affinities of the oxygen on the cytosine and boron in BX3, are the most stable ones with their combination energies of −234.21 and −228.23 kJ.mol−1 (B3LYP method, BSSE corrected). Based on the calculation results, a reasonable method was employed to calculate the change in the enthalpies and Gibbs energies to form eight complexes in the gaseous state at 298.15K and 101.325 kPa. It can be shown that the conformers (a) and (e) are the most stable and form readily.

Fusion algebras, symmetric polynomials, and [formula omitted]-orbits of [formula omitted

A method of computing fusion coefficients for Lie algebras of type A N − 1 on level k was recently developed by A. Feingold and M. Weiner [A. Feingold, M. Weiner, Type A fusion rules from elementary group theory, in: S. Berman, P. Fendley, Y.-Z. Huang, K. Misra, B. Parshall (Eds.), Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory, Proceedings of an International Conference on Infinite-Dimensional Lie Theory and Conformal Field Theory, May 23–27, 2000, University of Virginia, Charlottesville, Virginia, in: Contemp. Math., vol. 297, Amer. Math. Soc., Providence, RI, 2002, pp. 97–115] using orbits of Z N k under the permutation action of S k on k-tuples. They got the fusion coefficients only for N = 2 and 3. We will extend this method to all N ⩾ 2 and all k ⩾ 1 . First we show a connection between Young diagrams and S k -orbits of Z N k , and using Pieri rules we prove that this method works for certain specific weights that generate the fusion algebra. Then we show that the orbit method does not work in general, but with the help of the Jacobi–Trudi determinant, we give an iterative method to reproduce all type A fusion products.

Effects of derivatization on solar-induced decomposition of polycyclic aromatic hydrocarbons in aqueous media

The solar-induced decomposition of 10 polycyclic aromatic hydrocarbons (PAHs) was observed in aqueous media. All 10 PAHs observed were half-decomposed within 120 min. Among anthracene derivatives, the decomposition rates were: anthracene = 1-methylanthracene < 2-methylanthracene < 9-methylanthracene < 9,10-dimethylanthracene ∼ 2-aminoanthracene. The addition of commercial humic acid had no effect on the decomposition rates of these PAHs. Deuterium water also hastened the decomposition of PAH. The products obtained by the solar radiation of PAH after extraction to DCM were mainly ketone and hydroxyl derivatives. To explaine these results, reactivities and electron charges at the constituent carbon atoms in each anthracene derivative were examined by an ab initio molecular orbital calculation method.

A notion of rank for unitary representations of reductive groups based on Kirillov's orbit method

We introduce a new notion of rank for unitary representations of semisimple groups over a local field of characteristic zero. The theory is based on Kirillov's method of orbits for nilpotent groups over local fields. When the semisimple group is a classical group, we prove that the new theory is essentially equivalent to Howe's theory of N-rank (see [Ho4], [L2], [Sc]). Therefore our results provide a systematic generalization of the notion of a small representation (in the sense of Howe) to exceptional groups. However, unlike previous works that used ad hoc methods to study different types of classical groups (and some exceptional ones; see [We], [LS]), our definition is simultaneously applicable to both classical and exceptional groups. The most important result of this article is a general “purity” result for unitary representations which demonstrates how similar partial results in these authors' works should be formulated and proved for an arbitrary semisimple group in the language of Kirillov's theory. The purity result is a crucial step toward studying small representations of exceptional groups. New results concerning small unitary representations of exceptional groups will be published in a forthcoming paper [S]

フラグメント分子軌道法に基づいた生体巨大分子の電子状態計算の現状と今後の展望

1999年に北浦らにより提唱されたフラグメント分子軌道(FMO)法は、分子系をフラグメントに分割し、フラグメントのモノマー、ダイマー・・・の計算から系全体を計算する方法であり、タンパク質やDNAのような巨大分子系全体を量子論的に扱う計算方法として、近年注目を集めている。本稿では、FMO法の概要と、多層FMO(MLFMO)法に基づいたタンパク質の励起状態計算、及びFMO法に基づいたconfiguration analysis for fragment interaction (CAFI)やvisualized cluster analysis of protein-ligand interaction (VISCANA)といった解析方法について報告し、FMO法の今後について展望する。

Electronic Structures of Dyes and Phthalocyanines Estimated with “Photo-Electron Spectroscopy in Air (PESA)”

AbstractThe near-edge electronic structures of several dyes and phtalocyanines were investigated using Photo-Electron Spectroscopy in Air (PESA). The ionization potentials (IPs) of N3, N719, Z907, D102, D149 and D205 were derived from observed photoemission threshold energies to be 5.88, 5.47, 5.44, 5.53, 5.44 and 5.49eV, respectively. Density of states (DOS) of Fe-, Ni-, Cu- and H2-phthalocyanines were deduced from differentiation of observed photoemission yields with incident photon energies. DOS thus obtained were well compared with calculated ones estimated with use of the DV-Xα molecular orbital calculation method.

2P058 フラグメント分子軌道(FMO)法を用いたRAN結合タンパク質Pumilioの配列認識特異性に関する理論研究(蛋白質(構造・構造機能相関),ポスター発表,第45回日本生物物理学会年会)

2P058 フラグメント分子軌道(FMO)法を用いたRAN結合タンパク質Pumilioの配列認識特異性に関する理論研究(蛋白質(構造・構造機能相関),ポスター発表,第45回日本生物物理学会年会)

Intermolecular interaction effects on second hyperpolarizabilities of clusters including charged species

We investigate the intermolecular-interaction effects on the longitudinal second hyperpolarizabilities (γ) for two types of π−π stacking clusters: C$_{5}$H$_{7}^{p}$ dimer and π-conjugated main chains (C$_{n}$H$_{np2}$, 6 l n l 16) interacting in both end regions with two allyl cations (C$_{3}$H$_{5}^{p})$. The γ values are calculated by the finite-field approach using several ab initio molecular orbital and density functional methods. It is found that in the first model the π− π interaction between the upper and lower π-orbitals significantly reduces the magnitude of effective γ per monomer, while the second model exhibits a remarkable enhancement of γ values as compared to those of isolated main chains. The analysis using the hyperpolarizability density and orbital interaction elucidates that the reduction of longitudinal γ value in the first model originates in the reduction of longitudinal π-conjugated electron distributions due to the perpendicular π−π orbital interactions, whereas the enhancement of longitudinal γ in the second model is caused by the intermolecular charge transfer between both end perturbing molecules via the main chain. On the basis of these results, we discuss a novel guideline of controlling third-order nonlinear optical properties of clusters.