Analytical technique for electroelastic field in piezoelectric bodies belonging to point group D ∞

2015 ◽  
Vol 61 (3) ◽  
pp. 270-284 ◽  
Author(s):  
Masayuki Ishihara ◽  
Yoshihiro Ootao ◽  
Yoshitaka Kameo
Keyword(s):  
Point Group ◽  
Electroelastic Field ◽  
Analytical Technique ◽  
Group D

A Conformational Analysis of the Spirocyclic Quaternary Ammonium Cation [(CH2)4N(CH2)4]+ in its Bromide and Picrate Salts

2004 ◽  
Vol 59 (3) ◽  
pp. 259-263 ◽  
Author(s):  
Uwe Monkowius ◽  
Stefan Nogai ◽  
Hubert Schmidbaur
Keyword(s):  
Gas Phase ◽  
Quaternary Ammonium ◽  
Point Group ◽  
High Yield ◽  
X Ray Diffraction ◽  
X Ray ◽  
Quaternary Ammonium Cations ◽  
Twist Conformation ◽  
Twist Form ◽  
Group D

High-yield syntheses of the bromide (1a) and picrate salts (1b) of the 5-azonia-spiro[4]nonane cation [(CH2)4N(CH2)4]+ are reported. In the single crystal X-ray diffraction analyses of the two salts the spirocyclic quaternary ammonium cations have their five-membered rings in envelop and twist conformations modified by packing forces. The conformation found experimentally for 1a has C2-symmetry as predicted for the gas phase by quantum-chemical calculations (RI-DFT, RI-MP2), but the five-membered rings are intermediate between the expected envelop and the twist form. For 1b, both of the two independent cations can be described as a combination of rings in an envelop and a twist conformation. According to the NMR spectra, in solution the cations are highly flexible and pseudosymmetrical (point group D2d)

scholarly journals Complex symmetrized calculations on ammonia vibrational levels

2005 ◽  
Vol 3 (3) ◽  
pp. 556-569
Author(s):  
Svetoslav Rashev ◽  
Lyubo Tsonev ◽  
Dimo Zhechev
Keyword(s):  
Vibrational Excitation ◽  
Point Group ◽  
Hamiltonian Formalism ◽  
Taylor Series Expansion ◽  
Excitation Energies ◽  
Molecular Potential ◽  
Vibrational Overtone ◽  
Symmetry Species ◽  
Molecular Potential Energy ◽  
Group D

AbstractThis paper introduces a fully symmetrized Hamiltonian formalism designed for description of vibrational motion in ammonia (and any XH3 molecule). A major feature of our approach is the introduction of complex basis vibrational wavefunctions in product form, satisfying the complex symmetry species (CSS) of the molecular symmetric top point group (D 3h). The described formalism for ammonia is an adaptation of the approach, previously developed and applied to benzene, based on the CSS of the point group D 6h. The molecular potential energy surface (PES) is presented in the form of a Taylor series expansion around the planar equilibrium state. Using the described formalism, calculations have been carried out on the vibrational overtone and combination levels in 14NH3 up to vibrational excitation energies corresponding to the fourth N-H stretch overtone. The results from the calculations are adjusted to experimentally measured data, in order to determine the values of the harmonic and some anharmonic force constants of the molecular PES.

Darstellung und Charakterisierung von Dekachlorodiiridat(IV), [Ir2Cl10]2-, und Normalkoordinatenanalyse an Dioktaederkomplexen des Typs [M2X10]2-, M = Re, Os, Ir, Pt; X = Cl, Br / Preparation and Characterization of Decachlorodiiridate(IV), [Ir2Cl10]2-, and Normal Coordinate Analysis of Bioctahedral Complexes [M2X10]2-, M = Re, Os, Ir, Pt; X = Cl, Br

1992 ◽  
Vol 47 (8) ◽  
pp. 1115-1118 ◽  
Author(s):  
P. Hollmann ◽  
W. Preetz
Keyword(s):  
Raman Spectra ◽  
Point Group ◽  
Ir And Raman Spectra ◽  
Normal Coordinate ◽  
Bridging Ligands ◽  
Valence Force ◽  
Group D ◽  
Ir And Raman ◽  
Good Agreement

On heating the tetraethylammonium salt of [IrCl6]2- with trifluoroacetic acid the edge sharing bioctahedral anion [Ir2Cl10]2- is formed, the IR and Raman spectra of which are assigned according to point group D2h. Normal coordinate analyses, based on a general valence force field, for [M2X10]2-, M = Re, Os, Ir, Pt; X = Cl, Br have been performed, resulting in a good agreement of the calculated frequencies with the bands observed in the IR and Raman spectra. Due to the stronger bonding of the terminal as compared to the bridging ligands, the valence force constants fd(MXt) are significantly higher than fd(MXb).

Laser Raman Spectra and Normal Coordinate Analysis of Some Uranyl Tetrachloride Complexes

1980 ◽  
Vol 34 (3) ◽  
pp. 327-331 ◽  
Author(s):  
Ken Ohwada
Keyword(s):  
Raman Spectra ◽  
Point Group ◽  
Normal Coordinate Analysis ◽  
Force Constants ◽  
Normal Coordinate ◽  
Magic Formula ◽  
Vibrational Assignments ◽  
Laser Raman ◽  
Laser Raman Spectra ◽  
Group D

Laser Raman spectra of uranyl tetrachloride complexes [K2UO2Cl4, Rb2UO2Cl4, Cs2UO2Cl4, (NH4)2UO2Cl4] have been measured in the region from 3500 to 10 cm−1. Vibrational assignments as well as normal coordinate analyses have been carried out with the assumption that all the complexes contain discrete (UO2Cl4)2− ions belonging to a point group D4h. To understand the nature of the uranyl bonds in the complexes, approximate π-bonding energies of such bonds have been estimated from the U—O stretching force constants. The reliability of the values obtained are discussed in detail on the basis of Mulliken's magic formula.

HIGH RESOLUTION RAMAN SPECTROSCOPY OF GASES: XV. ROTATIONAL SPECTRUM AND MOLECULAR STRUCTURE OF CYCLOBUTANE

1962 ◽  
Vol 40 (6) ◽  
pp. 725-731 ◽  
Author(s):  
R. C. Lord ◽  
B. P. Stoicheff
Keyword(s):  
Molecular Structure ◽  
Raman Spectroscopy ◽  
High Resolution ◽  
Bond Length ◽  
Raman Spectra ◽  
Point Group ◽  
Rotational Spectrum ◽  
Rotational Constants ◽  
Group D

An investigation of the rotational Raman spectra of normal and fully deuterated cyclobutane (C4H8 and C4D8) has given values of the rotational constants for these molecules. From these results it was found that the C—C bond length is 1.558 ± 0.003 Å, irrespective of whether cyclobutane belongs to the molecular point group D4h (planar C4 ring) or D2d (puckered C4 ring).

A Structural Study on Indium Tris-thiocarbamates

1994 ◽  
Vol 49 (2) ◽  
pp. 193-198 ◽  
Author(s):  
S. Bhattacharya ◽  
Miss Neena Seth ◽  
V. D. Gupta ◽  
H. Nöth ◽  
M. Thomann
Keyword(s):  
Structural Study ◽  
Nmr Spectra ◽  
Variable Temperature ◽  
Point Group ◽  
Molecular Structures ◽  
X Ray ◽  
H Nmr ◽  
Group D

Indium tris(thiocarbamates) In(S2CNiPr2)3 (1), In(SOCNiPr2)3 (2) and In(S2CNC4H4)3 (3) have been synthesized and characterized. Variable temperature 1H NMR spectra of 1 and 2 are reported. The X-ray molecular structures of 1 and 3 are found to be quite similar; the symmetry of the In(S2C)3 unit in 3 is close to point group D3 with small asymmetry in the In-S bonds.

scholarly journals Vibrational Spectra and Force Constants of Tetrasulfurtetranitride, S4N4 [1]

1981 ◽  
Vol 36 (8) ◽  
pp. 850-858 ◽  
Author(s):  
Ralf Steudel
Keyword(s):  
Force Field ◽  
Raman Spectra ◽  
Vibrational Spectra ◽  
Point Group ◽  
Force Constants ◽  
Infrared And Raman Spectra ◽  
Valence Force ◽  
Group D ◽  
Single Bonds ◽  
Good Agreement

Abstract Infrared and Raman spectra of solid and dissolved S414N4 and of solid S415N4 have been recorded and assigned in accordance with the molecular point group D2d. 22 of the 28 fundamental vibrations of both molecules have been identified and used to calculate force constants applying a modified Urey-Bradley force field with 9 independent constants. Good agreement between observed and calculated wavenumbers was obtained, and both Urey-Bradley and valence force constants are given. The results indicate that-S4N4 basically contains eight SN single bonds and two extremely weak SS bonds.

scholarly journals Schwingungsspektren und Normalkoordinatenanalyse der Acetatohalogenodimetallate M2(O2CCH3)4X2, M = Re, Tc; X = CI, Br/Vibrational Spectra and Normal Coordinate Analysis of Acetatohalogenodimetalates M2(O2CCH3)4X2, M = Re, Tc; X = Cl, Br

1992 ◽  
Vol 47 (4) ◽  
pp. 482-490 ◽  
Author(s):  
J. Skowronek ◽  
W. Preetz
Keyword(s):  
Point Group ◽  
Normal Coordinate Analysis ◽  
Normal Coordinate ◽  
Valence Force ◽  
Valence Force Field ◽  
First Time ◽  
Deformation Modes ◽  
Group D ◽  
Ir And Raman ◽  
Equatorial Ligand

Abstract The orange-red Tc2(O2CCH3)4Br2 has been prepared for the first time by reaction of [Tc2Br8]2- with glacial acetic acid and acetic anhydride. The IR and Raman spectra have been recorded at 80 K and are compared with those of the analogous compounds Tc2(O2CCH3)4Cl2, Re2(O2CCH3)4Cl2 and Re2(O2CCH3)4Br2. The assignment according to the point group D4h is supported by normal coordinate analysis based on a general valence force field. The quadruple M - M bond is stabilized by the bridging acetato and destabilized by the axial halogeno ligands. The valence force constants fd(MM) are determined to 3,96-4,08 mdyn/Å. The interaction constants fdd(MM/MX), fdd(MM/MO) and fdα (MM/MMO) are about three times higher for the technetates as compared with the rhenates. The stronger interaction between oppo­site bonds in the equatorial ligand sphere is revealed by the stretching interaction constants fdd', which are about two times higher than fdd for M - O bonds at right angles. The strong coupling of the ring co-ordinates implies extensive mixing of the M - O valence and deformation modes. The electronic spectra of Tc2(O2CCH3)4X2, agree with those of the corresponding Re compounds.

scholarly journals Affine coxeter group Wa(A4), quaternions, and decagonal quasicrystals

2014 ◽  
Vol 11 (04) ◽  
pp. 1450031 ◽  
Author(s):  
Mehmet Koca ◽  
Nazife Ozdes Koca ◽  
Ramazan Koc
Keyword(s):  
Coxeter Group ◽  
Dihedral Group ◽  
Golden Ratio ◽  
Point Group ◽  
Canonical Projection ◽  
Face Centered Cubic ◽  
Coxeter Number ◽  
Decagonal Quasicrystals ◽  
Coxeter Plane ◽  
Group D

We introduce a technique of projection onto the Coxeter plane of an arbitrary higher-dimensional lattice described by the affine Coxeter group. The Coxeter plane is determined by the simple roots of the Coxeter graph I2(h) where h is the Coxeter number of the Coxeter group W(G) which embeds the dihedral group Dh of order 2h as a maximal subgroup. As a simple application, we demonstrate projections of the root and weight lattices of A4 onto the Coxeter plane using the strip (canonical) projection method. We show that the crystal spaces of the affine Wa(A4) can be decomposed into two orthogonal spaces whose point group is the dihedral group D5 which acts in both spaces faithfully. The strip projections of the root and weight lattices can be taken as models for the decagonal quasicrystals. The paper also revises the quaternionic descriptions of the root and weight lattices, described by the affine Coxeter group Wa(A3), which correspond to the face centered cubic (fcc) lattice and body centered cubic (bcc) lattice respectively. Extensions of these lattices to higher dimensions lead to the root and weight lattices of the group Wa(An), n ≥ 4. We also note that the projection of the Voronoi cell of the root lattice of Wa(A4) describes a framework of nested decagram growing with the power of the golden ratio recently discovered in the Islamic arts.

scholarly journals DarsteIlung und Schwingungsspektren des 13C- und 18O-Hiarkierten trans-Dioxotetracyanoosmats(VI), [OsO2(CN)4]2- / Preparation and Vibrational Spectra of 13C and 18O Labelled trans-Dioxotetracyanoosmate(VI), [OsO2(CN)4]2-

1988 ◽  
Vol 43 (1) ◽  
pp. 94-98 ◽  
Author(s):  
W. Preetz ◽  
C. Sartori
Keyword(s):  
Acetic Acid ◽  
Anhydrous Methanol ◽  
Mutual Exclusion ◽  
Point Group ◽  
Tetragonal Symmetry ◽  
Weak Band ◽  
Stretching Vibration ◽  
Group D ◽  
Ir And Raman ◽  
Good Agreement

Abstract Through careful acidification of the aqueous solution of [OsO2(OH)4]2- in the presence of CN- or 13CN- with acetic acid, [OsO2(CN)4]2- or [OsO2(12CN)4]2- are formed, respectively. The reaction of Os18O4 and tetrabutylammonium cyanide with glacial acetic acid in anhydrous methanol yields [Os18O2(CN)4]2- . The shifts of the infrared and Raman bands of the isotopically labelled complexes are in good agreement with Teller-Redlich calculations. The degenerate E modes, expected for tetragonal symmetry, are split by approx. 15 cm-1, indicating an orthorhombic distortion of the complex ion in the solid state. Therefore, all the observed IR- and Raman frequencies are assigned according to point group D2h. For the complex containing an 18O=Os=18O axis, the symmetry is lowered to C2v, and the rule of mutual exclusion is restricted. This results in a weak absorption in the infrared spectrum of the Raman active symmetric OsO stretching vibration and vice versa a weak band in the Raman spectrum for the antisymmetric infrared active mode.

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