Tensor Operator Algebra for Point Groups

1979 ◽  
pp. 13-20
Author(s):  
E. König ◽  
S. Kremer
Keyword(s):  
Operator Algebra ◽  
Tensor Operator ◽  
Point Groups

Darstellung, Schwingungsspektren und Normalkoordinatenanalyse von Chloro-Bromo-Rhodaten(III) / Preparation, Vibration Spectra and Normal Coordinate Analysis of Chloro-Bromo-Rhodates(III)

1989 ◽  
Vol 44 (10) ◽  
pp. 1221-1227 ◽  
Author(s):  
W. Preetz ◽  
W. Kuhr
Keyword(s):  
Exchange Chromatography ◽  
Trans Isomers ◽  
Normal Coordinate ◽  
Valence Force ◽  
Trans Influence ◽  
Diethylaminoethyl Cellulose ◽  
Point Groups ◽  
First Time ◽  
Ir And Raman ◽  
Good Agreement

The mixed chloro-bromo-rhodates(III) [RhClnBr6-n]3-, n = 1-5, have been separated for the first time by ion exchange chromatography on diethylaminoethyl-cellulose. Due to the stronger trans-effect of Br, as compared with Cl, on treatment of [RhBr6]3- with conc. HCl nearly pure cis/fac-isomers for n = 2, 3, 4 are formed. The reaction of [RhCl6]3- with conc. HBr yields mixtures of the cis/trans-isomers for n = 2, 4, which cannot be separated, but mer-[RhCl3Br3]3 is formed stereospecifically. The IR and Raman spectra of all isolated mixed ligand complexes are completely assigned according to point groups Oh, D3d, C4v, C3v and C2v, supported by normal coordinate analyses based on a general valence force field. The good agreement of calculated and observed frequencies confirms the assignments. Due to the stronger trans-influence of Br as compared to Cl, in all asymmetric Cl—Rh—Br axes the Rh—Br bonds are strengthened and the Rh—Cl bonds are weakened, indicated by valence force constants for Rh—Br approximately 14% higher, for Rh—Cl 10% lower, as compared with the values calculated for symmetric Br—Rh—Br and Cl—Rh—Cl axes, respectively.

scholarly journals Operator Algebras with Unique Preduals

2011 ◽  
Vol 54 (3) ◽  
pp. 411-421 ◽  
Author(s):  
Kenneth R. Davidson ◽  
Alex Wright
Keyword(s):  
Banach Space ◽  
Operator Algebra ◽  
Free Semigroup ◽  
Operator Algebras ◽  
Compact Operators ◽  
Semigroup Algebra ◽  
Dense Subalgebra

AbstractWe show that every free semigroup algebra has a (strongly) unique Banach space predual. We also provide a new simpler proof that a weak-∗ closed unital operator algebra containing a weak-∗ dense subalgebra of compact operators has a unique Banach space predual.

Teaching Molecular Symmetry of Dihedral Point Groups by Drawing Useful 2D Projections

2015 ◽  
Vol 92 (8) ◽  
pp. 1422-1425 ◽  
Author(s):  
Lan Chen ◽  
Hongwei Sun ◽  
Chengming Lai
Keyword(s):  
Molecular Symmetry ◽  
Point Groups
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