Chapter 5. Vibrational problem in symmetry coordinates

2014 ◽  
Keyword(s):  
Symmetry Coordinates ◽  
Vibrational Problem

Vibrational Analysis of Polymeric Hydrogen Fluoride: Cyclic (HF)6

1973 ◽  
Vol 28 (11) ◽  
pp. 1787-1793 ◽  
Author(s):  
S. J. Cyvin ◽  
V. Devarajan ◽  
J. Brunvoll ◽  
Ø . Ra
Keyword(s):  
Electron Diffraction ◽  
Hydrogen Fluoride ◽  
Secular Equation ◽  
Point Group ◽  
Vibrational Analysis ◽  
Irreducible Representations ◽  
Mean Amplitudes Of Vibration ◽  
Symmetry Coordinates ◽  
Vibrational Problem ◽  
Complex Characters

The molecular vibrations of cyclic (HF)6 are studied. The consequences of complex characters for irreducible representations of the appropriate point group (C6h) are elucidated. The secular equation of the vibrational problem is solved in terms of real coordinates. Those of the degenerate species were obtained by a transformation of the complex symmetry coordinates. The force constants were taken from solid HF data. Mean amplitudes of vibration were calculated and compared with electron diffraction results.

Symmetry Coordinates, Harmonic Force Field, and Mean Amplitudes for Light and Heavy Dibenzene Chromium

1971 ◽  
Vol 54 (4) ◽  
pp. 1517-1522 ◽  
Author(s):  
S. J. Cyvin ◽  
J. Brunvoll ◽  
Lothar Schäfer
Keyword(s):  
Force Field ◽  
Harmonic Force ◽  
Symmetry Coordinates

Symmetry Coordinates and Lattice Vibrations of LaCl3

1964 ◽  
Vol 40 (3) ◽  
pp. 743-753 ◽  
Author(s):  
J. Murphy ◽  
H. H. Caspers ◽  
R. A. Buchanan
Keyword(s):  
Lattice Vibrations ◽  
Symmetry Coordinates

Schwingungsberechnungen der Species Ti2Cl102− , Ti2Cl9− und TiCl5− / Molecular Vibration Analysis of Ti2Cl102− , Ti2Cl9− and TiCl5−

1979 ◽  
Vol 34 (3) ◽  
pp. 362-368 ◽  
Author(s):  
A. F. Demiray ◽  
W. Brockner ◽  
B. N. Cyvin ◽  
S. J. Cyvin
Keyword(s):  
Potential Energy ◽  
Matrix Method ◽  
Vibration Analysis ◽  
Molecular Model ◽  
Molecular Vibration ◽  
Normal Coordinate ◽  
Energy Distributions ◽  
Mean Amplitudes Of Vibration ◽  
Symmetry Coordinates ◽  
The Mean

AbstractNormal coordinate analyses of the chlorotitanate ions Ti2Cl102−Ti2Cl9− - and TiCl5− have been carried out following Wilson's FG matrix method. The final force constants are given in terms of symmetry coordinates, which are thoroughly specified for a Ti2Cl9− molecular model. Assignments of the vibrational frequencies of the title compounds are proposed, and the corresponding potential energy distributions are given. The final force fields were used to calculate the mean amplitudes of vibration, of which those of TiCl5− and selected values of Ti2Cl102− andTi2Cl9− are reported.

Symmetry Coordinates and Tentative Force Field Analysis of a PMo12O40 Model with the Keggin Structure

1976 ◽  
Vol 31 (12) ◽  
pp. 1589-1600 ◽  
Author(s):  
Lennart Lyhamn ◽  
S. J. Cyvin ◽  
B. N. Cyvin ◽  
J. Brunvoll
Keyword(s):  
Experimental Data ◽  
Force Field ◽  
Force Constant ◽  
Raman Spectra ◽  
Vibrational Analysis ◽  
Field Analysis ◽  
Infrared And Raman Spectra ◽  
Symmetry Coordinates ◽  
Force Field Analysis ◽  
Complex Ion

Abstract A complete vibrational analysis is performed for the 53 atomic PMo12O40 model of Td symmetry. The symmetry coordinates are classified into those of (a) ligand vibrations, (b) framework-ligand couplings, (c) framework vibrations, and (d) interligand vibrations. Simple valence force fields are estimated, and the influence of inclusion of redundancies on the calculated frequencies and symmetry force constants is investigated. Comments are made on calculated symmetry force constant values up to 345 mdyne/Å. Vibrational frequencies are calculated for the Mo3O7 and Mo3O13 units and for the PMo12O403- complex ion. For the latter compound the calculated values are compared with experimental data from infrared and Raman spectra.

Normalkoordinatenanalyse und Frequenzberechnungen für die isotopomeren closo-Hydrohexaborate 11Bn10B6-nH62- , n = 0 – 6 / Normal Coordinate Analysis and Frequency Calculations of Isotopomeric closo-Hydrohexaborates 11Bn10B6-nH62- , n = 0 – 6

1990 ◽  
Vol 45 (5) ◽  
pp. 641-646 ◽  
Author(s):  
J. Thesing ◽  
W. Preetz
Keyword(s):  
Potential Energy Distribution ◽  
Geometric Isomers ◽  
Normal Coordinate ◽  
Valence Force Field ◽  
Small Coupling ◽  
Atomic Displacements ◽  
Symmetry Coordinates ◽  
Statistical Frequency ◽  
Degenerate Modes ◽  
Ir And Raman

Normal coordinate analyses for the ten isotopomers Cs211Bn10B6-nH6, n = 0 — 6, including the pairs of geometric isomers for n = 2, 3, 4 have been performed, based on a general valence force field. The shift of the bands as well as the splitting of degenerate modes by lowered symmetry due to exchange of 10B by 11B or H by D is exactly calculated by a set of six force constants. The characteristic band patterns observed in the IR and Raman spectra of Cs2B6H6 with natural abundance of B isotopes (80.22% 11B, 19.78% 10B) measured at 10 K are explained by the superposition of the calculated spectra of the different isotopomers present, according to their statistical frequency distribution. The calculated atomic displacements and the potential energy distribution on the symmetry coordinates reveal only a small coupling (PED < 10%) between the cage (in-phase displacements of H and B) and substituent vibrations (anti-phase motions of B and H). Based on the normal coordinate analyses previously obtained assignments for several bands are revised.

Mixing of symmetry coordinates in methyl cyanide and methyl isocyanide

1964 ◽  
Vol 20 (6) ◽  
pp. 1065-1070 ◽  
Author(s):  
William H. Fletcher ◽  
Charles S. Shoup ◽  
William T. Thompson
Keyword(s):  
Methyl Cyanide ◽  
Symmetry Coordinates ◽  
Methyl Isocyanide
Sign in / Sign up

Export Citation Format

Share Document