scholarly journals On the planarity of the NSi3 skeleton in the trisilylamine molecule. A normal coordinate analysis involving complex symmetry coordinates

1979 ◽  
Vol 57 (14) ◽  
pp. 1779-1784 ◽  
Author(s):  
H. F. Shurvell ◽  
A. Dunham ◽  
S. J. Cyvin ◽  
J. Brunvoll
Keyword(s):  
Secular Equation ◽  
Point Group ◽  
Irreducible Representations ◽  
Complex Numbers ◽  
Normal Coordinate ◽  
Energy Distributions ◽  
Normal Vibrations ◽  
Interaction Terms ◽  
Symmetry Coordinates ◽  
Unusual Problem

Normal coordinate calculations have been carried out for the N(SiH3)3 molecule. A model with C3h symmetry was used, which is based on a planar NSi3 skeleton. The presence of complex numbers for the characters of degenerate irreducible representations of the point group C3h leads to an unusual problem when factoring the G and F matrices. A set of real degenerate symmetry coordinates for the E′ and E′′ species can be constructed, but these are not true symmetry coordinates under the C3h point group. However, they can be obtained from the genuine (complex) symmetry coordinates by a unitary transformation. For a degenerate species, this procedure leads to a and b blocks of the factored G and F matrices, which contain interaction terms. Consequently both blocks must be taken together when forming the secular equation, and subsequently the calculated frequencies appear as pairs of identical numbers.A valence force field that includes all reasonable interactions has been obtained and used to predict the wavenumbers of the 15N and d9 isotopic molecules. Details of the normal vibrations in the three molecules have been obtained from potential energy distributions. The results show reasonable agreement with the limited experimental data available for the isotopic molecules.

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.

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.

Schwingungsspektren und Kraftkonstanten der Hexacyano-Komplexe des Mangan(I), Technetium(I) und Rhenium(I) / Vibrational Spectra and Force Constants of the Hexacyano Complexes of Mangan(l), Technicium(I) and Rhenium(l)

1972 ◽  
Vol 27 (8-9) ◽  
pp. 1193-1196 ◽  
Author(s):  
W. Krasser ◽  
K. Schwochau
Keyword(s):  
Force Field ◽  
Raman Spectra ◽  
Vibrational Spectra ◽  
Point Group ◽  
Force Constants ◽  
Irreducible Representations ◽  
Infrared And Raman Spectra ◽  
Valence Force ◽  
Valence Force Field ◽  
Complex Salts

The infrared and Raman spectra of the complex salts K5[Mn(CN)6], K5[Tc(CN)6] and K5[Re(CN)s] have been recorded in the range from 4000 to 40 cm-1. All expected fundamental vibrations have been observed and could be assigned to the irreducible representations of the sym­metry point group Oh . The calculation of the force constants is based on the concept of the generalized valence force field. The low CN-valence force constants indicate the relatively strong Π-bonding character of the metal carbon bond, which is especially pronounced for K5[Tc(CN)6).

Vibrational Spectra of Phenylphosphonic and Phenylthiophosphonic Acid and their Complete Assignment

2010 ◽  
Vol 65 (3) ◽  
pp. 357-s374 ◽  
Author(s):  
Wolfgang Förner ◽  
Hassan M. Badawi
Keyword(s):  
Conformational Equilibrium ◽  
Dihedral Angles ◽  
Torsional Angle ◽  
Vibrational Modes ◽  
Infrared And Raman Spectra ◽  
Normal Coordinate ◽  
Energy Distributions ◽  
Phenylphosphonic Acid ◽  
Low Intensity ◽  
Complete Assignment

The structures and conformational stabilities of phenylphosphonic acid and phenylthiophosphonic acid were investigated using calculations mostly at DFT/6-311G** and ab initio MP2/6-311G** level. From the calculations the molecules were predicted to exist in a conformational equilibrium consisting of two conformers which as enantiomers have the same energy, but rather unexpected dihedral angles XPCC (X being O or S) which are not equal to zero. The antisymmetric potential function for the internal rotation was determined for each one of the molecules. In these functions the conformers with zero dihedral angles appear to be stable minima (also optimization converges to this), but the vibrational frequency for the torsion turned out to be imaginary, indicating that they are maxima with respect to this symmetry coordinate. Only optimization without any restrictions and starting from a non-zero torsional angle converged to a real minimum with such a geometry (“non-planar”). For that minimum structure infrared and Raman spectra were calculated, and those for phenylphosphonic acid were compared to experimental data, showing satisfactory agreement. This gives confidence to present the spectra of phenylthiophosphonic acid as a prediction. The rather low intensity of the OH bands in the experimental infrared spectrum (as compared to normal organic acids) indicates rather weak hydrogen bonding. Normal coordinate calculations were carried out, and potential energy distributions were calculated for the molecules in the non (near)-planar conformations providing a complete assignment of the vibrational modes to atomic motions in the molecules. From the rather low rotational barriers we conclude, in agreement with results from the literature (for other P=O compounds) based on localized orbitals that conjugation effects are absent - or at least negligible - as compared to electrostatic and steric ones in determining the structures of the stable conformers in the phenyl derivatives. The P=O (and also the P=S) bond is highly polarized according to our analysis of Mulliken populations. The polarization turned out to be smaller in the thiophosphonic acid due to the smaller electronegativity of sulfur as compared to oxygen.

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.

Vibrational Total Energy Distributions in Terms of Symmetry Coordinates, Forces and Momenta

1980 ◽  
Vol 35 (4) ◽  
pp. 464-465
Author(s):  
Alain J. P. Alix ◽  
Erling Rytter
Keyword(s):  
Total Energy ◽  
Polyatomic Molecules ◽  
Vibrational Modes ◽  
Energy Distributions ◽  
Symmetry Coordinates ◽  
Generalized Symmetry ◽  
Normal Vibrational Modes

Abstract The fundamental definitions of the Total Energy and of the Vibrational Total Energy Distributions are presented in details in terms of either symmetry coordinates, or generalised symmetry forces, or generalized symmetry coordinates. This, give now a uniform tool for physicists and chemists in the field of characterisation of the normal vibrational modes of polyatomic molecules.

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