Normal Coordinate Calculations

The spectral assignment of vibrational bands in any molecular system, and in particular the assignment of the metal-ligand vibrations as well as the 

A normal coordinate analysis (NCA) for hexazacyclophane Cu(II) complex was performed by using the Wilson s force field geometrical matrix (FG) method . An INDO/1 optimized molecular geometry was used to build the G matrix . The CuN distance is 1.84 A for the copper atom in the macrocycle plane this bond length is relatively short in comparison to that reported for the non-macrocycle tris-(l,10-phenantroline)Cu(II) (2.1 A) the planar macrocycles copper porphin (2.031 and tetraazacyclotetradecane Cu(II) derivatives (2.08 

The force constant values sequence for the CC bonds FCC has been proposed on the basis of INDO/1 bond orders. The same follows for the FCN values. No attempt to improve the difference between the experimental and calculated frequencies was performed.  

The most relevant experimental and calculated frequencies along with the potential energy distribution (FED) are displayed in Table 14.2. Due to the extended 7t electronic system, the FED shows a high degree of coupling between most of the normal modes. 

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The frequencies of some vibrational bands are sensitive to molecular conformation. Normal coordinate calculations are useful for assigning observed vibrational spectra and deducing from them precise structural information. Normal coordinate calculations were... 

Schachtsneider, J. H. and Snyder, R. G. Vibrational analysis of the n-paraffins - II Normal coordinate calculations. Spectrochim. Acta 19, 117 (1963). 

Formic acid H.COOH and acetic acid CH3.COOH were studied in the crystalline state by Carlson, Witkowski and Fateley, 66> in the far infra-red region, while Fukushima and Zwolinski, 67> gave a normal coordinate calculation of acetic acid dimers (CH3.COOH)2 the acetate ion in Li(CH3.C00).2H20 was studied by Cadene 168>, while DiLauro, Califano and Adembri 169> studied the crystal spectra and normal modes of the anhydrides of maleic and succinic acids in polarized light. 

Only some publications are devoted to the vibration spectra of nitrobenzothiazoles [214, 785, 786, 795, 1113, 1114]. The infrared and Raman frequencies of 2-amino-6-nitrobenzothiazole have been assigned to different modes of vibrations on the basis of normal coordinate calculations assuming Cs point group symmetry [1114], The structure of Alkoxysilane Dye on the base of nitrobenzothiazole has been confirmed by IR spectra [786] ... 

HedbCTg, L. Hedbag, K. Cheng, P.-C. Scott, L. T. Gas-phase molecular structure of corannulene, C20H10. An electron-diffraction study augmented by ab initio and normal coordinate calculations, J. Phys. Chem. A 2000,104, 7689-7694. 

When appropriate, normal coordinate calculations were run to confirm the band assignments and to deduce force fields for the trapped species. 

Normal coordinate calculations were used to model this splitting by lowering of the N-0 or Cl-0 force constant of the coordinated... 

Clearly, the effects of ion pair formation in matrix isolation spectra are apparent, particularly in the removal of degeneracy of vibrational modes. However, these can be fit quite well with normal coordinate calculations which show that ion pairing effects cause significant force constant changes. Moreover, it is apparent that the energetics of ion pair formation do provide a limit as to the species which can be studied in this fashion. However, for the species which can be stabilized in this manner, the technique is still effective and provides a model for both ion-molecule reactions and CsF catalysis. 

In the Raman spectrum of polyethylene the main peak of the bending vibrations is observed at 1437 cm, while a wagging vibration shows a weak band at 1370 cm and a twisting vibration gives a strong band at 1295 cm The stretching vibrations of the C-C chain are observed at 1126 and 1059 cm, respectively, in the Raman spectrum (Figs. 4.1-2A and 4.1-3). A normal coordinate calculation of polyethylene is published by Tasumi et al. (1962). 

Two types of parameters appear in this expression, m/ represents bond dipole moments, while dm/ / d/ /. represents derivatives of the bond dipole moment with respect to the internal coordinates (bond stretching, angle deformation, out-of-plane deformation, and torsion). These parameters are referred to as electro-optical parameters (eop). All other quantities are derived from the structure or from the normal coordinate calculation. The electro-optical parameters can be derived from measured intensities, like force constants are derived from measured frequencies. Compared to the determination of force constants, the problem in this case is that the number of parameters is much higher. 

In the solid state, Se02 has a polymeric structure of comer-linked flattened SeOs pyramids, each carrying a pendant terminal O atom. Mass spectrometric studies of the vapor over solid Se02 at 400 K indicate small amounts (1%) of dimeric Se02 in the gaseous phase. A normal-coordinate calculation for the four possible syrmnetries of (Se02)2 prove the centrosymmetric Cih chair configuration (11) for the dimeric molecule. ... 

Pyrazole, in all possible states, either free or complexed, shows C symmetry, with positions 3 and 5 clearly differentiated, even if it is not possible to assign individual bands to these positions, for example t (CH) or y (CH). Both research groups carried out normal coordinate calculations using different potentials. In spite of the large amount of data obtained, the problem is not definitively settled and more experimental work and quantum mechanical calculations are to be expected in the next few years. 

In the absence of normal coordinate calculations for the free bases all investigations of the infrared spectra of bipyridyl and phenanthroline complexes have necessarily been empirical. 

Normal coordinate calculations of large hydrocarbon molecules and... 

Begun et al. (2) report the infrared (gas phase) and Raman (liquid phase) spectra and correlate the observations by means of normal coordinate calculations for the similar molecules BrF, IF, 5 XeOF. The fundamental frequencies are taken from Begun et al. (2) except for Ug which was beyond the range of their Infrared measurements. The value Wg = 245 cm" for the gas has been observed by McDowell and Asprey (2) and is confirmed by 237 cm" found in the Raman spectra of the liquid. Raman values from the liquid were used for the infrared inactive fundamentals and Vg. One Raman active frequency, persumably Vg, is not observed in any of the four molecules. The value Vg = 281 cm" was obtained from the normal coordinate calculation. Previous Raman studies were reported by Stephenson and Jones (4). 

Rogers et al. (6), and with the X-ray crystal structure obtained by Robinson and Bensey (7 ). Bond distances were based on those in the crystal and the bond angle was assumed to be 90 , slightly larger than those in the crystal (80.5-86.5 ). Begun et al. (2) indicate that the angle in the gaseous molecule is probably not exactly 90 but that the normal coordinate calculations are not... 

In the past, force constant and normal coordinate calculations of water molecules were reported for all internal librations ... 

Butadiene (CH2=CH—CH=CH2) has two C=C bonds and one C—C bond. It has been shown experimentally that the most stable rotamer has the planar s-trans structure . The lengths of the C=C and C—C bonds are 1.341 and 1.463 A, respectively. The infrared and Raman spectra of 1,3-butadiene in the vapour, liquid and solid phases have been studied The spectra of deuterated and C-substituted analogs have been studied for the purpose of the assignments of vibrational spectra. On the basis of these vibrational spectra, normal coordinate calculations have been performed by the use of empirical force fields . The stmcture and vibrational frequencies of the s-trans conformer have been calculated by ab initio MO methods . The assignments of all the fundamental bands have been established. 

A gas-phase electron diffraction smdy has shown that irons-hexatriene has a planar structure and the lengths of the terminal C=C, central C=C and C—C bonds are 1.337, 1.368 and 1.458 A, respectively. The infrared and Raman spectra of irons-hexatriene and its deuterated analogs have been reported. Normal coordinate calculations have been performed by the extended Pariser-Parr-Pople Cl method, the QCFF/Pl method and ab initio MO methods . There are 36 normal modes l3ag + 6 u+ l2 u + 5 . 

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