Stretching and bending

The analogous coupling between the antisyimnetric stretch and bend is forbidden in the H2O Hamiltonian because of syimnetry.) The 2 1 resonance is known as a Femii resonance after its introduction [ ] in molecular spectroscopy. The 2 1 resonance is often very prominent in spectra, especially between stretch and bend modes, which often have approximate 2 1 frequency ratios. The 2 1 couplmg leaves unchanged as a poly ad number the sum ... 

Figure Al.2.11. Resonant collective inodes of the 2 1 Fenni resonance system of a coupled stretch and bend with an approximate 2 1 frequency ratio. Shown is one end of a syimnetric triatomic such as H2O. The nomial stretch and bend modes are superseded by the horseshoe-shaped modes shown in (a) and (b). These two modes have different frequency, as further illustrated in figure Al.2.12.

The above expressions are empirical approaches, with m and D. as parameters, for including an anliamionic correction in the RRKM rate constant. The utility of these equations is that they provide an analytic fomi for the anliamionic correction. Clearly, other analytic fomis are possible and may be more appropriate. For example, classical sums of states for Fl-C-C, F1-C=C, and F1-C=C hydrocarbon fragments with Morse stretching and bend-stretch coupling anhamionicity [M ] are fit accurately by the exponential... 

Figure A3.13.9. Probability density of a microcanonical distribution of the CH cliromophore in CHF within the multiplet with cliromophore quantum nmnber V= 6 (A. g = V+ 1 = 7). Representations in configuration space of stretching and bending (Q coordinates (see text following (equation (A3.13.62)1 and figure A3.13.10). Left-hand side typical member of the microcanonical ensemble of the multiplet with V= 6...

One can start building up a list of MM3 parameters by use of the TINKER analyze command. Don t expect to build up the entire set, which occupies about 100 pages in the MM3 user s manual, but do obtain a few representative examples to get an idea of how a parameter set is constr ucted. From previous exercises and projects, you should have input and output geometries for an alkene, an alkane, and water. From these, the object is to determine the stretching and bending parameters for the C—C, C=C, C—H, and O—H bonds. The C—H bond parameters are not the same... 

Table 4-2 Some Stretching and Bending Parameters from the MM3 Parameter Set...

In the case of ethylene, because of 2-fold symmetry, odd terms drop out of the series, V3, V5,... = 0. In the case of ethane, because of 3-fold symmeti-y, even temis drop out, V2, V4,... = 0. Terms higher than three, even though permitted by symmetry, are usually quite small and force fields can often be limited to three torsional terms. Like cubic and quaitic terms modifying the basic quadratic approximation for stretching and bending, terms in the Fourier expansion of Ftors (to) beyond n = 3 have limited use in special cases, for example, in problems involving octahedrally bound complexes. In most cases we are left with the simple expression... 

Amides —CO— (See also Table 7.49 for NH stretching and bending-) Primary —CONH2 In solution ca 1690 Amide I C=0 stretching... 

In addition to the descriptions of group vibrations as stretch and bend (or deformation) the terms rock, twist, scissors, wag, torsion, ring breathing and inversion (or umbrella) are used frequently these motions are illustrated in Figure 6.13. 

For aromatic hydrocarbon molecules, in particular, the main acceptor modes are strongly anharmonic C-H vibrations which pick up the main part of the electronic energy in ST conversion. Inactive modes are stretching and bending vibrations of the carbon skeleton. The value of Pf provided by these intramolecular vibrations is so large that they act practically as a continuous bath even without intermolecular vibrations. This is confirmed by the similarity of RLT rates for isolated molecules and the same molecules imbedded in crystals. 

Fig. 4.59. Raman spectrum of methyl mercaptan (a) and SERS spectrum of methyl mercaptide (b) formed by adsorption ofthe mercaptan on a silver surface. The surface reaction is proven by the disappearance ofthe S-H stretching and bending bands at 2575 cm" and 806 cm", respectively. The Raman shift ofthe C-S stretching band at approximately 700 cm" is reduced during adsorption by withdrawal of electron density from the C-S, because of bonding to the silver. The symmetric methyl stretching appears above 2900cm" [4.303].

Infrared (IR) spectroscopy (Section 13.20) Analytical technique based on energy absorbed by a molecule as it vibrates by stretching and bending bonds. Infrared spectroscopy is useful for analyzing the functional groups in a molecule. 

Morterra and Low109,110 proposed that thermal crosslinking may occur between 300°C and 500°C where phenolic hydroxyl groups react with methylene linkages to eliminate water (Fig. 7.43). Evidence for this mechanism is provided by IR spectra which show decreased OH stretches and bending absorptions as well as increased complexity of the aliphatic CH stretch patterns in this temperature range. 

Fig. 18 Raman spectra of the stretching and bending vibrations of pSg at two different temperatures corresponding to the twofold disorder of one-third of the molecules (373 K) and to the ordered structure (40 K), after [146]. Spectral resolution was 0.75 cm ...

First attempts to model the vibrational spectrum of polymeric sulfur have been reported by Dultz et al. who assumed a planar zig-zag chain structure [172]. The calculated vibrational DOS was in qualitative agreement with the observed Raman spectrum of fibrous sulfur. However, some details of the spectrum like the relative intensities of the modes as well as the size of the gap between stretching and bending vibrations could not be reproduced exactly by this simplified model [172]. 

Ground-state effects, i.e., the effects on the bond lengths and angles, stretching and bending force constants, and other spectroscopic properties of the other ligands. 

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