Frequency of stretch vibrations

The Overend s [9] Fermi resonance (FR) theory was adopted according to Odinokov [10] in the calculation of the bridging hydroxyl frequencies of stretching vibration v(OH) and overtones of inplane 25(OH) and out-of-plane 2y(OH) vibrations unperturbed by Fermi resonance from the experimental spectrum. It is considered that the separation of unperturbed AE° = - E% and... 

Frequency of stretching vibrations of OH groups vibrating in the largest pores and/or cages of the respective zeolites abbreviated as OH frequency . 

The frequencies of stretching vibrations can usually be roughly predicted from knowledge of the bond order and the atomic masses. However, the values of the force constants involved in deformations are not obvious, so that their frequencies often appear to be rather arbitrary. The total number of vibrations for a nonlinear molecule is given by the relation, 3N-6, where N is the number of atoms. 

According to various possible hydrolysis mechanisms described in the literature, a proton is transferred either from an oxygen atom (o" Ser-195 or oxygen in water), or from a nitrogen atom in the imidazole ring. The frequencies of stretching vibrations of the 0-H bond in water and alcohol (Ser) are similar and equal to 3650 cm . ... 

It is also possible to measure microwave spectra of some more strongly bound Van der Waals complexes in a gas cell ratlier tlian a molecular beam. Indeed, tire first microwave studies on molecular clusters were of this type, on carboxylic acid dimers [jd]. The resolution tliat can be achieved is not as high as in a molecular beam, but bulk gas studies have tire advantage tliat vibrational satellites, due to pure rotational transitions in complexes witli intennolecular bending and stretching modes excited, can often be identified. The frequencies of tire vibrational satellites contain infonnation on how the vibrationally averaged stmcture changes in tire excited states, while their intensities allow tire vibrational frequencies to be estimated. 

The symmetric stretching vibration. During this vibration the ellipsoid breathes (i.e. expands and contracts) at the frequency of the vibration (Fig. 4). The dimensions of the ellipsoid obviously change during the vibration and consequently the vibration is Raman active. 

Infrared activity of vibrations is readily deduced. The symmetric stretching vibration has no associated dipole moment change during the vibration and is, therefore, infrared inactive. The asymmetric stretching vibration has an associated dipole moment which fluctuates with the frequency of the vibration. The vibration is, therefore, infrared active. 

The value of stretching vibrational frequency can be calculated fairly easily by application of HOOK s law which may be represented as ... 

Neither of these vibrations corresponds to stretching vibrations of AH or BH. The antisymmetric vibrational mode represents translational motion in the transition state and has an imaginary force constant. The symmetric transition-state vibration has a real force constant but the vibration may or may not involve motion of the central H(D) atom2,12 13. If the motion is truly symmetric, the central atom will be motionless in the vibration and the frequency of the vibration will not depend on the mass of this atom, i.e. the vibrational frequency will be the same for both isotopically substituted transition states. It is apparent that under such circumstances there will be no zero-point energy difference... 

Characteristic frequencies of molecular vibrations. In the case of HCN, for example, there are four vibrational frequencies that may be calculated from a polynomial equation of degree four, by making appropriate assumptions about the stiffness of bond stretching and bond angle deformation. 

The estimated frequency (v) falls into the submillimeter region. Such behavior was predicted [16, 51] from experimental spectroscopic studies. The mean transverse-vibration amplitude is about 0.5 A (see Table XXI). About the same is also the mean path (8h) = r sin (50) of fluctuations stipulated by rotational motions. Note that the estimated amplitude of stretching vibrations is only approximately 0.2 A [see Eq. (311)]. 

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