Molecular normal vibrations: bond stretching

Further evidence for pi bonding is provided by the temperature coefficients of the resonance frequencies of these complex ions (see Table 6). The temperature coefficient is normally expected to be negative because of the decrease in the effective electric field gradient with increasing molecular bending vibrations (36,68, 69). Stretching vibrations do not reduce the principle electric field gradient (70). From Table 6... 

Thus, the force constants of the bonds, the masses of the atoms, and the molecular geometry determine the frequencies and the relative motions of the atoms. Fig. 2.1-3 shows the three normal vibrations of the water molecule, the symmetric and the antisymmetric stretching vibration of the OH bonds, and Va, and the deformation vibration 6. The normal frequencies and normal coordinates, even of crystals and macromolecules, may be calculated as described in Sec. 5.2. In a symmetric molecule, the motion of symmetrically equivalent atoms is either symmetric or antisymmetric with respect to the symmetry operations (see Section 2.7). Since in the case of normal vibrations the center of gravity and the orientation of the molecular axes remain stationary, equivalent atoms move with the same amplitude. 

The amplitude of the fundamental Raman wave is therefore determined by the variation of the molecular polarizability with the corresponding normal vibrational coordinate and this is turn is calculated by way of the variation of the tensor with local internal coordinates. Internal vibrational coordinates sq, such as local bond stretches, angle bends and torsions, are written as sums over the set of normal vibrational coordinates 49)... 

Six vibrational modes are expected for the pseudohalide hydracids for which the normal mode description and energies together with the molecular force constants are shown in Table 6. It is worth noting here that the N-H bond stretching force constant for HN3 is lower than that for HNCO and HNCS. This indicates that the latter are thermodynamically more stable compared with HN3. 

Here G and F are the mass and potential energy matrices on the internal coordinate basis R, A is the diagonal matrix of the squared vibrational frequencies, and L is the transformation matrix to normal coordinates, R = LQ. The choice of internal coordinates is the key to the success of the GF method. Internal coordinates are directly related to chemical descriptions of molecular motions in terms of bond stretches, bends, and torsions. The internal coordinates in Fig. 6.3, for example, describe in-plane vibrations of polyenes. 

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