Water antisymmetric stretch

The IR spectmm of water at room temperature and one atmosphere pressure [61 63] is peaked at about 3400 cm 1 and has a weak shoulder at about 3250 cm 1 and a FWHM of about 375cm 1. Raman spectra are quite different [49, 64 70] The VV spectmm is bimodal, with strong peaks at about 3400 and 3250 cm 1, and an FWHM of about 425 cm 1, while the VH spectmm peaks at about 3460 cm l, is quite asymmetric, and has a FWHM of about 300 cm 1. Note that the gas-phase water molecule has symmetric and antisymmetric stretch fundamentals (both of which are IR and Raman active) at 3657 and 3756 cm 1, respectively, and so the liquid-state spectra are significantly red-shifted from these values furthermore, the breadths of the liquid-state spectra are substantially larger than this gas-phase splitting. 

By the symmetry of a normal mode of vibration, we mean tbe symmetry of the nuclear framework under the distortion introduced by the vibration. Pictorially, the symmetry of the normal mode is equal to the symmetry of the pattern of arrows drawn to indicate the directions of the nuclear displacements. The normal modes of vibration of water are the symmetric and antisymmetric stretches, and the angle bend, shown in Figure 6-1. 

FIGURE 3.13 The three normal vibrational modes of water. For the top mode (the symmetric stretch) both O-H bonds are extended or compressed at the same time. For the middle mode (the antisymmetric stretch) one O-H bond is extended when the other is compressed. The bottom mode is called the bend. In every case the hydrogen atoms move more than the oxygen, because the center of mass has to stay in the same position (otherwise the molecule would be translating). For a classical molecule (built out of balls and perfect springs) these three modes are independent. Thus, for example, energy in the symmetric stretch will never leak into the antisymmetric stretch or bend modes. 

Since the symmetry coordinates of water are good approximations of the normal vibrations, the pictorial representations are applicable to them as well. Indeed, the three normal modes of Figure 5-4 are the same as the symmetry coordinates we just derived. The A symmetry stretching mode is called the symmetric stretch while the B2 mode is the antisymmetric stretch. 

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. 

Figure 2.1-3 Motional degrees of freedom of the water molecule, T, are translations and Ri rotations of the whole molecule, i = x, y, z Os is the symmetric, Ua the antisymmetric stretching vibration, 6 the deformation vibration.

In the case of strong distortion, i.e., energy differences > 180 cm for OH modes and > 130 cm for OD modes, coupling of the two OH (OD) vibrations of the H2O (D2O) molecules to a symmetric and an antisymmetric stretching mode (vj and V3) does not take place as for the OH and OD vibrations of HDO molecules. This was shown and estabhshed first by Schiffer and Homig In this case, the frequencies of the two uncoupled bands resemble those of the H2O (D2O) bands in the spectra of the neat hydrates and deuterohydrates, respectively. The most distorted H2O molecules known so far are found in MgS03 3 H2O with Avod(oh) 210(390) cm In the case of undistorted, i.e., symmetrical, water molecules, the uncoupled HDO bands (vqh and Vqd) (or the mean values of the two OH and OD bands of distorted molecules) are found intermediate between Vi and V3 of the H2O and D2O molecule, provided that there is no intermolecular coupling (see Sect. 4.1) of the water bands in the neat compounds. 

The lattice site distortion of water molecules is further shown by the relative intensities of Vi and V3 of H2O (D2O) in the Raman spectra. In the case of not (or only little) distorted H2O molecules, the Raman intensities of the antisymmetric stretching modes V3 are very low ... 

Fig. 3.21 Normal modes of vibralion of (he water molecule (a) symmetrical stretching mode. (b) bending mode, Mi (c) antisymmetrical stretching mode. and their transformations under Cj,. symmetry operations.

Classically, a transducer is a device able to convert energy of one type into energy of other type for instance, a microphone converts pressure vibrations in air into an electrical current. In this case, we extend the use of the term transducer to include, for instance, changes in molecular potentials due to the vibrational movement of the atoms. When comparing the molecular potentials versus the movement of atoms due to their vibrational modes, we find that a linear relation (transduction process) takes place due to the bending mode of the water molecule (Fig. 12.9b). Another transduction is observed, at least for small displacements, from the antisymmetric stretching mode (Fig. 12.9c), and a full rectification can be observed from the symmetric stretching mode (Fig. 12.9d). 

So far, we constructed molecules and reasoned their 3D structures in such a fashion that some of you may get the impression that these objects are motionless. The fact is that molecules are very much restless and perform many motions all at the same time. Scheme 9.10 shows the motions that a small molecule like water performs all at once. The molecule vibrates in three modes (Scheme 9.10a) one is a symmetric stretch where the two bonds stretch and shrink in the same direction, and the other is an antisymmetric stretch wherein one bond stretches while the other is shrinking, and finally the two O—H bonds perform a scissoring motion, closing and opening the HOH angle. Additionally, the molecule as a whole also performs rotations around three different axes. 

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