Diatomic molecules bond stretching mode

Thus, the Morse potential is the most appropriate for estimating bond energy in a molecule [4-9], The C-X and C-Y bond stretching modes in YCX3 molecules are treated as anharmonic Morse-like diatomic, non-linear coupled oscillators. The well-known [26-37] effective Hamiltonian of the local and normal mode model is used. 

Diatomic molecules, such as HF, are having only a single vibrational mode. HF belongs to the point group Coov. and in the standard symmetry the axis of the molecule is set along the Z-axis. For the single bond stretch mode the two atoms move out of phase with one another and we can derive the irreducible representation by inspection with reference to Figure 6.4. 

Figure 6.4 The bond stretch mode of a diatomic molecule such as HF.

Because an applied field in the y direction Ev can induce a dipole M with a component in the x direction Mx as well as the component in the y direction My, it is necessary that we specify the components of the polarizability tensor by two subscripts (Fig. 3). If the bond A—B of a diatomic molecule stretches during a vibrational mode, Mx and Mv will vary and therefore the corresponding polarizability tensor components will vary. 

When a molecule absorbs energy in the infrared region (1-300 pm), the a bonds of the molecule begin to vibrate. For simple diatomic molecules, such as H. or HC1, the only possible vibration is a movement of the two atoms away from and back to each other. This mode is referred to as a bond stretch. Triatomic molecules such as CO, have two distinct stretching modes—an asymmetrical and a symmetrical mode. In the symmetrical stretch, both oxygen atoms move away from the carbon atom at the same time. Conversely, in the asymmetrical stretch, one oxygen atom moves toward the carbon atom while the second oxygen atom moves away from the carbon atom. 

We note that the nuclear spin-vibration interaction, anticipated in equation (4.15), is actually identically zero. This is because the only vibrational mode for a diatomic molecule is that associated with bond stretching. Such motion does not generate any angular momentum and so does not produce a magnetic field with which the nuclear spin can interact. 

Infrared radiation causes excitation of the quantized molecular vibration states. Atoms in a diatomic molecule, e.g. H—H and H—Cl, vibrate in only one way they move, as though attached by a coiled spring, toward and away from each other. This mode is called bond stretching. Triatomic molecules, such as CO2 (0=C=0), possess two different stretching modes. In the symmetrical stretch, each O moves away from the C at the same time. In the antisymmetrical stretch, one O moves toward the C while the other O moves away. 

If the masses v4, B,C,D... are all similar and the force constants/,/2,/j... are of the same magnitude, the vibrations of individual atoms are strongly coupled with the result that no band can be assigned solely to any particular group of atoms. If, however, the mass of atom A is considerably smaller than those of the other atoms, one mode of vibration will involve the stretching of the bond between A and the rest of the molecule. The system can be considered as approximating to a diatomic molecule A—X, and the wavenumber of the vibration is then given by... 

The application of this result to the determination of bond stretching force constants in molecules encounters two difficulties. First, real molecules are not exactly harmonic oscillators. Secondly, although the only mode of vibration possible in diatomic molecules is a bond stretching motion, the vibrations of polyatomic molecules are much more complicated, and cannot be expressed as consisting only of a combination of bond stretching motions. We discuss these two problems in turn in the next two sections. 

The absorptions just described seem to be correctly identified as the stretching modes, v of the H bond between water molecules. Assuming the simplest possible model, that v, is equivalent to the vibration of a diatomic molecule with atoms of mass 18, the absorption at 212 cm" corresponds to a force constant of 0.2-10 dynes/cm. This is in acceptable accord with the value obtained for formic acid (0.3-10 dynes/cm). 

Thus, a simple diatomic molecule A-B has (3 x 2) - 5 = 1 vibrational mode, which corresponds to stretching along the A-B bond. This stretching vibration resembles the oscillations of two objects connected by a spring. Thus, to a first approximation, the model of a harmonic oscillator can be used to describe this vibration, and the restoring force (F) on the bond is then given by Hooke s law ... 

Vibrations of atoms in a molecule can be divided in six different forms symmetrical and antisymmetrical stretching, rocking, scissoring, twisting and wagging. Simple diatomic molecules have only one bond, and only one fundamental vibrational mode (the interatomic stretching mode) is seen in the spectrum. More complex molecules, such as hydrogels, have many bonds, and their vibrational spectrum is much more complex. 

Each polyatomic ion or molecule has its own specific set of vibrational frequencies, and different polyatomic ions or molecules have different sets of vibrations. The number of absorptions depends on the number of atoms in the polyatomic ion or molecule and on the structure or specific arrangement of the atoms. The intensity of these absorptions depends on the kinds of atoms. For a diatomic molecule such as hydrogen chloride, HCl, only one simple vibrational pattern called a fundamental mode is possible. This involves the stretching and compression of the bond between the two atoms as shown in FIGURE 42.1a. For molecules with a greater number of atoms, the vibrational motion appears more complex, but is still comprised of a rela-... 

I shall first discuss briefly the experimental techniques Involved. I shall then review the effects of bond dissociation anharmonlclty in a diatomic molecule. Next I shall introduce the idea of local modes with a simple classical model, and then extend this to a mathematically defined quantum mechanical model which I shall discuss in detail for the case of two symmetry related stretching vibrations, as in the water molecule. I shall then introduce the effects of Fermi resonance, and describe some of our recent work on the dlchloromethane molecule. I shall also describe similar fits to the overtones of carbonyl stretching vibrations in metal carbonyls. Finally I shall comment briefly on the implications of this work for intramolecular vibrational relaxation (IVR) and chemical dynamics. 

A diatomic molecule will have only a single vibrational mode and it will be a stretching mode that lies along the intemuclear axis, as shown in Figure 9.2. One can consider the two nuclei in the AX bond to be attached by an imaginary spring that allows them to simultaneously stretch to their maximum amplitude, pass back... 

Another variation has three different atoms connected by bonds, such as the H-O-C bond in methanol (8). Bending a diatomic molecule such as 13 is rather difficult. With 16, there are two bonds and different modes for bending. There are a symmetrical (19) and an asymmetric (20) bend, as shown. Once again, each of these occurs at a different frequency, although these vibrations are usually lower in energy than the stretching vibrations. 

---