Stretching vibrations mechanical model

In order to visualize normal vibrations, let us consider a mechanical model of the CO2 molecule shown in Fig. 1-10. Flere, the C and O atoms are represented by three balls, weighing in proportion to their atomic weights, that are connected by springs of a proper strength in proportion to their force constants. Suppose that the C—O bonds are stretched and released... 

The emerging picture is one in which the quantum-mechanical equivalents of the constants of motion for the two valence electrons in these atoms are like those associated with the near-rigid rotations, bending vibrations, and stretching vibrations we normally associate with linear triatomic molecules. These new results bring into question the range of validity of the nearly-independent-particle model, the quantum-mechanical counterpart of Bohr s planetary model, for atoms with more than one valence electron. 

Figure 8.3. A semiclassical vibronic treatment of proton transfer. This model, which is valid only for small Hu, treats the carbon-proton stretching vibration quantum mechanically and the rest of the system classically. In this way, we monitor the energy gap between the vibronic states Ej + hoH/2(n] + 1 /2) and 2 + hcoH/(n2 + 1 /2) for trajectories of the system with a fixed X-H bond length (see Ref...

A-2 Mechanical Model of a Stretching Vibration in a Diatomic Molecule... 

The characlcrisiics of an atomic stretching vibration can be approximated by a mechanical model consisting of two masses connected by a spring. A disturbance of one of these masses along the axis of the spring results in a ibration called a simph harmonic moiion. 

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. 

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