Genuine normal vibration

Inspection of the character table shows that the translations and rotations span the representations Ag + 2Bg + Au + 2Bu. On deleting these from the total number constituting F, we are left with the following list of the representations spanned by the genuine normal vibrations ... 

In the section 32 we have expressed in equation (32-5) the energy which the genuine normal vibrations of a polyatomic molecule contribute in the absence of rotation. Before considering the simultaneous presence of vibration and rotation we shall first discuss the simpler problem that all the nuclei are kept at their equilibrium distances and that the molecule rotates as a rigid body. 

Symmetry Types of the Normal Modes. For this nonlinear four-atomic molecule there are 3(4) -6 = 6 genuine internal vibrations. Using a set of three Cartesian displacement coordinates on each atom, we obtain the following representation of the group C3l, ... 

With this model, we can discuss the known fact that isotope effects for proton transfers differ considerably from one reaction to another. The asymmetric stretch can be left out of consideration for the moment. It is not a genuine vibration, for it represents the process by which H is transferred from A to B. Thus, if reaction is to occur, it must be devoid of the restoring force that causes a normal vibrational motion to reverse its direction once a certain maximum amplitude is reached. It is called the motion along the reaction coordinate and does not affect the zero-point... 

High resolution studies by conventional spectroscopy are genuinely hampered by Doppler-broadening of the rotation-vibration lines in the low pressure regime. Individual Doppler-shifted frequencies contribute to the (normalized) Doppler-broadened line shape, due to the distribution of molecular velocities along the direction of observation... 

Of the nine normal modes of the Li X unit, there is only one triple-degenerate, genuine vibrational mode that involves movement of the lithium atom. Consequently, only this vibrational mode will change frequency on the substitution of Thi for L1. 

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