Molecule local stretching mode

The quantum numbers va,vh,vc denote the three local stretching modes, while vd and v1 denote the two bending modes. For tetratomic molecules, it becomes... 

There are also approaches [, and M] to control that have had marked success and which do not rely on quantum mechanical coherence. These approaches typically rely explicitly on a knowledge of the internal molecular dynamics, both in the design of the experiment and in the achievement of control. So far, these approaches have exploited only implicitly the very simplest types of bifiircation phenomena, such as the transition from local to nonnal stretch modes. If fiittlier success is achieved along these lines m larger molecules, it seems likely that deliberate knowledge and exploitation of more complicated bifiircation phenomena will be a matter of necessity. 

Even the dynamics of C—H stretching modes can reflect the hydrogen bond status of alcohol molecules [99, 100], in particular the local hydrogen bond... 

The vibrational motion of polyatomic molecules encompasses all nuclei in the molecule and, as long as the displacement from the equilibrium configuration is sufficiently small, it can be broken down into the so-called normal-mode vibrations (see Appendix E). In special cases these vibrations take a particular simple form. Consider, e.g., a partially deuterated water molecule HOD. In this molecule, the H OD and HO-D stretching motions are largely independent and the normal modes are, essentially, equivalent to the local bond-stretching modes. To that end, consider the following reaction that has been studied experimentally [6,7] as well as theoretically [8] ... 

The intramolecular coupling of the two OH vibrations of a water molecule to a symmetric (vi) and an antisymmetric (V3) stretching mode is removed for strongly distorted H2O molecules, where the separation between Vi and V3 has increased compared to that of free H2O, viz. 99 cm, (see Sect. 4.2.2 and Table 3). In many hydrates with symmetric water molecules - site symmetry C2V (or an effective local potential of C2V or nearly C2V symmetry) - this separation is reduced (see also Sect. 4.2) to <40 cm as in the case of CUCI2 2 H2O ) and Bal2 H20 >. 

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. 

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