Vibrational spectra polyatomics

Polyatomic molecules vibrate in a very complicated way, but, expressed in temis of their normal coordinates, atoms or groups of atoms vibrate sinusoidally in phase, with the same frequency. Each mode of motion functions as an independent hamionic oscillator and, provided certain selection rules are satisfied, contributes a band to the vibrational spectr um. There will be at least as many bands as there are degrees of freedom, but the frequencies of the normal coordinates will dominate the vibrational spectrum for simple molecules. An example is water, which has a pair of infrared absorption maxima centered at about 3780 cm and a single peak at about 1580 cm (nist webbook). 

In this section, we focus our attention on applications of the CDF protocol to control of population transfer between vibrational levels of a nonrotating polyatomic molecule. The vibrational spectrum of a polyatomic molecule is rich, and if one wishes to transfer population between two states in a subset of selected states that is embedded in the complete manifold of molecular vibrational states, it is... 

The Detection of the Vibrational Spectrum of a Polyatomic Chemical Species IR and Raman Spectroscopies... 

The importance of the Raman spectrum lies especially in the fact that it also occurs for homonuclear molecules, which, according to sections 22 and 23, have no rotation and vibration-rotation spectra. Hence, it may be used to supplement the evidence derived from electronic bands, regarding the energy of vibrational and rotational levels in the ground state, and for a confirmation of the values of and thus obtained. Researches of this sort have actually been carried out on HCl by Wood and on Hg, Ng, Og, CO by Rasetti (for literature see G) and (lO)) and, more recently, on CO by Amaldi(is). Really essential, however, is the Raman effect in analysing the possible vibrations of polyatomic molecules, as we shall see in the next chapter. For such molecules very rarely have sharply defined electronic bands, while the rotation and vibration-rotation data usually are insufficient to arrive at a unique description of the molecular behaviour. 

Table 24 represents the vibration spectrum of CO2 it consists of two valence vibrations and one break vibration the frequency of the latter is considerably lower than that of the two former the same holds for the deformation vibrations of water. The lower frequencies point to smaller values for the force of deformation compared with the force of separation. This is shown in Tables 26, 26 and 27, in which data for a series of diatomic, of branched triatomic or polyatomic molecules are tabulated in every instance, the force of deformation d is considerably smaller than the valence force /. The nuclear distance and the valence angle in the rest posi tion are also inserted. A few data for pyramidal molecules are given in Table 28, and for tetrahedral in Table 29. 

The two bonds in this system are known as coupled oscillators . This type of system occurs often in the vibrations of polyatomic molecules in which two oscillators (which can be bonds or groups of bonds) couple to give symmetric and antisymmetric combinations. (In this case, where the system is exactly symmetrical, the symmetric combination will not be observed in the IR spectrum because the dipole moment of the molecule does not change.)... 

At low vibrational excitations polyatomic molecules exhibit a well-defined vibrational spectrum (particularly so if it is initially quite cold). We discuss in this section at what energy a large molecule changes its behavior to become de facto its own heat bath. This change involves a sudden increase in the density of vibrational states as the energy of the molecule approaches the dissociation threshold. Even... 

A combination of both methods was realized by Uehara et al. 85,88) They investigated the Stark spectrum of polyatomic molecules in strong electric fields by probing the different Stark components with the Zeeman-tuned laser line. Since the molecular constants of the vibrational ground state are often known from microwave investiga-... 

However, in polyatomic molecules, transitions to excited states involving two vibrational modes at once (combination bands) are also weakly allowed, and are also affected by the anharmonicity of the potential. The role of combination bands in the NIR can be significant. As has been noted, the only functional groups likely to contribute to the NIR spectrum directly as overtone absorptions are those containing C-H, N-H, O-H or similar functionalities. However, in combination with these hydride bond overtone vibrations, contributions from other, lower frequency fundamental bands such as C=0 and C=C can be involved as overtone-combination bands. The effect may not be dramatic in the rather broad and overcrowded NIR absorption spectrum, but it can still be evident and useful in quantitative analysis. 

Fluorescence always occurs from the lowest singlet state even if the initial excitation is to higher energy state (Kasha s rule). Azulene and some of its derivatives are exceptions to this rule. Because of vibrational relaxation of initially excited vibronic state, the fluorescence spectrum may appear as a minor image of the absorption spectrum for large polyatomic molecules. The shape of the emission spectrum is independent of the exciting wavelength. 

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