Information from vibrational spectra

There are, as expected, two C-type and two A-type IR bands, all coinciding with depolarized Raman bands, and one Raman band without a counterpart in the IR spectrum. Three of the four ai modes have already been identified, and the remaining ai mode must be that at lowest frequency. 

Another example of the complete assignment of an IR spectmm is given in the on-line supplement to Chapter 8. 

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Fundamental information from vibrational spectra is important for understanding a wide range of chemical and physical properties of surfaces, e.g., chemical reactivity and forces involved in the atomic rearrangement (relaxation and reconstruction) of solid surfaces. Practical applications of HREELS include studies of ... 

DERIVATION OF BOND INFORMATION FROM VIBRATIONAL SPECTRA... 

Information from vibrational spectra 8.8.1 Quantitative information... 

The first factor is associated with the electronic dipole transition probability between the electronic states the second factor is associated between vibrational levels of the lower state v" and the excited state V, and is commonly known as the Franck-Condon factor, the third factor stems from the rotational levels involved in the transition, J" and /, the rotational line-strength factor (often termed the Honl-London factor). In particular, the Franck-Condon information from the spectrum allows one to gain access to the relative equilibrium positions of the molecular energy potentials. Then, with a full set of the spectroscopic constants that are used to approximate the energy-level structure (see Equations (2.1) and (2.2)) and which can be extracted from the spectra, full potential energy curves can be constructed. 

Although the above equations imply that a lot of symmetry analyses must be performed, that is not always the case. Equations 14.2 and 14.3 allow for the possibility of broad statements about which transitions will and will not be allowed for particular atomic or molecular systems. Such general statements, ultimately based on quantum mechanics and symmetry, are called selection rules. Selection rules allow us to easily determine which transitions will occur. When one is faced with a spectrum to interpret, knowledge of the selection rules is an indispensable tool in deriving physical information from the spectrum. Rotational and vibrational spectroscopy, in this chapter, are simplified to a large extent thanks to selection rules. 

To gain structural information from the experimentally recorded Raman spectrum, it is necessary to determine what vibrational mode corresponds to each band in the... 

A small fraction of the molecules are in vibrationally excited states. Raman scattering from vibrationally excited molecules leaves the molecule in the ground state. The scattered photon appears at higher energy, as shown in Figure lb. This anti-Stokes-shifted Raman spectrum is always weaker than the Stokes-shifted spectrum, but at room temperature it is strong enough to be useful for vibrational frequencies less than about 1500 cm 1. The Stokes and anti-Stokes spectra contain the same frequency information. 

Vibrational spectroscopy can help us escape from this predicament due to the exquisite sensitivity of vibrational frequencies, particularly of the OH stretch, to local molecular environments. Thus, very roughly, one can think of the infrared or Raman spectrum of liquid water as reflecting the distribution of vibrational frequencies sampled by the ensemble of molecules, which reflects the distribution of local molecular environments. This picture is oversimplified, in part as a result of the phenomenon of motional narrowing The vibrational frequencies fluctuate in time (as local molecular environments rearrange), which causes the line shape to be narrower than the distribution of frequencies [3]. Thus in principle, in addition to information about liquid structure, one can obtain information about molecular dynamics from vibrational line shapes. In practice, however, it is often hard to extract this information. Recent and important advances in ultrafast vibrational spectroscopy provide much more useful methods for probing dynamic frequency fluctuations, a process often referred to as spectral diffusion. Ultrafast vibrational spectroscopy of water has also been used to probe molecular rotation and vibrational energy relaxation. The latter process, while fundamental and important, will not be discussed in this chapter, but instead will be covered in a separate review [4],... 

As the interpretation of the vibrational spectrum of sohd state samples can provide information concerning the cation-anion interactions, it is of special interest to the chemist. In some cases information about the crystal structure can be obtained from the interpretation of spectra of the solid state when the substance possesses an anion of high symmetry. 

The vibrations indicated in Figure 25-4 are often termed normal modes of vibration during each of these, all atoms pass through their equilibrium positions at the same instant. For a vibration to give rise to absorption in the infrared, it is necessary (but not sufficient) that it be one of the normal modes of vibration. Only those of the normal modes in which the dipole moment varies in the course of a vibration will affect the vibration spectrum. For a simple illustration of information obtained from infrared spectra, see Exercise 10. 

For the finer differences in bond energy of various bonds between similar atoms, information can be obtained from vibration frequencies in the infrared and Raman spectrum and from small variations in the bond length, which are connected with each other and with the bond energy through semi-empirical relations (Badger s rule etc.). 

Temperature information from CARS spectra derives from spectral shapes either of the 2-branches or of the pure rotational CARS spectra of the molecular constituents. In combustion research it is most common to perform thermometry from nitrogen since it is the dominant constituent and present everywhere in large concentration despite the extent of chemical reaction. The 2-branch of nitrogen changes its shape due to the increased contribution of higher rotational levels which become more populated when the temperature increases. Figure 6.1-21 displays a calculated temperature dependence of the N2 CARS spectrum for experimental parameters typically used in CARS thermometry (Hall and Eckbreth, 1984). Note that the wavenumber scale corresponds to the absolute wavenumber value for the 2320 cm 2-branch of N2 when excited with the frequency doubled Nd.YAG laser at 532 nm ( 18796 cm ), i. e. = 18796 -1- 2320 = 21116 cm. The bands lower than about 21100 cm are due to the rotational structure of the first vibrational hot band. 

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