Vibrational from rotational and

Laser Raman Microprobe. A more sophisticated microscope is the Laser Raman Microprobe, sometimes referred to as MOLE (the molecular orbital laser examiner). This instmment is designed around a light microscope to yield a Raman spectmm (45) on selected areas or particles, often <1 ia volume. The data are related, at least distantly, to iafrared absorption, siace the difference between the frequency of the exciting laser and the observed Raman frequency is the frequency of one of the IR absorption peaks. Both, however, result from rotational and vibrational states. Unfortunately, strong IR absorption bands are weak Raman scatterers and vice versa hence there is no exact correspondence between the two. 

Table A4.1 summarizes the equations needed to calculate the contributions to the thermodynamic functions of an ideal gas arising from the various degrees of freedom, including translation, rotation, and vibration (see Section 10.7). For most monatomic gases, only the translational contribution is used. For molecules, the contributions from rotations and vibrations must be included. If unpaired electrons are present in either the atomic or molecular species, so that degenerate electronic energy levels occur, electronic contributions may also be significant see Example 10.2. In molecules where internal rotation is present, such as those containing a methyl group, the internal rotation contribution replaces a vibrational contribution. The internal rotation contributions to the thermodynamic properties are summarized in Table A4.6.

Of the 3n coordinates needed to describe an n-atom molecule, three are used for center of mass motion, three describe angular displacement (rotation, hindered rotation, or libration) (two if the molecule is linear, 0 if monatomic), the remaining 3n—6 (3n—5, if linear, 3n—3 = 0, if monatomic) describe atom-atom displacements (vibrations). In some cases it may not be possible to separate translation cleanly from rotation and vibration, but when the separation can be made it is a convenience. Elementary treatments assume... 

S.P.A. Sauer, J. Oddershede, J.F. Ogilvie, Evaluation of parameters in radial functions from rotational and vibration-rotational spectra and calculation of rotational and vibrational g... 

Figures 2.3a,b show the model of Bernal and Fowler (1933) for the water molecule. The molecular geometry is well known (Benedict et al 1956) from rotational and vibrational spectra. The oxygen atom has eight electrons, and has the electronic configuration ls22s22p4. Each hydrogen atom has a Is1 electron these electrons are shared with two bonding electrons of oxygen, to constitute the water molecule.

Temperature from Rotational and Vibrational Raman Scattering Effects of Vibrational-Rotational Interactions and Other Corrections... 

The final results for v = 0 and 1 are summarised in table 10.3, using data from rotational and vibration-rotation transitions for all four isotopomers. 

K the value of RT is approximately 2.5 kJ mol"1,) However Aevib is usually much greater than kT and under these circumstances vibrations do not contribute significantly to heat capacity (Fig. 9.7). Thus for nitrogen at room temperature the rotational contribution is approximately iiTand the vibrational contribution almost zero. Thus Cv 5/2)1 and y w 7/5 = 1.40 as opposed to the classical prediction of 1,29. For iodine the vibrational spacings are closer (Table 9.1) and we would predict y 1.29 in accord with the classical value. If the temperature is varied the heat capacity of a diatomic or polyatomic gas may show steps as the contributions from rotations and vibrations rise as the energy separations become comparable to kT, The positions of the steps depend on the moments of inertia and the vibrational frequencies of the molecules. 

Internal Partition Functions for Polyatomic Molecules.— The internal partition function for a polyatomic molecule comprises contributions from nuclear spin and electronic levels, and from rotational and vibrational degrees of freedom. On the assumption that the corresponding energies are additive and independent, these contributions can be factored, and the corresponding contributions to the thermodynamic functions are additive. 

There are some similarities between the Raman and the infrared methods. Both methods arise from rotational and vibrational transitions in a molecule. For simple molecules a combination of the two methods will aid in the determination of structure, utilizing a mathematical treatment e.g., group theory). Generally the mathematical treatment is beyond the limits of contemporary theory for most molecules. However, useful information can be obtained by the use of both spectra, regardless of the complexity of a molecule. 

Midey A J and Viggiano A A 1998 Rate constants for the reaction of Ar" with O2 and CO as a function of temperature from 300 to 1400 K derivation of rotational and vibrational energy effects J. Chem. Phys. at press... 

Estimating the energy from translation, rotation and vibrations. 

Here te, tc are the correlation times of rotational and vibrational frequency shifts. The isotropic scattering spectrum corresponding to Eq. (3.15) is the Lorentzian line of width Acoi/2 = w0 + ydp- Its maximum is shifted from the vibrational transition frequency by the quantity coq due to the collapse of rotational structure and by the quantity A due to the displacement of the vibrational levels in a medium. 

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