Selection rules vibration

Linear molecules belong to either the (with an inversion centre) or the (without an inversion centre) point group. Using the vibrational selection rule in Equation (6.56) and the (Table A. 3 7 in Appendix A) or (Table A. 16 in Appendix A) character table we can... 

As we proceed to molecules of higher symmetry the vibrational selection rules become more restrictive. A glance at the character table for the point group (Table A.41 in Appendix A) together with Equation (6.56) shows that, for regular tetrahedral molecules such as CH4, the only type of allowed infrared vibrational transition is... 

For a spherical rotor belonging to the octahedral Of, point group, Table A.43 in Appendix A, in conjunction with the vibrational selection rules of Equation (6.56), show that the only allowed transitions are... 

Some characteristics of, and comparisons between, surface-enhanced Raman spectroscopy (SERS) and infrared reflection-absorption spectroscopy (IRRAS) for examining reactive as well as stable electrochemical adsorbates are illustrated by means of selected recent results from our laboratory. The differences in vibrational selection rules for surface Raman and infrared spectroscopy are discussed for the case of azide adsorbed on silver, and used to distinguish between "flat" and "end-on" surface orientations. Vibrational band intensity-coverage relationships are briefly considered for some other systems that are unlikely to involve coverage-induced reorientation. 

Bunker, P. R. The vibrational selection rules and torsional barriere of ferrocene. Molecular Physics 9, 247 (1965). 

According to (6.65), the IR vibrational selection rules are determined by the integral... 

In determining vibrational selection rules (Section 10.6) we shall need to determine whether integrals of the types / y r/V J dz are nonzero, where the function f is a, y, z, a2, y2, z2, xy, yz, za, or any combinations or sets thereof. Also, is totally symmetric and j/ may belong to any irreducible representation. Identify the irreducible representations to which if/1 may belong in order to give nonzero integrals for molecules of symmetry C4t. and Z)3f/. 

Vibrational selection rules the Franch-Condon principle... 

Non-totally symmetrical vibrations can be shown to involve no change in origin of the normal coordinates, thus the value of the integral (7) is identically zero for Av odd and small for Av even (zero excluded). Taken together with the expectation for totally symmetrical vibrations this leads to two vibrational selection rules, namely (Herzberg and Teller, 1933),... 

Equations (6.5) and (6.12) contain terms in x to the second and higher powers. If the expressions for the dipole moment /i and the polarizability a were linear in x, then /i and a would be said to vary harmonically with x. The effect of higher terms is known as anharmonicity and, because this particular kind of anharmonicity is concerned with electrical properties of a molecule, it is referred to as electrical anharmonicity. One effect of it is to cause the vibrational selection rule Av = 1 in infrared and Raman spectroscopy to be modified to Av = 1, 2, 3,. However, since electrical anharmonicity is usually small, the effect is to make only a very small contribution to the intensities of Av = 2, 3,. .. transitions, which are known as vibrational overtones. 

This result is the same as the infrared vibrational selection rule in Equation (6.55). 

Raman Depolarization Ratio. A more complete discussion of vibrational selection rules must take into account the vector properties of the dipole moment and the tensor character of the polarizability a. Thus Eq. (1) should be written... 

The vibrational selection rules treated in Sec. 2.7 are strictly valid in the gas phase, because intermolecular interactions are mostly absent. As an example we present the rotation-vibration infrared and Raman spectra of benzene CgHg in Fig. 4.3-1 on a common scale. According to the rule of mutual exclusion (see Sec. 2.7.3.4), none of the fundamentals should coincide in the two spectra. Of the 20 normal vibrations of QHf, four are infrared active (1A2 , 3 i ), seven Raman active (24 E g, and nine... 

Type of autoionization Molecule State r(cm-1) (obs) /(calc) Vibrational selection rules... 

We need then to assess the number, frequencies, and intensities of all the absorptions associated with a given molecule before drawing on the evidence of distinctive features due to specific groups, analogies with known compounds, or the vibrational selection rules in order to formulate its likely identity. 

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