Totally symmetric. Raman lines, polarization

Vibrations of totally symmetric species (defined by the first row of the character tables) emit Raman lines which are polarized, the depolarization ratio pk can assume, according to Eqs. 2.4-11. .. 13 values of 0 < p < 6/7. All other Raman-active vibrations are emitting lines which are depolarized, they have a depolarization ratio of 6/7. The value 6/7 is appropriate for an arrangement, where the Raman radiation s investigated without an analyzer. If an analyzer is used 3/4 has to be taken instead. Cubic and icosahedral point groups are a special case the depolarization ratio for totally symmetric vibrations is 0. 

The symmetry property of a normal vibration can be determined by measuring the depolarization ratio. From an inspection of character tables (Appendix 1), it is obvious that d is nonzero only for totally symmetric vibrations. Then, Eq. 1.192 gives 0 < p < f, and the Raman lines are said to be polarized. For all nontotally symmetric vibrations, d is zero, and p = Then, the Raman lines are said to be depolarized. If the exciting line is plane polarized, these criteria must be changed according to... 

Actually, experimental evidence helped to resolve these conflicting assignments. Polarization measurements of the Raman lines observed in IF AsF solution in HF I have shown that the intense 711 cm line was polarized whereas the weak 732 cm line was depolarized. In octahedral species the totally symmetric vibration Pi is indeed polarized, whereas the P2 vibration is depolarized. This therefore provided clear support for the assignments that I l < t 2 Similar results were later also obtained in the study of BrFjAsFg in HF solution ), in vdiich the intense lower frequency 661 cm was polarized and the weaker buthighci frequency at 671 cm was depolarized, also indicating that < i 2-... 

Fi om Table XVI-3, several statements about the rotational fine structure in the Raman effect may be made immediately. The polarized, totally symmetric band of a linear rigid rotor will resemble a perpendicular (.L) infrared band of the same type of rotor, except that the line spacing is twice as great ( AJ1 = 2 instead of jA./j = 1). The degenerate Raman band, on the other hand, will more nearly resemble a parallel (j ) infrared... 

The depolarization ratio of a Raman line depends on the symmetry of the molecular vibration involved (i.e., the change in molecular symmetry induced by the corresponding vibration) the maximum value of depolarization observed with linearly polarized light is p[" = 3/4. If a Raman line shows this extent of depolarization, it is said to be depolarized, whereas, if the degree of depolarization is smaller, the line is polarized. It can be shown [3] that only Raman lines corresponding to totally symmetric vibrations can have a degree of depolarization smaller than the maximum value, that is, can be polarized. 

The observed Raman spectrum shows five lines including two polarized ones. Since polarized lines originate from totally symmetric normal modes, and the number of observed fundamentals exceeds those deduced for point group Tj and D411, the BU4 ion must have C2v symmetry. Note that this geometry is consistent with the prediction of VSEPR theory. The normal modes that give rise to polarized Raman lines are sketched below. 

Pi provides a unique possibility for examining the symmetry of vibrational transitions. Since a[ vanishes for distortions belonging to a non-fiilly symmetric species, it easily can be realized that - 3/4. Depolarization ratio assumes its minimum value for the totally-symmetric vibrations of spherical top molecules. In these cases the Raman line is fidly polarized and y/ and pj are zero. 

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