Selection Rules for IR and Raman-Active Vibrational Modes

A comparison of the Morse potential (blue) and the harmonic oscillator potential (green), showing the effects of anharmonicity of the potential energy curve, where is the depth of the well. [ Mark M Sa moza/CCC-BY-SA 3.0/G FDL /Wikimedia Commons reproduced from http //en.wikipedia.org/wiki /Morse potential (accessed December 27, 2013).] 

The Bom—Oppenheimer approximation is the assumption that because the nuclei are several thousand times more massive than the electrons, the nuclei are essentially clamped in place during the absorption so that the wave function can be separated into its respective electronic and vibrational parts. The probability of a transition occurring between two different energy levels is proportional to the square of the transition moment integral, /VIqi, shown in Equation (9.10), where u is the dipole moment operator. Expansion of this equation yields Equation (9.11), where e is the 

Typically, only the ground vibrational level (v = 0) is substantially populated at room temperature. Furthermore, we will choose our normal ccxardinate q such that every symmetry operation in the point group converts q into q, so that q will always be converted into itself. Thus, the symmetry of always be equal 

Finally, the symmetry of the excited vibrational level is given by TvES- Because F q5 is always the totally symmetric IRR, the product Tii r Gs will have the same symmetry as F. As we learned earlier, the only way for a direct product to contain the totally symmetric IRR is for both of the species to have identical symmetries. Thus, in order for a vibrational mode to be IR-active, the symmetry of the vibrational mode, TvES. must be identical to the symmetry of one of the components (x, y, or z) of the dipole moment operator F.  

Some useful rules regarding the symmetries of the vibrational modes follow  

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SELECTION RULES FOR IR AND RAMAN-ACTIVE VIBRATIONAL MODES... 

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