Vibrational spectroscopy fundamental vibration selection rule

The vibrational selection rule for the harmonic oscillator, Au = 1, applies to polyatomic molecules just as it did to diatomic molecules. Vibrational energy can, therefore, change in units of hcoi/ln. Transitions in which one of the three normal modes of energy changes by Au = - -1 (for example Ui = 0 1, U2 = U3 = 0 or 1 = 1) 2 = 3, i>3 = 2 3) result from absorption of a photon having one of three fundamental frequencies of the molecule. In the actual case, anharmonicities also allow transitions with Au, = 2, 3,... so that, for example, weak absorption also occurs at 2coi, 3(Ui, etc. and at coi + coj, 2vibrational transitions often play major roles in planetary spectroscopy. 

An alternative experiment that measures the same vibrational fundamentals subject to different selection rules is Raman spectroscopy. Raman intensities, however, are more difficult to compute than IR intensities, as a mixed third derivative is required to approximate the change in the molecular polarizability with respect to the vibration that is measured by the experiment. The sensitivity of Raman intensities to basis set and correlation is even larger than it is for IR intensities. However, Halls, Velkovski, and Schlegel (2001) have reported good results from use of the large polarized valence-triple-f basis set of Sadlej (1992) and... 

This result is tremendously useful, it not only leads to selection rules for vibrational spectroscopy but also, as was the case with electronic wavefunctions (see 8-2), allows us to predict from inspection of the character table the degeneracies and symmetries which are allowed for the fundamental vibrational wavefunctions of any particular molecule. 

The considerations on the symmetries of the ground and excited states and the above conditions lead to the selection rule for infrared spectroscopy A fundamental vibration will be infrared active if the corresponding normal mode belongs to the same irreducible representation as one or more of the Cartesian coordinates. 

Raman Selection Rules. For polyatomic molecules a number of Stokes Raman bands are observed, each corresponding to an allowed transition between two vibrational energy levels of the molecule. (An allowed transition is one for which the intensity is not uniquely zero owing to symmetry.) As in the case of infrared spectroscopy (see Exp. 38), only the fundamental transitions (corresponding to frequencies v, V2, v, ...) are usually intense enough to be observed, although weak overtone and combination Raman bands are sometimes detected. For molecules with appreciable symmetry, some fundamental transitions may be absent in the Raman and/or infrared spectra. The essential requirement is that the transition moment F (whose square determines the intensity) be nonzero i.e.. 

With both types of vibrational spectroscopy, distinctive spectra and facility in interpretation are possible because only vibrational transitions corresponding to changes in the vibrational quantum number of+1 are allowed by the spectral selection rules. That is, An = 1, where n is the vibrational quantum number. Due to this, the frequencies observed are usually the fundamental frequencies. In addition, because of analogies between the mathematical descriptions of classical and quantum mechanical vibrating molecular systems, it is possible to rationalize many spectral observations by analogy with classical vibrating systems that possess characteristic force constants and reduced masses. This rationalization has become the basis for systematizing much of the structural and chemical information derived from vibrational spectra. 

One of these methods is the vibrational spectroscopy which has its roots in the late 1920 s and early 1930 s. One of them was the fundamental understanding of molecular vibrations on the basis of quantum mechanics it was first put in evidence by the absorption of infrared radiation and later also found in the modulations of scattered visible light in the Raman effect. The two methods complement each other dramatically because of their different response to the selection rules which control the transition probabilities between different vibrational states of a molecular framework. The other root was a gradual and substantial improvement of the experimental techniques, such as stronger and more uniform sources of the primary radiations, higher resolution in the spectroscopic part of the equipment, and, perhaps most of all, more sensitive and reliable receivers. 

Among the theoretical aspects involved in the use of IR spectroscopy, the vibrational activity is the most relevant one. In fact, some vibrational modes have stronger activity in the IR than others and this determines the corresponding peak absorption intensity. The IR activity of a certain fundamental vibrational mode depends on the general IR selection rule which states that the permanent dipole moment of a given molecular group (/x) must have a non-zero derivative, with respect to the particular normal coordinate, for the equilibrium... 

Infrared (400-4000 cm ) spectroscopic investigations of silica gel consolidation have been performed by numerous research groups. (See, for example, refs. [35,146,154].) Due to the selection rules, asymmetric vibrations are infrared allowed, therefore the infrared spectra of silica gels complement the Raman spectra discussed in the previous section. One drawback of IR spectroscopy is that bulk silicates are totally absorbing for wave numbers below about 2400cm" , so infrared investigations of the fundamental framework vibrations often require dilution in infrared transparent media such as KBr or Nujol. ... 

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