Selection rules for rotation

Finally, for the determination of selection rules for rotational spectroscopy it is necessary to find the wavefimcdons for this problem. This subject will be left for further development as given in numerous texts on molecular spectroscopy. 

The selection rule for rotational Raman transitions are AJ = 2. This result relates to the involvement of two photons, each with angular momentum h, in the scattering process. Also allowed is A J = 0, but since such a transition implies zero change in energy it represents Raleigh scattering only. 

The relation between the spherical components AJ0( ) of a general tensor A of rank 2 and the cartesian components A, ( ) are given in Appendix 4. Equations (3.36) will form the basis for derivation of selection rules for rotation-internal motion transitions of SRMs presented in the next section. They also may serve for derivation of the transformation properties of the electric and magnetic dipole moment operators referred to the laboratory system (VH G... 

Equation (4.15) is strictly analogous to Eq. (3.37) for SRMs. It plays therefore the same role in formulation of Wigner-Eckart theorems and selection rules for rotating-vibrating molecules as does Eq. (3.37) for SRMs. 

Analysis of the fluorescence from electronically excited molecules in a conventional static gas system21 provides a way of investigating vibrational relaxation of such molecules, and is also a means of studying selection rules for rotational relaxation22. It is now well established that multiple quantum rotational jumps can occur with high probability (see Section 6). 

Equation (6.1.43) yields the well known selection rules for rotational transitions. For unpolarized light, the transition probability is calculated by taking the average of the transition probabilities for the three light polarization possibilities, p = 0, +1 and —1. To calculate a transition intensity, it is sufficient to evaluate the transition probability for one polarization component (p = 0 is usually most convenient) and one body-fixed /i-component (q = 0 for AQ = 0 parallel transitions, q = +1 or —1 for Aft = +1 perpendicular transitions). The total intensity is obtained by summing over the transition probabilities for all M values, i.e. over squares of 3-j coefficients. Due to the orthogonality relations among the 3-j coefficients,... 

We begin this section by deriving the El selection rules for rotational transitions in symmetric tops, since spherical and linear molecules may be considered special cases of symmetric tops. Foi El-allowed transitions from state JKM to state J K M y, we require a nonzero electric dipole transition moment... 

Pure rotational spectra can be observed in the gas phase however the selection rule for rotational transitions requires the molecule to have a permanent electric dipole. Homonuclear diatomics are, again, an important group of molecules which do not show microwave absorption because of this selection rule. 

A FIGURE 9.5 The dipole selection rule for rotational transitions. A polar molecule can be induced to change its rotational state by interaction with the electric field of a photon, as long as the field vector has some component that is parallel to the dipole moment of the molecule (a). If the electric field vector of the photon is perpendicular to the dipole moment (b), or if the dipole moment is zero (c), there is no allowed interaction. 

Although the most fundamental selection rule for rotational spectroscopy is that the molecule should have a nonvanishing permanent dipole moment, we note that molecules without a permanent dipole moment can have perturbation-allowed rotational spectrum [22]. For spherical tops, for example, centrifugal distortion effects can produce a small permanent dipole moment that allows the observation of the rotational spectrum [1, 37]. 

The selection rules for Raman transitions are different from those of absorption or emission, and this makes it possible to observe transitions that are forbidden in emission or absorption spectroscopy. The Raman selection rules for rotational and vibrational transitions are ... 

It is possible to deduce the same kinds of structural information from Raman spectra as from infrared and microwave spectra. From the selection rule for rotation, Eq. (23.7-3a), the Raman shift of the Stokes rotational lines of a diatomic molecule is given in the rigid-rotor approximation by... 

The selection rules for rotational transitions in linear polyatomic molecules are also the same as for diatomic molecules. The transition AJ is equal to 1 in infrared spectroscopy and -nl in purely rotational spectroscopy (i.e. microwave spectroscopy) but only if the molecule has a non-zero dipole moment (see Section 6.7). A rotational transition for H-C=C-C1 will be observed whereas for H-C=C-H no rotational transition will be observed due to its zero dipole moment. 

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