Selection Rules and Intensities

To predict the spectrum for a two-spin system we now need only one more piece of information—the requirements for transitions between two energy levels. 

Equations 2.12 and 2.17 provided the results of using time-dependent perturbation theory to assess the interaction between the x component of magnetization (proportional to Ix) and the applied rf field B,. The essential qualitative result for the single nucleus then being considered was the selection rule 

Equation 6.33 is completely general. For the two-spin system, it results in the transitions we identified in Fig. 6.2, while the double quantum transition between f and f 4, and the zero quantum transition between 02 and 03 are forbidden. Note that this statement is true for this treatment, which employs stationary state wave functions and time-dependent perturbations, but as we shall see in Chapter 11, it is easy with suitable pulse sequences to elicit information on zero quantum and quantum double processes. For our present purposes in the remainder of this chapter we accept the validity of Eq. 6.33. 

---

Problem 40-2. Discuss the selection rules and intensities for the three dimensional harmonic oscillator with characteristic frequencies vx, vy, and v ... 

Problem 40-4. Using Equation 40-21, obtain selection rules and intensities for p,. 

Infrared Selection Rules and Intensities for the Harmonic Oscil... 

Following the initial experiments by Kaiser, Axe (1964) extended the theories of Judd (1962) and Ofelt (1962) to calculate selection rules and intensities of two-photon transitions in solids doped with lanthanides. The theoretical predictions with later extensions by Bader and Gold (1968) laid largely untested as an hiatus occurred in the experimental studies in this area, the emphasis having shifted in this period to the observation of (4f) states buried in allowed (5d) or conduction bands. Interest has since returned following the work of Degenais (1981), Downer et al. (1982) and Down and Bivas (1983) on Gd " in LaFj. As noted in fig. 20, these workers observed a number of violations of the selection rules developed by Axe in both the intensity and polarization dependence and were able to trace the descrepancies to various approximations necessary in the... 

A third molecular property to be considered is the electric dipole moment. The selection rules and intensity of the rotational transitions of asymmetric tops depend on the dipole moment components along the principal inertial axes, that is, on pa> Pb. and pc> which give rise to a-, b-, and c-type spectra, respectively. All conformers possess the same connectivity between the atoms but they differ in the orientation of the functional groups, and this necessarily produces diverse charge distributions reflected in different values of the dipole moment components, as can be seen in Table 1. The microwave power necessary for optimal polarization depends on the dipole moment component involved in a rotational transition. Hence, the difference in the values of the dipole moment components of conformers can be exploited to discriminate between specific conformers just by varying the polarization power. By itself, it cannot be used as a conclusive tool, but it can always corroborate the conformer identification achieved with the previously described molecular properties. 

Rotamers N and O have very similar quadrupole coupling constants comparison of their values with those predicted ab initio indicate that they are necessarily conformers la and III a (see Tables 1 and 2). Because of the similar orientation of the amino group in these forms (see Fig. 6), they cannot be discriminated on the basis of the quadrupole constants. We can distinguish them from their selection rules and intensities of the observed transitions. The rotational spectrum of rotamer N shows strong Pa typc transitions and fairly weak Pc-type transitions, while form O presents strong Pa type transitions and medium-strength pb- and Pc-type transitions. No pb-type transitions have been detected for conformer N. Considering the predicted dipole moment components of Table 1, these data are consistent with... 

Skoog et al. [2] emphasized the instmmentation advances of the 1980s and early 1990s. Both Fourier-transform Raman (FT-Raman) spectrometers and single-stage spectrographs are discussed. There is some discussion of optical fiber probes, but none of the Raman microprobe. The authors sketch the theory of Raman scattering and present a classical (polarizability derivative) treatment of selection rules and intensity. Resonance enhancement and surface enhancement are treated briefly. In a textbook noted for its emphasis on instrumentation, there is little discussion of current applications. 

Centrifugal Distortion and Vibration-Rotation Interactions Hyperfine Interactions Selection Rules and Intensity of Transitions Quantum Chemical Prediction of Rotational Spectra... 

Miiller-Dethlefs K (1991) Zero kinetic energy electron spectroscopy of molecules - rotational symmetry selection rules and intensities. Journal of Chemical Physics 95 4821-4839. 

---