Electromagnetic radiation selection rules

Electronic transitions mostly involve interaction between the molecule and the electric component of the electromagnetic radiation (Section 2.1). The selection rules are, therefore. 

The model fundamental to all analyses of vibrational motion requires that the atoms in the system oscillate with small amplitude about some defined set of equilibrium positions. The Hamiltonian describing this motion is customarily taken to be quadratic in the atomic displacements, hence in principle a set of normal modes can be found in terms of these normal modes both the kinetic energy and the potential energy of the system are diagonal. The interaction of the system with electromagnetic radiation, i.e. excitation of specific normal modes of vibration, is then governed by selection rules which depend on features of the microscopic symmetry. It is well known that this model can be worked out in detail for small molecules and for crystalline solids. In some very favorable simple cases the effects of anharmonicity can be accounted for, provided they are not too large. 

When exposed to electromagnetic radiation of the appropriate energy, typically in the infrared, a molecule can interact with the radiation and absorb it, exciting the molecule into the next higher vibrational energy level. For the ideal harmonic oscillator, the selection rules are Av = +1 that is, the vibrational energy can only change by one quantum at a time. However, for anharmonic oscillators, weaker overtone transitions due to Av = +2, + 3, etc. may also be observed because of their nonideal behavior. For polyatomic molecules with more than one fundamental vibration, e.g., as seen in Fig. 3.1a for the water molecule, both overtones and... 

Electric-quadrupole transition, 123,127 Electromagnetic radiation, 114-117. See also Radiation, electromagnetic Electromagnetic spectrum, 115 Electronic energy, 57,64,148 Electronic spectra, 130, 296-314 of diatomics, 298-306 and molecular structure, 311 of polyatomics, 71-72, 73, 75, 306-314 selection rules for, 297-301, 306-307 Electronic structure of molecules, 56-76 Electron spectroscopy for chemical analysis (ESCA), 319-320 Electron spin resonance (ESR), 130, 366-381... 

Spectroscopy is concerned with the observation of transitions between stationary states of a system, with the accompanying absorption or emission of electromagnetic radiation. In this section we consider the theory of transition probabilities, using time-dependent perturbation theory, and the selection rules for transitions, particularly those relevant for rotational spectroscopy. 

In most of the examples described in this book, the rotational angular momentum is coupled to other angular momenta within the molecule, and the selection rules for transitions are more complicated than for the simplest example described above. Spherical tensor methods, however, offer a powerftd way of determining selection rules and transition intensities. Let us consider, as an example, rotational transitions in a good case (a) molecule. The perturbation due to the oscillating electric component of the electromagnetic radiation, interacting with the permanent electric dipole moment of the molecule, is represented by the operator... 

The rules are derived by considering whether or not an interaction with the electric vector of electromagnetic radiation is possible in going from the initial to the proposed final states of the chemical species. Frequently, the symmetry properties of the wavefunctions involved suffice to exclude certain transitions, so that the selection rules are a way of representing the possibilities that remain, although they say nothing about the absolute intensities of the interactions. 

In this chapter, we have discussed the unique interactions of electromagnetic radiation with semiconductor NWs that lead to resonant absorption and scattering, the importance of Raman selection rules and phonon confinement in determining the crystal structure of NWs, and the ways in which Raman spectroscopy can be used to measure composition, strain, and temperature quantitatively with submicron resolution. These qualities of Raman spectroscopy are already commonly employed in the characterization of semiconductor NWs, and one may anticipate Raman spectroscopy to be used even more widely as the applications to NW... 

When electromagnetic radiation interacts with a molecule, certain transitions between states can occur, and others cannot. There are selection rules which tell us which transitions are possible and which are not. The detailed theory underlying these selection rules is fairly complicated, but some important general conclusions can be stated. 

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