Oscillating electromagnetic radiation

Transitions between the two spin states (+1/2 and -1/2) can be induced by oscillating electromagnetic radiation (v in the microwave region) applied perpendicularly to 77. The energy-level splitting is referred to as the Zeeman effect, illustrated in Figure 16.1. Normally in the EPR measurements, v is maintained at a fixed value and 77 is permitted to vary until the resonance is matched. 

The electric field of electromagnetic radiation completes 4.00 x lO - " complete cycles in 1.00 s. What are the period and frequency of the oscillation, and what is its wavelength What is the frequency in units of cm ... 

The interaction of electromagnetic radiation with matter can be explained using either the electric field or the magnetic field. For this reason, only the electric field component is shown in Figure 10.2. The oscillating electric field is described by a sine wave of the form... 

The vibrational motions of the chemically bound constituents of matter have fre-quencies in the infrared regime. The oscillations induced by certain vibrational modes provide a means for matter to couple with an impinging beam of infrared electromagnetic radiation and to exchange energy with it when the frequencies are in resonance. In the infrared experiment, the intensity of a beam of infrared radiation is measured before (Iq) and after (7) it interacts with the sample as a function of light frequency, w[. A plot of I/Iq versus frequency is the infrared spectrum. The identities, surrounding environments, and concentrations of the chemical bonds that are present can be determined. 

We only consider static response properties in this chapter, which arise from fixed external field. Their dynamic counterparts describe the response to an oscillating electric field of electromagnetic radiation and are of great importance in the context of non-linear optics. As an entry point to the treatment of frequency-dependent electric response properties in the domain of time-dependent DFT we recommend the studies by van Gisbergen, Snijders, and Baerends, 1998a and 1998b. 

The rapidly varying electric held of the incident electromagnetic radiation can, therefore, cause a rapid fluctuation in the dipole moment of the molecule. The magnitude of this oscillation depends on the polarisability of the molecule but is generally small. 

X-ray diffraction. The mechanism by which atoms diffract or scatter electromagnetic radiation via the coupling of the electron cloud of the atom to the incident oscillating electric field was discussed in the section on SERS. The X-rays scattered by an atom are the resultant of the waves... 

Students will be familiar with the absorption or emission of electromagnetic radiation as the basis for spectroscopic methods. Electromagnetic radiation itself is perceived as mutually perpendicular oscillating electric and magnetic fields. The total energy of the radiation, which has a number of components, is determined by the relationship shown in equation 3.1 ... 

A molecule must have a permanent dipole moment to be micro-wave active. As it rotates, the changing dipole moment interacts with the oscillating electric field of the electromagnetic radiation, resulting in absorption or emission of energy. This requirement means that homonuclear molecules such as H2 are microwave inactive, but heteronuclear molecules such as SO3, S02, NO and, of course, H20 are active. 

Figure 12.2 Sine wave representation of electromagnetic radiation. It consists of two in-phase waves, with oscillation of the electric field in the xy plane, and the magnetic field perpendicular to it, in the vz plane.

Figure 2.1 Electromagnetic radiation. A representation of electromagnetic radiation with the electric field (E) and the magnetic field (M) at right angles to the direction of the wave movement. Both fields oscillate at the same frequency.

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. 

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