Dichroic Infrared IR-LD Spectroscopy Background

One prerequisite for the mathematical formalism describing these phenomena is that the amplitudes of molecular vibrations are extraordinarily small, compared to the length of the chemical bonds involved and the equilibrium values of valence angles. Therefore, the dipole moment of any molecule containing N atoms can be expressed with the so-called harmonic approximation, by the first two members of the following expression  

According to the latter, active vibrations (IRJ in the IR spectrum are those for which (3 j,/3r) 0, that is, an addition ([toT O) or generation ( J,o=0) of an oscillating dipole moment with frequency V occur. In the opposite case, (3 a/3r) = 0, 

The vector M is the moment of transition, which shows that the change of the dipole moment for the i-vibration is determined not only by its value but also by its direction. Therefore, A depends on the orientation of with respect to the oscillating vector Ei with frequency v, which characterizes the electrical component of the monochromatic IR light interacting with the molecule. The latter vector is located on a plane perpendicular to the irradiation beam trajectory. In other words, the intensity of A is proportional to the square of the scalar product, as expressed below  

Here 9 is the angle, determined by the projection of on the plane defined by The maximum value of the amplitude A is reached with mutually parallel orientations of both vectors (9 = 0°, cos 9 = 1), whereas with perpendicular orientation of the latter (9 = 90°, cos 9 = 0) the corresponding value is zero. 

FIGURE 1.1 Optical scheme for a measurement of IR-LD spectra source of irradiation, polarizer, oriented sample, and detector. (See color insert.) 

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