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Unformatted text preview: 07Feb2011 Chemistry 21b Spectroscopy Lecture # 15 The Raman Effect & Rovibrational Band Structure Although the Raman effect has been known of for over fifty years, its employment as a routine spectroscopic method was quite limited until the development of high power lasers which provided a source of highly monochromatic radiation. Well first look at Raman scattering from a classical perspective. Unlike pure rotational or rovibrational spectroscopy, the Raman effect does not involve the direct absorption or emission of radiation. Instead, it involves the scattering of incident radiation which has been modified by some internal change in the system. The scattering can either be elastic, in which case there is no change in the internal state of the molecule, or inelastic, in which the molecule either gains energy from or contributes energy to the electromagnetic radiation field. The Raman effect is straightforward to understand when one considers the electrical nature of matter. Atoms and molecules consist of collections of oppositely charged particles whose relative positions can be altered by the application of external electric fields. This alteration leads to an electric dipole moment being introduced ino the system. These ease with which a molecule or atom may be distorted by an electric field is measured by the electric polarizability . We have already considered static polarizabilities in the context of the Stark effect, as analyzed by perturbation theory. For atoms, where the symmetry is spherical, the polarizability will be the same in all directions and it can be expressed by a single scalar quantity. For molecules with lower- than-spherical symmetry, the polarizability will not be the same along all directions, and just as is true for the moment(s) of inertia, the full polarizability is described by a tensor. In matrix form, the induced dipole is given by I = E or Ix Iy Iz = xx xy xz yx yy yz zx zy zz E x E y E z The polarizability tensor is clearly symmetric, and just as the principal axes diagonalize the moment-of-inertia tensor so too can the polarizability tensor be diagonalized and a polarizability ellipsoid defined. The isotropic polarizability, which is what matters in many applications, is then < > = 1 3 ( x x + y y + z z ) , where the primes denote the principal polarizability axes. If the molecule is undergoing some sort of internal motion, such as vibration or rotation, this can alter the isotropic polarizability such that = + A sin 2 i t , 111 where i is the frequency of the internal motion. If a time-varying electric field characterized by E = E sin(2 Laser t ) is applied, the induced moment is then given by I = E = E ( + A sin 2 i t )sin 2 Laser t or I = E sin 2 Laser t + 1 2 AE cos 2 ( Laser + i ) t + 1 2...
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