Electric Raman transition

FIGURE 10.18 Comparison of (a) Raman scattering process and (b) gradient-field Raman (GFR) scattering process. ED and EQ denote electric dipole and electric quadrupole transitions, respectively. 

A similar idea is exploited in recent work with the infrared (IR) echo, although with IR-active rather than Raman-active vibrations (35-42). Although the basic concepts in the Raman and IR echoes are the same, they each work best on different systems. The infrared echo is best for vibrations with strong IR transitions (and therefore potential for resonant energy transfer and sensitivity to local electric fields), for dilute solutes, and for systems with slow rotation. In contrast, the Raman echo is best for vibrations with strong Raman transitions (and generally weak IR transitions),... 

It is important to note that the two electric fields that lead to a Raman transition can have different polarizations. Information about how the transition probability is affected by these polarizations is contained within the elements of the many-body polarizability tensor. Since all of the Raman spectroscopies considered here involve two Raman transitions, we must consider the effects of four polarizations overall. In time-domain experiments we are thus interested in the symmetry properties of the third-order response function, R (or equivalently in frequency-domain experiments... 

One of the most important aspects in both experimental and theoretieal studies in molecular spectroscopy is, undoubtedly, the characterization of intensities induced by electromagnetic radiation. We are, of course, interested in obtaining information concerning infrared and Raman transitions which are driven by electric dipole and quadrupole operators, respectively. These transitions can be represented as... 

Find the symmetry selection rules for electric dipole and Raman transitions in a molecule. 

The Raman transition selection rules are available the same way as the electric dipole selection rules, but the transition moment operator has the symmetry of the second order firnctions x, y, z, xy, yz, and xz. If we think of the Raman transition represented in Fig. 6.17 as a dual process—absorption and then emission—then this makes sense the probability of the Raman transition depends on the transition moment for reaching the virtual state (when the incident photon hits the molecule)... 

SOLUTION We take the direct product of the representations for the initial and final states, and then look to see if the result contains a representation for any of the functions that correspond to electric dipole (x, y, or z) or Raman (x, xy,. . . ) transition moments. Because Aj is the totally symmetric representation, we know right away that Aj (x) = , so we can go straight to the character table for the point group of NH3, We see there that the functions column for E includes (x,y), which is sufficient for electric dipole transitions, and (xy,yz), which means Raman transitions will also be allowed. 

The transition moments can be identified in the character tables by the Cartesian coordinates in the functions column x, y, or z signify electric dipole transitions, whereas x, xy, or other quadratic terms signify Raman transitions, b. The transition is allowed by symmetry selection rules if the symmetry representation F for the initial state and Fy for the final state obey the relations... 

What are the possible states in symmetry-allowed Raman and electric dipole transitions from the Ai state of 1,1-dibromoethene ... 

What Raman and what electric dipole transitions are allowed from one of the A2 electronic states of NH3 ... 

With a little group theory, we can determine whether or not the vibration has a dipole derivative. The same symmetry selection rules apply to vibrations as to electronic transitions for a transition to be allowed, the direct product of the representations for the initial and final states must be one of the representations for the transition moment. The transition moments for electric dipole or infrared selection rules correspond to the functions x, y, and z. For Raman transitions, the transition moments correspond to any of the second-order functions of x, y, and z, such as xz or -I- y. The representation of the ground vibrational state is always the totally symmetric representation, so F, F is equal to Fy for fundamental transitions. Therefore, the selection rule for fundamental transitions is F, (x) Fy = F = F. For example, the group theory predicts that for CO2 the transitions V2 = 0 1 and V3 = 0 1 are infrared-allowed, because those vibrational modes have TTu (x,y) and (z) symmetry, respectively. On the other hand, the symmetric stretch transition Vj = 0 1 is forbidden by infrared selection rules but allowed by Raman selection rules, because that vibrational mode has (x + y, z ) symmetry. Here are the relevant rows from the character table in Table 6.4 ... 

In Raman transitions, the rotational selection rules differ from those for electric dipole transitions. Derive an equation for the rovibrational transition energy in terms of tOg, (OgXg, B and for the S branch (AJ — +2) of a... 

Raman spectroscopy also has selection rules. The gross selection rule for a Raman-active vibration is related to the polarizability of the molecule. Polarizability is a measure of how easily an electric field can induce a dipole moment on an atom or molecule. Vibrations that are Raman-active have a changing polarizability during the course of the vibration. Thus, a changing polarizability is what makes a vibration Raman-active. The quantum-mechanical selection rule, in terms of the change in the vibrational quantum number, is based on a transition moment that is similar to the form of M in equation 14.2. For allowed Raman transitions, the transition moment [a] is written in terms of the polarizability a of the molecule ... 

M is the electric dipole transition moment vector T is the two-photon absorption tensor a is the Raman scattering tensor and is a unit vector in the direction of light polarization U. 

---