On the Theory of Raman Intensities

Abstract

The Herzberg-Teller development for vibronic transition moments is introduced into the Kramers-Heisenberg dispersion equation. It is shown how ``forbidden'' character (vibrationally induced intensity) in allowed electronic transitions is responsible for the Raman intensities of fundamentals. This suggests a direct link between certain vibronic spectroscopic observations and Raman intensities. The development is carried to the first order in nuclear displacements only—the higher terms give rise to Raman intensities of combinations and overtones. An equation for the polarizability components is obtained which leads directly to the Raman selection rules and in addition provides interesting predictions concerning the Raman and the resonance Raman effect in relation to excited electronic states. Rules are worked out governing the participation of excited electronic states in the Raman effect and these are employed to demonstrate a separability of σ and π contributions to the scattering of totally symmetric modes. The polarizability expression obtained here is compared with that of the semiclassical theory of Shorygin and an interesting resemblance is found. Finally it is shown how, depending on details of the electronic structure, the predicted form of the frequency dependence of scattered intensity ranges between the two expressions that have been commonly used to interpret observations.

Asymmetric excitation profiles in the resonance Raman response of armchair carbon nanotubes

“…2 by the second term of the dipole expansion 9,32 . Depending on the relative sign and magnitude of the A-and B-terms, the two contributions can interfere constructively or destructively.…”

Raman depolarization ratio of vibrational modes in solid C60

“…In addition, we note that the Raman scattering from solid C 60 is at resonance when excited with the 5145 A laser line [18]. According to the Albrecht's treatment of Raman intensity [19], two terms mainly contribute to the non-resonant scattering tensor: the A-( Frank-Condon) term is responsible for the elastic scattering and the B-(HerzbergTeller) term normally describes the one-phonon Raman scattering. However near a resonance the A-term can also contribute to the Raman scattering from the totally symmetric modes.…”

State-by-State Investigation of Destructive Interference in Resonance Raman Spectra of Neutral Tyrosine and the Tyrosinate Anion with the Simplified Sum-over-States Approach

“…First, the two terms in equation (4) are analogous to the Albrecht A and B terms. 23 As with the Albrecht A term, the first term in equation (4) has the derivative of the excitation energy Ωk with respect to the normal coordinate Q which is only nonzero for symmetric vibrational modes. Second, as the excitation frequency ω approaches the excitation energy Ωk, there is resonance with one of the excited electronic states and that state is expected to dominate the Raman intensity, which potentially allows us to restrict the summation to the excited states near or below the excitation frequency ω.…”