Resonance Raman theory

The traditional approach to evaluating RR intensities involves a summation over all unperturbed eigenstates of the resonant electronic state. This is a direct consequence of the quantum-mechanical derivation of the polarizability tensor components employing second order perturbation theory as given by the Kramers-Heisenberg-Dirac (KHD) relation for the transition polarizability tensor  

r is the pth component of the transition dipole moment associated with the transition / — r, fip being the dipole moment operator in the p direction, uiq and uj,-i 

Section 6.1.2.1.1 is contributed by W. Kiefer, Wurzburg and M. Spiekermann, Liibeck 

The interpretation of Eq. (6.1-1) is that Raman scattering is a two-photon process involving virtual absorption from the initial state / to the entire manifold of eigenstates of the unperturbed molecule, followed by virtual emission to the final state /. 

When the angular frequency of the exciting light (cuo) becomes elose to the transition angular frequency for an absorption band of the molecule (u ) the first term of Eq. (6.1-1) begins to dominate, and the resonant excited state dominates the sum over states of the Raman polarizability expression. Thus, for excitation into an absorption band (loq w LOri) Eq.(6.1-1) may now be rewritten as 

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Myers A B 1997 Time dependent resonance Raman theory J. Raman Spectrosc. 28 389—401... 

The theory discussed until now is based on the Kramers-Heisenberg-Dirac dispersion relation for the transition polarizability tensor as given in Eq. (6.1-1). The expression shown in this equation describes a steady state scattering process and contains no explicit reference to time. Therefore, the resonance Raman theory which is based on the KHD dispersion relation is sometimes also termed as time-independent theory (Ganz et al., 1990). 

Based on the two approaches to continuum resonance Raman theory, many spectra of diatomic molecules could be successfully simulated (Hartke, 1989, 1991 Ganz and Kiefer, 1993a, 1994). Besides the good simulations of continuum resonance Raman band... 

Resonance Raman theory (33) predicts an enhancement of the scattering intensity, when the excitation wavelength approaches iriax th long wavelength side. This effect is clearly seen... 

The behavior of insoluble monolayers at the hydrocarbon-water interface has been studied to some extent. In general, a values for straight-chain acids and alcohols are greater at a given film pressure than if spread at the water-air interface. This is perhaps to be expected since the nonpolar phase should tend to reduce the cohesion between the hydrocarbon tails. See Ref. 91 for early reviews. Takenaka [92] has reported polarized resonance Raman spectra for an azo dye monolayer at the CCl4-water interface some conclusions as to orientation were possible. A mean-held theory based on Lennard-Jones potentials has been used to model an amphiphile at an oil-water interface one conclusion was that the depth of the interfacial region can be relatively large [93]. 

RRS has also introduced the concept of a Raman excitation profile (REPy for thefth mode) [46, 4lZ, 48, 49, 50 and M]. An REP. is obtained by measuring the resonance Raman scattering strength of thefth mode as a fiinction of the excitation frequency [, 53]. Flow does the scattering intensity for a given (thefth) Raman active vibration vary with excitation frequency within an electronic absorption band In turn, this has led to transfomi theories that try to predict... 

Page J B and Tonks D L 1981 On the separation of resonance Raman scattering into orders in the time correlator theory J. Chem. Phys. 75 5694-708... 

Albrecht A C, Clark R J H, Oprescu D, Owens S J R and Svensen C 1994 Overtone resonance Raman scattering beyond the Condon approximation transform theory and vibronic properties J. Chem. Phys. 101 1890-903... 

Page J B 1991 Many-body problem to the theory of resonance Raman scattering by vibronic systems Top. Appi. Phys. 116 17-72... 

Pollard W T, Dexhelmer S L, Wang Q, Peteanu L A, Shank C V and Mathles R A 1992 Theory of dynamic absorption spectroscopy of nonstatlonary states. 4. Application to 12 fs resonant Raman spectroscopy of bacterlorhodopsin J. Phys. Chem. 96 6147-58... 

The resonance Raman effect — review of the theory and of applications in inorganic chemistry. R. J. H. Clark and B. Stewart, Struct. Bonding (Berlin), 1979, 36, 1-80 (110). 

Clarke RJH, Stewart B (1979) The Resonance Raman Effect. Review of the Theory and of AppUcations in Inorganic Chemistty 36 1-80... 

Resonance Raman spectroscopy has been applied to studies of polyenes for the following reasons. The Raman spectrum of a sample can be obtained even at a dilute concentration by the enhancement of scattering intensity, when the excitation laser wavelength is within an electronic absorption band of the sample. Raman spectra can give information about the location of dipole forbidden transitions, vibronic activity and structures of electronically excited states. A brief summary of vibronic theory of resonance Raman scattering is described here. 

Resonance Raman scattering, 21 326-327 Resonance stabilization of benzene, 3 599 Resonance theory, 20 774 Resonant cavity, 14 851 Resonant-cavity enhanced structures,... 

The geometry changes which transition metal complexes undergo when excited electronic states are populated are determined by using a combination of electronic emission and absorption spectroscopy, pre-resonance Raman spectroscopy, excited state Raman spectroscopy, and time-dependent theory of molecular spectroscopy. 

Excited State Distortions of W(C0)5pyridine and W(C0)5piperldlne from Time-Dependent Theory, Pre-resonance Raman Spectroscopy, and Electronic Spectroscopy... 

Calculation of Excited State Distortions of W(C0)rL. The emission spectrum discussed earlier, the theory discussed above and pre-resonance Raman data will now be used in concert to calculate the multi-mode distortions. The relative intensities of the peaks in the pre-resonance Raman spectra were determined by integrating the peaks. All of the peaks in the experimental spectrum having intensities greater than three percent of that of the most intense peak were measured and used in the calculations. 

The bond length changes determined from pre-resonance Raman spectra, electronic spectra and time dependent theory provide a detailed picture of the results of bonding changes caused by populating excited electronic states. There is a direct but not linear correlation between bond length changes and the... 

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