Resonant electronic states

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 ... 

Single-electronic-state (SES) limit The Raman spectroscopy in SES limit is where the incident photon energy is very close to, or falls within, the absorption band of an excited electronic state of a molecule, and the resulting Resonance Raman (RR) scattering is dominated by the properties of this resonant electronic state. 

A characteristic feature of scattering for totally symmetric modes is that contributions arise generally from all the vibrational levels of the resonant electronic state. The A-term scattering intensity depends on the square modulus of the scattering tensor, which is given by (resonant part only)... 

If the transition moment of the resonant electronic state is taken to lie in the z direction, the general set of three Raman invariants reduces effectively to only one Raman invariant... 

In addition, it can be shown that this Raman invariant is proportional to the square of the electronic absorption strength for the resonant electronic state through the relationship... 

The two principal resonance limits of the theory of ROA are the far-from-resonance (FFR) limit, the original form of the theory of ROA, and the single-electronic-state (SES) limit, for the case of strong resonance between a single excited electronic state and the incident laser radiation. In the case of FFR ROA, ab initio calculations have been carried out for direct comparison with experiment. The SES theory is so simple that the complete SES-ROA spectrum can be predicted from the parent resonance Raman spectrum and the electronic circular dichroism spectrum of the resonant electronic state. 

From these relationship emerges a deep connection between RROA in the SES limit and the electronic CD of the resonant electronic state. Since the anisotropy ratio, is defined as the ratio of the CD intensity to the parent intensity, the following expression is found... 

Figure Al.6.14. Schematic diagram showing the promotion of the initial wavepacket to the excited electronic state, followed by free evolution. Cross-correlation fiinctions with the excited vibrational states of the ground-state surface (shown in the inset) detennine the resonance Raman amplitude to those final states (adapted from [14].

One of the most interesting features of the Raman spectmm is its dependence on tire incident light frequency, coj. When Wj is on resonance with the excited electronic state, the scattering process closely resembles a process of absorption followed by emission. However, as Uj is detuned from resonance there are no longer... 

Infrared and Raman spectroscopy each probe vibrational motion, but respond to a different manifestation of it. Infrared spectroscopy is sensitive to a change in the dipole moment as a function of the vibrational motion, whereas Raman spectroscopy probes the change in polarizability as the molecule undergoes vibrations. Resonance Raman spectroscopy also couples to excited electronic states, and can yield fiirtlier infomiation regarding the identity of the vibration. Raman and IR spectroscopy are often complementary, both in the type of systems tliat can be studied, as well as the infomiation obtained. 

The siim-over-states method for calculating the resonant enlrancement begins with an expression for the resonance Raman intensity, /.y, for the transition from initial state to final state /in the ground electronic state, and is given by [14]... 

Figure Bl.3.5. Four WMEL diagrams for fiilly resonant Raman scattering (RRS). Diagrams (a) and (b) both have doorway stage rr(A.j2 ) (Figure B 1.3.4(a)), in which a vibrational coherence is created in the ground electronic state, g. For the window event in (a), field 1 promotes the bra from the ground electronic state, g, to...

As already mentioned, electronically resonant, two-pulse impulsive Raman scattering (RISRS) has recently been perfonned on a number of dyes [124]. The main difference between resonant and nom-esonant ISRS is that the beats occur in the absorption of tlie probe rather than the spectral redistribution of the probe pulse energy [124]. These beats are out of phase with respect to the beats that occur in nonresonant ISRS (cosinelike rather tlian sinelike). RISRS has also been shown to have the phase of oscillation depend on the detuning from electronic resonance and it has been shown to be sensitive to the vibrational dynamics in both the ground and excited electronic states [122. 124]. 

The SHG/SFG technique is not restricted to interface spectroscopy of the delocalized electronic states of solids. It is also a powerful tool for spectroscopy of electronic transitions in molecules. Figure Bl.5.13 presents such an example for a monolayer of the R-enantiomer of the molecule 2,2 -dihydroxyl-l,l -binaphthyl, (R)-BN, at the air/water interface [ ]. The spectra reveal two-photon resonance features near wavelengths of 332 and 340 mu that are assigned to the two lowest exciton-split transitions in the naphtli-2-ol... 

The energies of this Cl and of the other ones calculated in this work are listed in Table III. The calculated CASSCF values of the energies of the two lowest electronically states are 9.0 eV (5i, vertical) and 10.3 eV ( 2, vertical) [99]. They are considerably higher than the expenmental ones, as noted for this method by other workers [65]. In all cases, the computed conical intersections lie at much lower energies than the excited state, and are easily accessible upon excitation to Si. In the case of the H/allyl Cl, the validity confirmation process recovered the CHDN and 1,3-CHDN anchors. An attempt to approach the third anchor [BCE(I)] resulted instead in a biradical, shown in Figure 43. The bhadical may be regarded as a resonance hybrid of two allyl-type biradicals. 

Figure 9.50 Processes involved in obtaining (a) an ultraviolet photoelectron spectrum, (b) a zero kinetic energy photoelectron (ZEKE-PE) spectrum by a one-photon process and (c) a ZEKE-PE spectrum by a two-photon process in which the first photon is resonant with an excited electronic state of the molecule...

More commonly, the resonant two-photon process in Figure 9.50(c) is employed. This necessitates the use of two lasers, one at a fixed wavenumber Vj and the other at a wavenumber V2 which is tunable. The first photon takes the molecule, which, again, is usually in a supersonic jet, to the zero-point vibrational level of an excited electronic state M. The wavenumber of the second photon is tuned across the M to band system while, in principle, the photoelectrons with zero kinetic energy are detected. In practice, however, this technique cannot easily distinguish between electrons which have zero kinetic energy (zero velocity) and those having almost zero kinetic energy, say about 0.1 meV... 

Figure 9.51 A zero kinetic energy photoelectron (ZEKE-PE) resonant two-photon spectrum of 1,4-difluorobenzene in which the first photon excites the molecule of the zero-point level of the S-[ excited electronic state of the molecule. (Reproduced, with permission, from Reiser, G., Rieger, D., Wright, T.G., Muller-Dethlefs, K. and Schlag, E.W., J. Phys. Chem., 97, 4335, 1993)...

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