Raman scattering, resonance

However, near resonance, the approximation made in the previous section, namely that the denominators were almost constant, is no longer valid. In this case, we recognize that most of the scattering will now be obtained from the first term alone since we have a rapidly converging Taylor series in which, when the factors i k) k f) are not small, the second term is several orders of magnitude less than the first. In the usual notation we write a p = A3- B 3- Q where 

This comes from the first term in Eq. (41). The terms B and C from the second term will be considered in Section 4.3. Since we are presumed near a resonance with a particular vibronic state, one term in these sums will dominate. The scattering intensity is then  

Note that when the Franck-Condon factors in Eq. (44) are small, it is also possible to obtain resonance Raman intensity from the second term in Eq. (41), when similar considerations apply. However, in this case we must consider contributions from the Herzberg-Teller effect, which is described in the next section. 

Note that this result is obtained irrespective of the distribution / vi- 

Such processes can be realized experimentally both in the time domain and in the energy domain. We may send a pulse of light of finite width, that is a wavepacket in momentum and energy spaces, onto the molecular system and monitor the scattered light as a function of frequency, direction, and time. Alternatively we may use a continuous wave (CW) field, a wave of infinite duration (relative to relevant 

In what follows we focus on long time, frequency-domain Raman scattering, which is easier to analyze. To simplify notation we denote the initial state, 11, vi, ki) by zzz) and the final state 1, v, k) by out. We also assume that a single zero-photon excited state Is ) = 2, V2,0) is close to resonance with the incident radiation, that is, in(vi, yi) = i,vi + — Es = 2,Vi. where mi = ki c and c is the speed of 

In (18.18) we have lumped together all the relevant continuous state manifolds that overlap with Eg into the group [/. In fact, the state out) formally belongs to this group as a member of the radiative continua, however, it has special status as the outgoing state of the process under discussion. 

Before proceeding, let us consider the expected dependence on the intensity of the incident field. The scattering process is obviously not linear in the molecule-field interaction, however, it is intuitively expected that for weak incident radiation the scattering signal will be linear in the incident intensity. To see this note that as in the previous section we simplify the theory by considering the scattering process l,vi,ki (lx) = 2, V2,0)) l,v,k), while in reality the process 

A progression in the excited-state frequency occurs in absorption. B. A progression in the ground-state frequency occurs in relaxed fluorescence where non-radiative relaxation processes occur faster than the emission process in the excited state. C. Excited state vibrational intervals may occur in hot luminescence where the speed of non-radiative relaxation is similar to, or slower than, that of the emission process 

Since the H-T terms are developed from the first-order terms active in the nonresonance Raman effect, they are usually the most important source of preresonance enhancement whereas the FC terms are active in proportion to the extent to which closure fails for the vibrational levels of the intermediate state. Some physical insight into these different scattering mechanisms is furnished by the following interpretation of the energy denominators of the scattering tensor. 

Discrete Resonance Raman Scattering (Resonance Fluorescence 1 

when closure over the vibrational levels begins to fail as resonance is approached and AE hcu, the implication is that the lifetime of the intermediate state is given by At . In the limit of exact resonance, when AE = 0, the lifetime is 

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In this section we will discuss more conventional spectroscopies absorption, emission and resonance Raman scattering. These spectroscopies are generally measured under single frequency conditions, and therefore our... 

Figure Al.6.15. Schematic diagram, showing the time-energy uncertainty principle operative in resonance Raman scattering. If the incident light is detuned from resonance by an amount Aco, the effective lifetime on the excited-state is i 1/Aco (adapted from [15]).

The more conventional, energy domain fonnula for resonance Raman scattering is the expression by Kramers-Heisenberg-Dirac (KHD). The differential cross section for Raman scattering into a solid angle dD can be written in the fomi... 

Shreve A P and Mathies R A 1995 Thermal effects in resonance Raman-scattering—analysis of the Raman intensities of rhodopsin and of the time-resolved Raman-scattering of bacteriorhodopsin J. Phys. Chem. 99 7285-99... 

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... 

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...

Lee S Y 1983 Placzek-type polarizability tensors for Raman and resonance Raman scattering J. Chem. Phys. 78 723-34... 

Hizhnyakov V and Tehver I 1988 Transform method in resonance Raman scattering with quadratic Franck-Condon and Herzberg-Teller interactions J. Raman Spectrosc. 19 383-8... 

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... 

Cable J R and Albrecht A C 1986 The inverse transform in resonance Raman scattering Conf. sponsored by the University of Oregon ed W L Peticolas and B Hudson... 

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... 

Joo T and Albrecht A C 1993 Inverse transform in resonance Raman scattering an iterative approach J. Phys. Chem. 97 1262-4... 

Marzocchi M P, Mantini A R, Casu M and Smulevich G 1997 Intramolecular hydrogen bonding and excited state proton transfer in hydroxyanthraquinones as studied by electronic spectra, resonance Raman scattering, and transform analysis J. Chem. Phys. 108 1-16... 

Tripathi G N R and Schuler R H 1982 Time-resolved resonance Raman scattering of transient radicals the p-aminophenoxyl radical J. Chem. Phys. 76 4289-90... 

Walmsiey I A, Wise F W and Tang C L 1989 On the difference between quantum beats in impulsive stimulated Raman scattering and resonance Raman scattering Chem. Phys. Lett. 154 315-20... 

Values aie foi noniesonant scatteiing of visible and neai-uv radiation by atmosphetic gases resonant Raman scattering approaches 10 cm /sr. 

Band gaps in semiconductors can be investigated by other optical methods, such as photoluminescence, cathodoluminescence, photoluminescence excitation spectroscopy, absorption, spectral ellipsometry, photocurrent spectroscopy, and resonant Raman spectroscopy. Photoluminescence and cathodoluminescence involve an emission process and hence can be used to evaluate only features near the fundamental band gap. The other methods are related to the absorption process or its derivative (resonant Raman scattering). Most of these methods require cryogenic temperatures. 

Utilization of resonance effects can facilitate unenhanced Raman measurement of surfaces and make the technique more versatile. For instance, a fluorescein derivative and another dye were used as resonantly Raman scattering labels for hydroxyl and carbonyl groups on glassy carbon surfaces. The labels were covalently bonded to the surface, their fluorescence was quenched by the carbon surface, and their resonance Raman spectra could be observed at surface coverages of approximately 1%. These labels enabled assess to changes in surface coverage by C-OH and C=0 with acidic or alkaline pretreatment [4.293]. 

Ren et al. reported a method to prepare a gold tip with a tip apex radius of 30 nm reproducibly [27]. They observed the TERS of a Malachite Green isothiocyanate (MGITC) monolayer on an Au(lll) surface and obtained an enhancement factor of about 1.6 X 10, by using the relation, q= /TERs/lRRs=g /l focus where q is the net increase in the signal. Iters snd rrs the signal intensities for TERS and RRS (resonance Raman scattering), respectively is the TERS enhancement (gis the field enhancement), a denotes the radius of the enhanced field, and Rfocus the radius of the laser focus. 

Resonance Raman scattering occurs when the incident photon of light (El) has enough energy to approach or become resonant with an electronic transition of the molecule (Eq + - e,) so that the first term in equation (3.2) becomes predomi-... 

Figure 3.1. Simple schematic diagram of resonance Raman scattering in a harmonic system. The initial state i> is excited by the incident photon of energy El that is resonant with the set of energy levels v>. The scattering of the photon with energy Eg takes the system from i> to f>.

Optical Properties and Resonance Raman Scattering of Carotenoids.89... 

OPTICAL PROPERTIES AND RESONANCE RAMAN SCATTERING OF CAROTENOIDS... 

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