Resonant polarizabilities

No doubt, the present author has his own private consensus which, in spite of his efforts, may inject itself into the review. In order to offset such an undesirable bias, as much as possible, and perhaps putting the cart before the horse, the author will state here his own conclusions and beliefs I am convinced that electric field amplification and enhanced emission near SERS-active surfaces due to resonating metal excitations (surface-plasmon polaritons, plasmonlike modes, shape resonances, or electron-hole pairs) is an active mechanism in most of the systems studied. However, in most systems, this contribution, though an important one, is minor compared to the total enhancement possible in SERS. The major mechanism, in my opinion, must be a resonance mechanism, in the sense of a resonance Raman process, i.e., a mechanism by which a part of the system (molecule, molecule-metal atoms, metal surface) becomes a strong scatterer by virtue of its large resonance polarizability and not as a result of strong fields exerted by the other parts of the system . 

While, in general, /the calculated and observed values shown in Table 25 agree fairly well, an exact correlation cannot be expected, nor is it obtained. The calculation neglects all resonance, polarizability, and solvation effects that cannot be included in the polar... 

C. Quantum Confinement and Size Scaling of Off-Resonant Polarizabilities of Polyenes... 

Figure 16. Variation of electronic oscillator frequencies Qy, effective dipole moments and first (a), third (y), fifth (e), and seventh (rj) off-resonant polarizabilities with the number of modes used for octatetraene N = 8). The polarizabilities will be defined later in this Section. Here convergence of the DSMA to the full TDHF calculation M= 16 is demonstrated. The magnitudes of polarizabilities are normalized at their converged values a = 3.2 x 10 esu, y = 6.6 X 10 esu, a = 1.4 x 10 esu, rj = 2.3 X 10 esu. Reprinted with permission from ref 300. Copyright 1996 American Institute of Physics.

For example, at an intensity I of the counterpropagating traveling laser waves producing the standing laser wave of the order of (c/87t)Eo = 1 kWcm , and for a tjqjical atomic off-resonance polarizability x 10 cm , the condition (5.2) is satisfied only for atoms with quite a low temperature T < 1 /itK. In the case of localization of atoms in a three-dimensional standing hght wave (an optical lattice) (Letokhov 1973c), the proportion of trapped atoms at normal temperature is very small. So, the... 

Equation (A 1.6.94) is called the KHD expression for the polarizability, a. Inspection of the denominators indicates that the first temi is the resonant temi and the second temi is tire non-resonant temi. Note the product of Franck-Condon factors in the numerator one corresponding to the amplitude for excitation and the other to the amplitude for emission. The KHD fonnula is sometimes called the siim-over-states fonnula, since fonnally it requires a sum over all intennediate states j, each intennediate state participating according to how far it is from resonance and the size of the matrix elements that coimect it to the states i. and The KHD fonnula is fiilly equivalent to the time domain fonnula, equation (Al.6.92). and can be derived from the latter in a straightforward way. However, the time domain fonnula can be much more convenient, particularly as one detunes from resonance, since one can exploit the fact that the effective dynamic becomes shorter and shorter as the detuning is increased. 

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. 

Flere, the linear polarizability, a (oip 2), corresponds to the doorway stage of the 4WM process while to the window stage. We also see the (complex) Raman resonant energy denominator exposed. Of the tliree energy denominator factors required at third order, the remaining two appear, one each, m the two Imear polarizability tensor elements. 

In fact, each linear polarizability itself consists of a sum of two temis, one potentially resonant and the other anti-resonant, corresponding to die two doorway events, and D, and the window events, and described above. The hyperpolarizability chosen in equation (B1.3.12) happens to belong to the generator. As noted, such tliree-coloiir generators caimot produce Class I spectroscopies (fiill quadrature with tliree colours is not possible). Only the two-colour generators are able to create the Class I Raman spectroscopies and, in any case, only two colours are nomially used for the Class II Raman spectroscopies as well. 

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

Figure 3-6. a) The charge distribution, b) the inductive effect, and c) the resonance effect, d) the polarizability effect, e) the steric effect, and f) the stereoelectronic effect,... 

Previous studies with a variety of datasets had shown the importance of charge distribution, of inductive effect), of r-electronegativity, resonance effect), and of effective polarizability, aeffi polarizability effect) for details on these methods see Section 7.1). All four of these descriptors on all three carbon atoms were calculated. However, in the final study, a reduced set of descriptors, shown in Table 3-4, was chosen that was obtained both by statistical methods and by chemical intuition. 

The knowledge base is essentially two-fold on one hand it consists of a series of procedures for calculating all-important physicochemical effects such as heats of reaction, bond dissociation energies, charge distribution, inductive, resonance, and polarizability effects (.see Section 7.1). The other part of the knowledge base defines the reaction types on which the EROS system can work. 

There were two schools of thought concerning attempts to extend Hammett s treatment of substituent effects to electrophilic substitutions. It was felt by some that the effects of substituents in electrophilic aromatic substitutions were particularly susceptible to the specific demands of the reagent, and that the variability of the polarizibility effects, or direct resonance interactions, would render impossible any attempted correlation using a two-parameter equation. - o This view was not universally accepted, for Pearson, Baxter and Martin suggested that, by choosing a different model reaction, in which the direct resonance effects of substituents participated, an equation, formally similar to Hammett s equation, might be devised to correlate the rates of electrophilic aromatic and electrophilic side chain reactions. We shall now consider attempts which have been made to do this. 

In general, the dissection of substituertt effects need not be limited to resonance and polar components, vdiich are of special prominence in reactions of aromatic compounds.. ny type of substituent interaction with a reaction center could be characterized by a substituent constant characteristic of the particular type of interaction and a reaction parameter indicating the sensitivity of the reaction series to that particular type of interactioa For example, it has been suggested that electronegativity and polarizability can be treated as substituent effects separate from polar and resonance effects. This gives rise to the equation... 

Although cTi estimates by different methods or from different data sets may disagree, it is generally held that the inductive effect of a substituent is essentially independent of the nature of the reaction. It is otherwise with the resonance effect, and Ehrenson et al. have defined four different ctr values for a substituent, depending upon the electronic nature of the reaction site. An alternative approach is to add a third term, sometimes interpreted as a polarizability factor, and to estimate the inductive and resonance contribution statistically with the added parameter the resonance effect appears to be substantially independent of reaction site. " " ... 

However, there is evidence against d-orbital overlap and the stabilizing effects have been attributed to other causes. In the case of a PhS substituent, carbanion stabilization is thought to be due to a combination of the inductive and polarizability effects of the group, and d-pn resonance and... 

To summarize, if the low-lying states connected to the ground state by allowed dipole transition are not valence states but present a predominant Rydberg character, we have to introduce a lot of n) states if not, the value of dynamic polarizability near the first resonance is poor. 

It can be seen from Figures 3.7 and 3.8 that the calculations reproduce very well not only the experimental spectra but also the experimentally observed isotopic shifts indicating a high reliability of the computational method. According to this comparison, definite attribution can be made for even the difficult Raman bands that cannot be assigned based solely on the experimental results. It is, however, necessary to mention at this point that the calculated Raman spectrum provided directly by the ab initio computations correspond to the normal Raman spectrum with the band intensity determined by the polarizability of the correlating vibration. Since the intensity pattern exhibited by the experimentally recorded resonance Raman spectrum is due to the resonance enhancement effect of a particular chromophore, with no consideration of this effect, the calculated intensity pattern may, in many... 

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