The Origin of Resonances

The origin of resonance Raman enhancement is explained in terms of Eq. 1.201. In normal Raman spectroscopy, Vo is chosen in the region that is far from the electronic absorption. Then, v vq, and a.p is independent of the exciting frequency vq. In resonance Raman spectroscopy, the denominator, Vq, becomes very small as vq approaches v. Thus, the first term in the square brackets of Eq. 1.201 dominates all other terms and results in striking enhancement of Raman lines. However, Eq. 1.201 cannot account for the selectivity of resonance Raman enhancement since it is not specific about the states of the molecule. Albrecht [103] derived a more specific equation for the initial and final states of resonance Raman scattering by... 

Finally, in this account of multiparameter extensions of the Hammett equation, we comment briefly on the origins of the a, scale. This had its beginning around 1956 in the a scale of Roberts and Moreland for substituents X in the reactions of 4-X-bicyclo[2.2.2]octane-l derivatives. However, at that time few values of o were available. A more practical basis for a scale of inductive substituent constants lay in the o values for XCHj groups derived from Taft s analysis of the reactivities of aliphatic esters into polar, steric and resonance effects . For the few o values available it was shown that o for X was related to o for XCHj by the equation o = 0.45 <7. Thereafter the factor 0.45 was used to calculate c, values of X from o values of XCH2 . ... 

The same method of analysis of emitted particles was applied to elucidate the origin of non-stability of piezoquartz resonators with silver electrodes [35]. 

Electron spin resonance (ESR), or electron paramagnetic resonance (EPR) as it is sometimes known, shares many similarities with its cousin, NMR. The origin of the phenomenon is the spin of the electron (rather than the nuclear spin) coupling with the nuclear spins of the atoms in the polymer, but much of the physics of their interactions are similar. The usual spin Hamiltonian, which is used to determine the energies of the interactions, can be written as... 

The origin of cyclopropenone chemistry goes back to the successful preparation of stable derivatives of the cyclopropenium cation <5 3), the first member of a series of Huckel-aromatic monocyclic carbo-cations possessing a delocalized system of (4n + 2)-7r-electrons. This experimental confirmation of LCAO-MO theory stimulated efforts to prepare other species formally related to cyclopropenium cation by a simple resonance description of electron distribution, namely cyclopropenone 7 and methylene cyclopropene (triafulvene) 8 ... 

Because trans dispositions commonly result from co-bonding (the near-linear alignment of the hyperbonding 3c/4e X—M- L triad), it is not surprising that the origin of the trans influence can be traced to the resonance nature of co-bonding. When H is placed trans to a halide or PH3, the dominant resonance structure will be that with a 2c/2e M—H bond and a donor pair of electrons on the halide or phosphine ligand, as depicted on the left in (4.93) ... 

As remarked in Section 5.1.2, the discovery of hydrogen bonding provoked ongoing controversy between proponents of a partial covalency and advocates of an electrostatic picture of H-bond formation. The former group emphasized the importance of resonance-type chemical forces of quantum-mechanical origin that could be represented as... 

The unique field penetration into the liquid of a nonevanescent resonant mode like Tlij(7)0 is very promising for the sensing applications. To understand the origin of this behavior and further optimize the devices, a ray optical picture71 is presented. This type of resonant modes exist as if rays are bounced at the liquid/silica interface and confined in the liquid region as plotted in Fig. 8.32. From the viewpoint of ray optics, light is partially reflected (termed ray 1) and partially transmitted when it is... 

---