Resonances, Class

The important quantity is the coupling matrix element divided by the energy difference, not the matrix element itself. As a result, the early time dynamics is dominated by a single, easily visualized process, the flow of probability between the bright state and the selected resonant class of dark states. 

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. 

Unlike the typical laser source, the zero-point blackbody field is spectrally white , providing all colours, CO2, that seek out all co - CO2 = coj resonances available in a given sample. Thus all possible Raman lines can be seen with a single incident source at tOp Such multiplex capability is now found in the Class II spectroscopies where broadband excitation is obtained either by using modeless lasers, or a femtosecond pulse, which on first principles must be spectrally broad [32]. Another distinction between a coherent laser source and the blackbody radiation is that the zero-point field is spatially isotropic. By perfonuing the simple wavevector algebra for SR, we find that the scattered radiation is isotropic as well. This concept of spatial incoherence will be used to explain a certain stimulated Raman scattering event in a subsequent section. 

The chapter is divided into sections, one for each general class of mass spectrometer magnetic sector, quadnipole, time-of-flight and ion cyclotron resonance. The experiments perfonned by each are quite often unique and so have been discussed separately under each heading. 

No molecule is completely rigid and fixed. Molecules vibrate, parts of a molecule may rotate internally, weak bonds break and re-fonn. Nuclear magnetic resonance spectroscopy (NMR) is particularly well suited to observe an important class of these motions and rearrangements. An example is tire restricted rotation about bonds, which can cause dramatic effects in the NMR spectrum (figure B2.4.1). 

Members of a class of arenes called polycyclic aromatic hydrocarbons possess subslanlial resonance energies because each is a colleclion of benzene rings fused logelher... 

The accepted configuration of naphthalene, ie, two fused benzene rings sharing two common carbon atoms in the ortho position, was estabUshed in 1869 and was based on its oxidation product, phthaUc acid (1). Based on its fused-ring configuration, naphthalene is the first member in a class of aromatic compounds with condensed nuclei. Naphthalene is a resonance hybrid ... 

Physical Methods of Examination. Physical methods used to examine coals can be divided into two classes which, in the one case, yield information of a stmctural nature such as the size of the aromatic nuclei, ie, methods such as x-ray diffraction, molar refraction, and calorific value as a function of composition and in the other case indicate the fraction of carbon present in aromatic form, ie, methods such as ir and nuclear magnetic resonance spectroscopies, and density as a function of composition. Some methods used and types of information obtained from them are (41) ... 

Quasi-resonant converters are a separate class of switching power supplies that tune the ac power waveforms to reduce or eliminate the switching loss within the supply. This is done by placing resonant tank circuits within the ac current paths to create pseudo-sinusoidal voltage or current waveforms. Because the tank circuits have one resonant frequency, the method of control needs to be modified to a variable frequency control where the resonant period is fixed and the control varies the period of the non-resonant period. The quasi-resonant converters usually operate in the 300 kHz to 2 MHz frequency range. 

Some of the structural features of this class of compounds which are in accord with the resonance picture are as follows ... 

Since Stork et al. introduced as a new synthetic method the alkylation and acylation of carbonyl compounds via enamines, this class of compounds has been the subjeet of intensive studies 1-3). The exceptional physical and chemical behavior of the enamine structure can be ascribed to resonance by conjugation of the unshared pair of electrons of the nitrogen atom with the 77 electrons of the double bond ... 

However, water is a much weaker nucleophilic reagent than most of the above substances and therefore would not remain strongly bound unless some further forces were operative. It is our belief that resonance is the principal cause of this extra stabilization. We have found that these resonances are varied in nature, but they all fit into one or the other of the following principal classes. 

Tire and NMR parameters of some 1-alkyl-4-benzimidazolyl-2-idene- (type 72) and l-alkyl-4-(5-methylpyrazolyl-3-idene)-l,4-dihydro pyridines (type 73) were discussed in 89CC1086 and 91JOC4223. Comparison of the shifts for DMSO-dg and CDCI3 solutions with data reported for quaternary pyridinium compounds as well as anionic species in the azole series and data obtained for mesoionic betaines of the azinium azolate class left no doubt that these heterofulvalenes have a betaine character and, therefore, the NMR signals correspond to their dipolar resonance form. 

---