Resonant systems

Figure Al.2.11. Resonant collective inodes of the 2 1 Fenni resonance system of a coupled stretch and bend with an approximate 2 1 frequency ratio. Shown is one end of a syimnetric triatomic such as H2O. The nomial stretch and bend modes are superseded by the horseshoe-shaped modes shown in (a) and (b). These two modes have different frequency, as further illustrated in figure Al.2.12.

The sharpness of the frequency response of a resonant system is conunonly described by a factor of merit, called the quality factor, Q=v/Av. It may be obtained from a measurement of the frill width at half maxuuum Av, of the resonator frequency response curve obtained from a frequency sweep covering the resonance. The sensitivity of a system (proportional to the inverse of tlie minimum detectable number of paramagnetic centres in an EPR cavity) critically depends on the quality factor... 

Ezra G S 1996 Periodic orbit analysis of molecular vibrational spectra-spectral patterns and dynamical bifurcations in Fermi resonant systems J. Chem. Phys. 104 26... 

Fig. 3. A block diagram schematic representation of a Fourier transform nmr spectrometer, ie, a superconducting magnetic resonance system.

The two sets of coefficients result in two sets of Fock matrices (and their associated density matrices), and ultimately to a solution producing two sets of orbitals. These separate orbitals produce proper dissociation to separate atoms, correct delocalized orbitals for resonant systems, and other attributes characteristic of open shell systems. However, the eigenfunctions are not pure spin states, but contain some amount of spin contamination from higher states (for example, doublets are contaminated to some degree by functions corresponding to quartets and higher states). 

In acid-base titrations the end point is generally detected by a pH-sensitive indicator. In the EDTA titration a metal ion-sensitive indicator (abbreviated, to metal indicator or metal-ion indicator) is often employed to detect changes of pM. Such indicators (which contain types of chelate groupings and generally possess resonance systems typical of dyestuffs) form complexes with specific metal ions, which differ in colour from the free indicator and produce a sudden colour change at the equivalence point. The end point of the titration can also be evaluated by other methods including potentiometric, amperometric, and spectrophotometric techniques. 

It is often asked whether or not the constituent structures of a resonating system, such as the Kekul4 structures for the benzene molecule, are to be considered as having reality. There is one sense in which this question may be answered in the affirmative but the answer is definitely negative if the usual chemical significance is attributed to the structures. A substance showing resonance between two or more valence-bond structures does not contain molecules with the configurations and properties usually associated with these structures. The constituent structures of the resonance hybrid do not have reality in this sense. 

The direct measurement of CH,- radicals, using a matrix isolation electron spin resonance system (MIESR), has previously demonstrated that surface-generated CH,-radicals are produced during the oxidative coupling of CH4 and emanate into the gas phase... 

X. and Du, J. (2012) Quantum factorization of 143 on a dipolar-coupling nuclear magnetic resonance system. 

Yariv, A., Critical coupling and its control in optical waveguide ring resonator systems, IEEE Photonics Technol. Lett. 2002, 14, 483 485... 

Nuclear magnetic resonance systems, electromagnets for, 23 857-861 Nuclear metallurgy, 76 127 Nuclear Nonproliferation Act of 1978, 77 550... 

Hydroxytriphenylmethane derivatives give rise to anionic charge-resonance systems that are isoconjugate with the corresponding amino-substituted dyes. Thus, for example, the oxonol analogue of malachite green is benzaurine (Scheme 6.33). The quinonoid neutral form (6.184), which is pale yellow, produces a violet anion (6.185) on the addition of alkali in... 

Fluorescein (6.198 X = H Cl Acid Yellow 73) is the xanthene analogue of phenolphthalein (6.190) and gives rise to an anionic charge-resonance system. This was the... 

The first cyanine dye was made in 1856 by Greville Williams. Thus the blue charge-resonance system 6.216 was produced when oxidative coupling took place between N-... 

The primary chemical aspect of a mesomeric pigment system concerns the correlation between tinctorial strength and extent of electron delocalization. A higher degree of conjugation in a molecule is associated with a bathochromic shift color strength improves with the intensity of absorption. A resonating system proliferates by ... 

The reverse is true for large substituents within a molecule which do not contribute to the resonating system. These may have an adverse effect on the tinctorial strength. 

An optical resonator system, which provides the optical feedback. 

The and spectroscopy of a solution of 2-chloro-3,5-dinitropyridine in liquid ammonia at-40°C showed the formation of the C-6 adduct (10). This adduct is rather stable, since after 1 hr standing, no change in the spectrum was observed. It is interesting that at a somewhat lower temperature (-60°C) the addition takes place at C-4, i.e., formation of (9). Apparently one deals with the interesting concept of kinetically and thermodynamically controlled covalent adduct formation. At -60°C the addition is kinetically controlled, and at -40°C the addition is thermodynamically favored. The higher stability of the C-6 adduct compared to the C-4 adduct is probably due to the more extended conjugate resonance system (Scheme II.9). 

Resonance-stabilized systems include car-boxylate groups, as in formate aliphatic hydrocarbons with conjugated double bonds, such as 1,3-butadiene and the systems known as aromatic ring systems. The best-known aromatic compound is benzene, which has six delocalized k electrons in its ring. Extended resonance systems with 10 or more 71 electrons absorb light within the visible spectrum and are therefore colored. This group includes the aliphatic carotenoids (see p.l32), for example, as well as the heme group, in which 18 k electrons occupy an extended molecular orbital (see p. 106). 

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