Classical resonance effects

The electromagnetic spectrum is a quantum effect and the width of a spectral feature is traceable to the Heisenberg uncertainty principle. The mechanical spectrum is a classical resonance effect and the width of a feature indicates a range of closely related r values for the model elements. 

It has long been known that a substituent X in an XGY system can exert an electrical effect on an active site Y. It is also well known that the electrical effect which results when X is bonded to an sp hybridized carbon atom differs from that observed when X is bonded to an sp or an sp hybridized carbon atom. As electron delocalization is minimal, in the first case, it has been chosen as the reference system. The electrical effect observed in systems of this type is a universal electrical effect which occurs in all systems. In the second type of system, a second effect (resonance effect) occurs due to delocalization, which is dependent both on the inherent capacity for delocalization and on the electronic demand of file active site. In systems of the second type the overall (total) electrical effect is assumed to be a combination of the universal and the delocalized electrical effects. For many years an argument has sometimes raged (and at other times whimpered) concerning the mode of transmission of the universal electrical effect. Two models were proposed originally by Derick, a through bond model (the inductive effect) and a through space model (the field effect). These proposals were developed into the classical inductive effect (CIE) and the classical field effect (CFE)" models. As the CIE model could not account... 

The classical Raman effect produces only very weak signals. There are two techniques which very successfully enhance this effect. The resonance Raman spectroscopy RRS is making use of the excitation of molecules in a spectral range of electronic absorption. The surface-enhanced Raman spectroscopy SERS employs the influence of small metal particles on the elementary process of Raman scattering. These two techniques may even be combined surface-enhanced resonance Raman effect SERRS. Such spectra are recorded with the same spectrometers as classical Raman spectra, although different conditions of the excitation and special sample techniques are used (Sec. 6.1). 

Both the valence-bond and molecular-orbital methods show that there is delocalization in benzene. For example, each predicts that the six carbon-carbon bonds should have equal lengths, which is true. Since each method is useful for certain purposes, we will use one or the other as appropriate. Recent ab initio, SCF calculations confirms that the delocalization effect acts to strongly stabilize symmetric benzene, consistent with the concepts of classical resonance theory. ... 

For meta- and para-substituted phenols, log values spread over 2 log units from 3-dimethylaminophenol to 4-nitro-3-trifluoromethylphenol. Their order is well explained by classical electronic effects. A dual-substituent parameter analysis gives equations 16 and 17, where crp and ctr are the Taft field-inductive and resonance substituent constants, respectively. 

Reactions with opposite signs of resonance and field reaction constants are rare. In our compilation, only 14 such reactions are mentioned (Zollinger, 1990, Table I), among them 6 involving dediazoniations (see Zollinger, 1994, Sect. 8.4). The main question is still open What is the basic reason that there are thousands of reactions for which the classical Hammett equation (i. e., field and resonance effects operate in the same direction) is applicable but only few processes in which the field and resonance effects have opposite signs. 

In 1945 Calvin and Wilson (50) first suggested the importance of "benzenoid resonance in metal chelates of /ff-ketoenolates. In their classic paper, Stability of Chelate Compounds , Calvin and Wilson attempted to "determine the influence of certain structural factors upon the stability of the chelate complexes of divalent copper in which four atoms bound to the metal are all oxygen. After determining stability constants for the copper chelate complexes, the authors conclude for j8-diketonate ligands that "in addition to their character as bases, a benzenoid resonance effect involving copper plays a very important role in determining the stability of these compounds. The canonical forms which Calvin and Wilson considered important are shown below. 

About SEFS as a spectroscopic feature, it can be said that this structure is a manifestation of effects of the strong electron-hole correlation (with a hole on the atom core level) upon excitation of the atom by an electron impact. As opposed to the classical autoionization effects (Fano effects), where the presence of a resonance level is assumed, in the present case a strongly correlated state is observed... 

ABSTRACT. The study of periodic orbits embedded in the continuum has provided a new tool for understanding the dynamics of molecular collisions, The application of periodic orbit theory to classical variational transition state theory, quantal threshold and resonance effects is presented. Special emphasis is given to the stability analysis of periodic orbits in collinear and three dimensional systems. Future applications of periodic orbit theory are outlined. 

The question of non-classical manifestations is particularly important in view of the chaos that we have seen is present in the classical dynamics of a multimode system, such as a polyatomic molecule, with more than one resonance coupling. Chaotic classical dynamics is expected to introduce its own peculiarities into quantum spectra [29, 77]. In Fl20, we noted that chaotic regions of phase space are readily seen in the classical dynamics corresponding to the spectroscopic Flamiltonian. Flow important are the effects of chaos in the observed spectrum, and in the wavefiinctions of tire molecule In FI2O, there were some states whose wavefiinctions appeared very disordered, in the region of the... 

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