Energy resonant

The partial wave decomposition of the incident-electron wave provides the basis of an especially appealing picture of strong, low-energy resonant scattering wherein the projectile electron spends a sufficient period of time in the vicinity... 

Figure B3.4.10. Schematic figure of a ID double-well potential surface. The reaction probabilities exliibit peaks whenever the collision energy matches the energy of the resonances, which are here the quasi-bound states in the well (with their energy indicated). Note that the peaks become wider for the higher energy resonances—the high-energy resonance here is less bound and Teaks more toward the asymptote than do the low-energy ones.

Quantum effects are observed in the Raman spectra of SWCNTs through the resonant Raman enhancement process, which is seen experimentally by measuring the Raman spectra at a number of laser excitation energies. Resonant enhancement in the Raman scattering intensity from CNTs occurs when the laser excitation energy corresponds to an electronic transition between the sharp features (i.e., (E - ,)" type singularities at energy ,) in the ID electronic DOS of the valence and conduction bands of the carbon CNT. 

Earlier studies of 4-aminopyridine 1-oxide were less conclusive. The solid-state infrared spectrum could be interpreted to indicate the existence of both the imino structure and/or, more probably, the amino structure. Comparison of the actual pKa value of 4-aminopyridine 1-oxide wdth the value calculated using the Hammett equation was considered to indicate that the compound existed as such or as an equilibrium mixture with l-hydroxypyrid-4-onimine, the latter possibility being considered the less likely on the basis of resonance and bond energies/ Resonance energy and ultraviolet spectral considerations have been advanced to support the 4-aminopyridine 1-oxide structure/ The presence of an infrared absorption band at... 

Hall, G. G., Proc. Roy. Soc. [London) A213, 113, The molecular orbital theory of chemical valency. XI. Bond energies, resonance energies and triplet state energies. ... 

The relevant Hamiltonian for the gas-phase solute molecules can be treated by the same three-orbitals four-electron model used in Chapter 2. Since the energy of 3 is much higher than that of , and d>2 (see Table 2.4), we represent the system by its two lowest energy resonance structures, using now the notation fa and fa as is done in eq. (2.40). The energies of these two effective configurations are now written as... 

FIGURE 3.3. A schematic description of the two low-energy resonance structures used to describe the S.v2 reaction [see eq. (3.26) for more details]. 

The Ca2+ Ion Provides Major Electrostatic Stabilization to the Two High-Energy Resonance Structures, 195... 

Remember that it is not the direct energy resonance between the vibrational levels in the two modes that is important. For cluster bond excitation, it is a resonance between the energy of the unoccupied vibrational levels in the weak cluster bond relative to the occupied excited level and quanta of thermal vibrational energy in... 

A second type of neutralization occurs through a resonance process, in which an electron from the sample tunnels to the empty state of the ion, which should then be at about the same energy. Resonance neutralization becomes likely if the electron affinity of the ion is somewhat larger than the work function of the sample, or if the ion has an unfilled core level with approximately the same energy as an occupied level in the target atom. The latter takes place when He+ ions come near indium, lead or bismuth atoms. The inverse process can lead to reionization. 

Figure 2 High-energy resonance behavior for some neutron cross sections.

Equation 1.132 has the property of never giving an energy that is lower than the true energy resonance principle cf Pauling, 1960). This property allows us to assign to the MO wave functions that are obtained by linear combination of the AO functions of the separate atoms (Linear Combination of Atomic Orbitals, or LCAO, method), by progressive adjustment of the combinatory parameters, up to achievement of the lowest energy. 

A DETAILED discussion of resonance energy can be found in books on quantum mechanics. A simple problem, the dependence of the energy resonance between two structures on the difference in energy of the structures, is discussed in the following paragraphs. 

The reaction Ne + (N2,Ne)N (Table III) is the only exoergic charge-transfer process for which the Cross section has been observed to increase with increasing vibrational quantum number of the neutral reactant.128 A probable rationale for this phenomenon is that both criteria of efficient charge transfer, namely, energy resonance and favorable Franck-Condon overlap, are satisfied if the reaction entails formation of a quartet N2+ state from the (v=2) vibrational level of N2 in the ground electronic state. 

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