A-term resonance

A-term resonance ct)(excited) ct)(ground), goC xcited) QoCground) totally symmetric vibrational modes are enhanced. 

For A-term resonance enhancement, either the frequency, m, or the equilibrium normal coordinate, Q, of the vibration must change between the ground and dipole-allowed excited electronic states. For B-term resonance enhancement, the vibration must be vibronically active for coupling the dipole-allowed excited electronic state to other excited electronic states. For C-term resonance enhancement due to a vibronically coupled excited electronic state, both the totally symmetric vibrational modes and the overtones and combinations of the vibronically active vibrational modes are enhanced. 

As seen in Eqs. 1.216 and 1.217, both A and B terms involve summation over v, which is the vibrational quantum number at the electronic excited state. Since the harmonic oscillator selection rule (Au = =t 1) does not hold for a large u, overtones and combination bands may appear under resonance conditions. In fact, series of these nonfundamental vibrations have been observed in the case of A-term resonance (Sec. 1.23). 

An example of the A-term resonance is given by I2, which has an absorption band near 500 nm and its fundamental at 2 lOcm. Figure 1.31 shows the RR spectrumof I2 in solution obtained by Kiefer and Bernstein [105] (excitation at 514.5 nm). It shows a series of overtones up to the seventeenth. The vibrational energy of an anharmonic oscillator including the cubic term is expressed as... 

Theoretical treatments of Raman intensities of these overtone series under rigorous resonance conditions have been made by Nafie et al. [107]. There are many other examples of RR spectra of small molecules and ions that exhibit A-term resonance. Section 2.6 includes references on RR spectra of the CrO and Mn04 ions. Kiefer [101] reviewed RR studies of small molecules and ions. 

B2y, and >42 vibrations are expected to be polarized (p), depolarized (dp), and inversely polarized (tp ), respectively. These polarization properties, together with their vibrational frequencies, were used by Spiro and his coworkers to make complete assignments of vibrational spectra of the Fe-porphin skeletons of a series of heme proteins. They showed that the resonance Raman spectrum may be used to predict the oxidation and spin states of the Fe atom in heme proteins. For example, the Fe atom in oxyhemoglobin has been shown to be low-spin Fc(IIl). It should be noted that the A2y mode, which is normally Raman inactive, is observed under the resonance condition. Although the modes are rather weak in Fig. I-19, these vibrations are enhanced markedly and exclusively by the excitation near the B band since the A-term resonance is predominant under such condition. The majority of compounds studied thus far exhibit the A-term rather than the l -term resonance. A more complete study of resonance Raman spectra involves the observation of excitation profiles (Raman intensity plotted as a function of the exciting frequency for each mode), and the simulation of observed excitation proliles based on various theories of resonance Raman spectroscopy. ... 

The term resonance has also been applied in valency. The general idea of resonance in this sense is that if the valency electrons in a molecule are capable of several alternative arrangements which differ by only a small amount in energy and have no geometrical differences, then the actual arrangement will be a hybrid of these various alternatives. See mesomerism. The stabilization of such a system over the non-resonating forms is the resonance energy. 

Af-Oxidation of pyrazines appears to result in increased shielding of the a and a carbon resonances by 6-11 p.p.m., whereas the /3 and /3 carbon atoms are deshielded by 3-4 p.p.m., a trend similar to that observed with substituted pyridines. These results have been qualitatively explained in terms of resonance polar effects (80OMR(l3)l72). 

Instead of formulating the wave function for a crystal as a sum of functions describing various ways of distributing the electron-pair bonds among the interatomic positions, as was done in the first section of this paper, let us formulate it in terms of two-electron functions describing a single resonating valence bond. A bond between two adjacent atoms ai and cq- may be described by a function < i3-(l, 2) in which 1 and 2 represent two electrons and the function i may have the simple Heitler-London form... 

Which of two formulas for benzene is correct The answer is neither. The two forms are called resonance structures. The term resonance is a bit misleading because it implies that the two forms are oscillating back and forth. In reality, the carbon-carbon bond lengths in a resonating structure such as benzene are all the same. Resonant structures have only one form, a resonance hybrid somewhere between the two possibilities. 

The F + H2 — HF + FI reaction is one of the most studied chemical reactions in science, and interest in this reaction dates back to the discovery of the chemical laser.79 In the early 1970s, a collinear quantum scattering treatment of the reaction predicted the existence of isolated resonances.80 Subsequent theoretical investigations, using various dynamical approximations on several different potential energy surfaces (PESs), essentially all confirmed this prediction. The term resonance in this context refers to a transient metastable species produced as the reaction occurs. Transient intermediates are well known in many kinds of atomic and molecular processes, as well as in nuclear and particle physics.81 What makes reactive resonances unique is that they are not necessarily associated with trapping... 

The first two terms in (5) are called D-terms or dipolar terms, which are nonzero only if Ape =/= 0. The two-photon resonance denominator, ( leg — 2hco), indicates that an electron is excited into the lower excited state e. If we consider a near resonance condition hco = %imaginary part of the D-terms can be written in SI units as ... 

Thus a single Lorentzian line is obtained that is centered at a weighted average resonant frequency and has a width proportional to a weighted average T2x plus a term proportional to the average lifetime and the square of the separation of the slow exchange resonances. 

Finally, we should also mention that assisted spin recoupling is by no means restricted to 1H, 13C, and 15N spin species but may also be used to facilitate H and 2H to low- spin transfers. This may be exploited in extensively deuterated samples using rf fields on JH and 2H which are matched to a rotary resonance condition to facilitate spin-diffusion between 13C spins in a longitudinal mixing process. This was recently demonstrated by van Rossum and coworkers in terms of the doublenucleus enhanced recoupling (DONER) experiment [143]. 

From polarity considerations, one can recognize that the prefactor CxeA> of the nonbonded term is minimized by the same concerted polarization pattern as that shown in (3.179), which is consistent with maximization of the one-center term. This is also consistent with higher ionic character and the X+ A Y resonance pattern shown in Fig. 3.78. 

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