B-term resonance

B-term resonance Excited state is vibronically coupled to other excited states vibronically active modes are enhaneed. 

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. 

In contrast to the A term, the B term resonance requires at least one more electronic excited state(s), which must be mixed with the e state via normal vibration, Qa. Namely, the integral (e I I s ) must be nonzero. The -term resonance is significant only when these two excited states are closely located so that the denominator, E — E, is small. Other requirements are that the and g s... 

Relaxation can be described in terms of the magnetization vector components. At resonance, the equilibrium magnetization M0 parallel to B0 decreases to Mz, due to the transitions between the nuclear magnetic energy levels caused by the alternating field B,. Following resonance, the equilibrium of the nuclear spins with their lattice and with each other is restored by relaxation. 

Written as the sum over the products, -AAmAfim, electrodynamic interactions show a kind of specificity. They prefer the interaction of like, resonating materials compared with the interaction of unlike species. This specificity, though, occurs as a difference between possible combinations of interactions If A and B are made of different substances, then the sum of A-A and B-B interactions is always less than two interactions A-B. Term by term in the sum, there is the inequality [from the inequality of geometric and arithmetic means that says ab < (a2 + b2)/2] ... 

Problem 11.8 (a) Give the delocalized structure (Problem 11.1) for the 3 benzenonium ions resulting from the common ground state for electrophilic substitution, C6H5G + E+. (b) Give resonance structures for the para-benzenonium ion when G is OH. (c) Which ions have G attached to a positively charged C (d) If the products from this reaction are usually determined by rate control (Section 8.5), how can the Hammond principle be used to predict the relative yields of op (i.e., the mixture of ortho and para) as against m (meta) products (e) In terms of electronic effects, what kind of G is a (i) op-director, (ii) m-director (/) Classify G in terms of its structure and its electronic effect. ... 

A few of the characteristics of the integrals that need to be solved in the secular determinant should be outlined. Haa and Hbb are called coulomb integrals and are described as the energy of an electron occupying the basis orbital A or B. The resonance integral, Hab, is the quantum mechanical interaction term of basis orbital A with basis orbital B. 5ab is the overlap integral, the quantitative measure of the volume in space where the two basis functions interact. Basis functions that have zero overlap are said to be mutually orthogonal while two functions that are exactly coincident have an overlap value equal to 1 Saa = Sbb = 1, hence the simplification in the secular determinant above). In the secular determinant for the H2+ system or any homonuclear diatomic system, Haa = Hbb-... 

Heisenberg portion of the Hamiltonian in earlier work (9) for the delocalization terms we assume that a single parameter B characterizes resonance interactions between each pair of sites. Hence, the spin Hamiltonian matrix becomes ... 

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). 

A typical example of the 5-term resonance is given by metalloporphyrins and heme proteins. As shown in Fig. 1.34, Ni(OEP) (OEPioctaethylporphyrin) exhibits two electronic transitions referred to as the Qq (or a) and B (or Soret) bands along with a vibronic side band (Qi or 3) in the 350-600 nm region. According to MO (molecular orbital) calculations on the porphyrin core of D4/, symmetry, Qq and B transitions... 

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