Coupling in two-electron

Physical conditions for various couplings in two-electron configurations. 

These couplings are generalizations of jj coupling in two-electron configurations. JJ coupling is widespread in the configurations... 

The substrates of catabolism—proteins, carbohydrates, and lipids—are good sources of chemical energy because the carbon atoms in these molecules are in a relatively reduced state (Figure 18.9). In the oxidative reactions of catabolism, reducing equivalents are released from these substrates, often in the form of hydride ions (a proton coupled with two electrons, H ). These hydride ions are transferred in enzymatic dehydrogenase reactions from the substrates... 

The binuclear Ir complex (93) is produced from the direct coupling reaction of the Ir-bound 5-chloro-phen ligand as shown in reaction Scheme 12.153 The nonplanar structure of the bridging ligand results in the electronic isolation of the two Ir centers. Hence both metal centers and ligands are oxidized and reduced, respectively, in two-electron processes. 

Craq002+ also acts as a catalyst for oxidations with O2 in the presence of HNO2. Radical coupling, this time with NO, is again an essential mechanistic step. The catalysis takes advantage of the demonstrated preference for an intermediate, Craq02 +, to react in two-electron, hydride-transfer steps with organic materials. Reactivity studies of potential intermediates in other systems may uncover new catalytic powers of LMOO species. 

In the theory of radiative transition, the dipole moment operator p. couples the two electronic energy states and the Franck-Condon overlap... 

We have presented a new technique for the investigation of intramolecular couplings in the electronic ground state 50. The new technique of CIS is based on the special population dynamics induced by the coherent excitation of a three-level system with two narrow-band Fourier-transform-limited laser pulses. It allows the investigation of high-lying intermolecular vibrational states in the electronic ground state of van der Waals complexes. These... 

The biochemical importance of flavin coenzymes ap-pears to be their versatility in mediating a variety of redox processes, including electron transfer and the activation of molecular oxygen for oxygenation reactions. An especially important manifestation of their redox versatility is their ability to serve as the switch point from the two-electron processes, which predominate in cytosolic carbon metabo-lism, to the one-electron transfer processes, which predomi-nate in membrane-associated terminal electron-transfer pathways. In mammalian cells, for example, the end products of the aerobic metabolism of glucose are C02 and NADH (see chapter 13). The terminal electron-transfer pathway is a membrane-bound system of cytochromes, nonheme iron proteins, and copper-heme proteins—all one-electron acceptors that transfer electrons ultimately to 02 to produce H20 and NAD+ with the concomitant production of ATP from ADP and P . The interaction of NADH with this pathway is mediated by NADH dehydrogenase, a flavoprotein that couples the two-electron oxidation of NADH with the one-electron reductive processes of the membrane. 

In the presence of coupling between the two excited manifolds, represented by the operator W, the bound states n) generated, for example, either by absorption of a photon (as illustrated in Figure 7.5), by electron impact, or in an atom-molecule collision will decay because they undergo transitions to the continuum states. W is assumed to be time-independent and for the discussion in this section its origin and particular form is not pertinent. It may represent nonadiabatic coupling between two electronic or two vibrational states, for example. We explicitly assume that W couples only the bound and the continuum states and that there is no coupling between the bound or between the continuum states,... 

In addition to the experimental aspects of the different types of materials, theoretical treatments also were discussed. These included the presentation of studies related to molecular vibrational dynamics, the problem of vibration-induced decay of electronic excited states, nanoscale spin-orbit coupling in two-dimensional silicon-based structures, and the growth of semiconductor clusters by combining both theoretical approaches with actual experimental data. 

Coupling of two electron-rich indolyl units to a trivalent phosphorus results in shielding of approximately 30 ppm relative to an acyclic mono-indolyl analogue <20050M37>. The shielding is not a result of any ring strain as an acyclic bis(indolyl) phosphine has a similar chemical shift (—65.1 ppm) to the dihydrophosphinine (—91.9 ppm). 

All the VB methods that deal with semilocalized orbitals use a generalization of the Coulson—Fischer idea (12), whereby a bond is described as a singlet coupling between two electrons in nonorthogonal orbitals that possess small delocalization tails resulting from the variational orbital optimization. Albeit formally covalent, this description implicitly involves some optimal contributions of ionic terms, as a decomposition of the wave function in terms of pure AO determinants would show (see Eqs. 3.5 and 3.6). For a polyatomic... 

When the two couples in the electron-transfer process are chemically identical, the reaction becomes one of electron exchange. Its rate can be determined by isotopically labelling a small fraction of one of the components as indicated in the equation... 

Fig. 3.5 Schematic representation of the coupling of two electronic states by an oscillating electric field (q represents an electron in an excited state and q an electron in its ground state). 

In principle, a Cl approach provides an exact solution of the many-electron problem. In practice, however, only a finite set of Slater determinants can be handled in the linear expansion. A common procedure is to retain all Slater determinants that differ from the HF determinant by one or two excitations (although one-electron excitations do not couple directly to the ground state they couple with two-electron excitations, which in turn affect the ground state indirectly). Unfortunately, such a procedure is not size consistent. For example, the energy of two highly separated monomers will not be twice that of a single monomer in such a truncated Cl calculation. Fortunately, a slightly modified approach called quadratic Cl has recently been developed (Pople et al., 1987) that is size consistent. 

This was the case for the vibrational modes of A2 symmetry in the 1,2-difluorobenzene, B, A2 symmetries in the case of the 1,3-difluorobenzene and 1,2,3-trifluorobenzene cations. As stated in Table 1 the interactions between some electronic states are negligible which appear as zero entries in the off-diagonal terms of (15), (8). But one should note that in case of a 3 x 3 coupling matrix the imperceptible coupling between two electronic states may have an important effect on the coupling of the other two electronic states. 

Quantum control methods make use of the time- and frequency dependence of the external laser field, usually assuming that the spatial dependence of the coupling between two electronic energy surfaces of a molecule is constant. In this work we ask what may be the influence of the spatial dependence of the coupling and can it be also used for steering molecular transitions ... 

In the previous sections, we demonstrated how a space-dependent coupling between two electronic potentials influences the transition probabilities between molecular energy levels. In the following, we ask whether the space-dependence of the coupling can be used to steer molecular transitions. There-... 

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