Transition degenerate

In this simple form of the Marcus theory, two terms, the reorganization of the inner coordination shell (AG m) and that of the solvent sheath (AG 0Ut), both describing the degenerate transition-state geometry, contribute to AG. While molecular mechanics might also be used to model the encounter complex, force field calculations have mainly been applied to the estimation of the inner coordination shell reorganization term (AGt,)19,143 1445. 

Calculations of such spectra have been reported assuming the molecule to be planar with C2v symmetry [36]. The lower symmetry of corrole removes the degeneracy present in porphyrins so that degenerate transitions are no longer expected and more transitions are allowed in the case of corrole than in that of porphyrin. The la2 and 8fc, levels in corrole correspond to the two components of the lowest vacant MO in porphyrins, the 4eg pair (LUMO). Similarly the 6a2 and 7 >1 orbitals correspond to the highest filled porphyrin orbital, alu and a2u (HOMO). In the case of porphyrins the Q and Soret (thus called because it was discovered in 1883 by Soret in the optical spectrum of hemoglobin) bands arise mainly from the alu, a2u and eg pair and the spectra of corroles closely resemble those of porphyrins (Table 6). 

Next we deal with the nature of the correction Awc. The resonance signals in a spectrum may be composed of overlapping, closely spaced components. Usually this is caused by either weak spin-spin couplings (we consider here only those which are included explicitly in the assumed model of an exchanging spin system) or by almost degenerate transitions in the spin multiplets. (81) Such effects should be compensated for by the correction Awc which can be determined from measurement of an apparent line-width, wa, in a theoretical spectrum calculated for a reasonably assumed value of the natural line-width, wtheor The correction (wa — wtheor) is virtually independent of the value... 

The H- ll9Sn HDMR experiments may often be applied to the analysis of type A X spin systems with degenerate transitions and only two groups of magnetically equivalent nuclei. For example, the energy level diagram for an A3X system is shown in Fig. 3. 

The free energy of activation AG consists of two parts, AG i and AG out- The first contribution, AG in, represents the energy investment to adapt the two coordination environments within the precursor to the degenerate transition state geometry. This energy of the concerted contraction and expansion of the two coordination shells is given by... 

In general the HOMO and LUMO of condensed aromatic hydrocarbons are not degenerate, so simple theory gives a HOMO- LUMO transition and a degenerate transition from the HOMO [Pg.72]

These give rise to two double degenerate transitions in. The two excited states of Eu symmetry that arise from these configurations are not pure but are mixed under the influence of interelectronic repulsion. 

In Fig. 14, we plot the correlation functions (146) and (147) computed from the equations of motion (96) for the case of degenerate transitions (A = 0) and two different values of p p = 0 corresponding to the case of perpendicular dipole moments, and p = 0.99 corresponds to almost parallel dipole moments. We have chosen p < 1 to avoid population trapping, which can appear for p = 1. The correlations show the characteristic photon antibunching effect [59] that g1-11 (x)... 

In order to correlate them, we can introduce a second (weaker) laser field of frequency coo — and the Rabi frequency IT < if which couples the degenerate transitions with dipole moments pn 7 and p22 v i as indicated in Fig. 19b. Treating the second field perturbatively, at zeroth order the coupling results in new doubly dressed states [63]... 

In the vicinity of a dipole allowed degenerate transition, polarized perpendicular to the optical axis, instead of (4.77) we have... 

The quadrupole spectra will have several degenerate transitions, and the appropriate summations are listed in Table 3.2 and Appendix 2. A dipole f f transition shows 1 1 intensity for a polycrystalline sample, and 5 3 and 1 3 intensity ratios for a single crystal with the y-ray axis perpendicular to and parallel to the principal axis of a symmetric electric field gradient tensor. 

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