Isoenergetic

As shown in Figure 27, an in-phase combination of type-V structures leads to another A] symmetry structures (type-VI), which is expected to be stabilized by allyl cation-type resonance. However, calculation shows that the two shuctures are isoenergetic. The electronic wave function preserves its phase when tr ansported through a complete loop around the degeneracy shown in Figure 25, so that no conical intersection (or an even number of conical intersections) should be enclosed in it. This is obviously in contrast with the Jahn-Teller theorem, that predicts splitting into A and states. 

A quantitative expression of these observations is shown in equation 1, where is the observed absorption maximum for the unsymmetrical carbocyanine and Xj is the arithmetic mean (isoenergetic wavelength) for the absorption maxima of the related symmetrical dyes. 

Within the class of polymer crystals having, ideally, long-range positional order for all the atoms, different crystalline forms (polymorphs) may arise as a result of having different almost isoenergetic macromolecular conformations (of the main chain, in most known cases) or as a result of different, almost isoenergetic modes of packing of macromolecules with identical conformations [1-3]. 

The backspillover O species on the Pt surface have an O Is binding energy 1.1 eV lower than on the same surface under open-circuit conditions. The Pt catalyst-electrode is surrounded by isoenergetic oxygen species both at the Pt/YSZ and at the Pt/vacuum interfaces.67... 

Fig. 4. Potential energy surface of the system C2H /C2H4 with respect to R and a in the gas phase (relative isoenergetic lines in kJ mol-1)...

As already described in part 2.3.2 for a set of pairs (R, a) (Fig. 3 a) the remaining geometric variables were optimized in keeping with a symmetry restriction (Fig. 3 b). The energy function E = f(R, a) obtained here in the gas phase is presented in Fig. 4 as a graphic representation of isoenergetic lines above the R-a-plane. Tire points marked by Roman numerals are minimas (educts I products III, IV, V) and the saddle... 

Any mechanism which involves isoenergetic, radiationless internal conversion from C, P, or T to a high vibrational level of the ground state would be expected to show a large deuterium isotope effect on the rate of internal conversion. In the direct photolysis of perdeuterio and perhydrostilbene, Saltiel<8a) found no isotope effect on the photostationary state or upon the quantum yields of cis-to-trans and trans-to-cis conversion. 

The conversion from St to S, is an isoenergetic process that is followed by vibrational relaxation of the new vibrationally hot state. 

Seminal studies on the dynamics of proton transfer in the triplet manifold have been performed on HBO [109]. It was found that in the triplet states of HBO, the proton transfer between the enol and keto tautomers is reversible because the two (enol and keto) triplet states are accidentally isoenergetic. In addition, the rate constant is as slow as milliseconds at 100 K. The results of much slower proton transfer dynamics in the triplet manifold are consistent with the earlier summarization of ESIPT molecules. Based on the steady-state absorption and emission spectroscopy, the changes of pKa between the ground and excited states, and hence the thermodynamics of ESIPT, can be deduced by a Forster cycle [65]. Accordingly, compared to the pKa in the ground state, the decrease of pKa in the... 

Adib, A. B., Entropy and density of states from isoenergetic nonequilibrium processes, Phys. Rev. E 2005, 71, 056128... 

It has been shown so far that internal and external factors can be combined in the control of the electron-transfer rate. Although in most cases a simple theoretical treatment, e.g. by the Marcus approach, is prevented by the coincidence of these factors, it is clear that the observed features for the isoenergetic self-exchange differ by the electronic coupling and the free energy of activation. Then it is also difficult to separate the inner- and outer-sphere reorganization energies. 

Our uncertainty is derived in part from the lack of a measured enthalpy of vaporization, cf Reference 67. However, what triggered our skepticism is the observation that the isomeric 1,2-and 1,4-dihydronaphthalenes have reported enthalpies of formation that differ by ca 13 kJ mol-1 while the corresponding species lacking the benzene ring, the isomeric 1,3- and 1,4-cyclohexadienes, are almost isoenergetic (see Section V.D of this chapter). From J. F. Liebman, in The Cyclophanes (Eds. P. M. Keehn and S. M. Rosenfeld), Academic Press, New York, 1983,... 

Figure 2.10 Maps of conformational energy of various isotactic polymers as function of backbone torsion angles 0i and 02 (a) Isotactic polystyrene, (b) polypropylene, (c) poly(l-butene), and (d) poly(4-methyl-l-pentene). Succession of torsion angles. .. 0i020i02 [s(M/N) symmetry] has been assumed. Isoenergetic curves are reported every 10 (a,c,d) or 5 (b) kJ/mol of monomeric units with respect to absolute minimum of each map assumed as zero.

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