Electrons overlapping

The tetrasubstituted isomer of the morpholine enamine of 2-methyl-cyclohexanone (20) because cf the diminished electronic overlap should be expected to exhibit lower degree of enamine-type reactivity toward electrophilic agents than the trisubstituted isomer. This was demonstrated to be the case when the treatment of the enamine with dilute acetic acid at room temperature resulted in the completely selective hydrolysis of the trisubstituted isomer within 5 min. The tetrasubstituted isomer was rather slow to react and was 96% hydrolyzed after 22 hr (77). The slowness might also be due to the intermediacy of quaternary iminium ion 23, which suffers from a severe. 4< strain 7,7a) between the equatorial C-2 methyl group and the methylene group adjacent to the nitrogen atom, 23 being formed by the stereoelectronically controlled axial protonation of 20. 

The enamines in which the protonation at the -carbon atom is not allowed due to the lack of coplanarity, or, in other words, the lack of electronic overlap, do not exhibit this characteristic absorption shift. For instance in the case of neostrychnine (134) where the overlap is not permitted since this would involve the formation of a double bond at the bridgehead, there is no appreciable difference in the C—C stretching region of the free amine and its perchlorate salt they absorb at 1666 cm and 1665 cm , respectively (70). 

In a covalent bond, each atom provides one electron. Overlap of an orbital containing an electron from one atom overlaps with another orbital containing an electron from the second atom. 

The filled (Is)2 cores lead to additional steric repulsions with the incoming donor hybrid. These combine with nuclear Coulomb repulsions to oppose high electronic overlap. Figure 3.6 displays the calculated increase in steric repulsion as each filled 2s spin-orbital of Li2 collides with the filled core Is of the opposite atom. The paired one-electron steric repulsions shown in Fig. 3.6 are similar to the ionic two-electron steric repulsions of Fig. 2.11, and the wave-mechanical origin of the steric pressure would be analogous to that described in the discussion surrounding Fig. 2.12. 

The exact form of the pre-exponential factor A (see Chapter 5) is still being debated from the preceding considerations it is apparent that we must distinguish two cases If the reaction is adiabatic, the pre-exponential factor will be determined solely by the dynamics of the inner and outer sphere if it is nonadiabatic, it will depend on the electronic overlap between the initial and final state, which determines the probability with which the reaction proceeds once the system is on the reaction hypersurface. 

Even though this contribution is always negative, the total capacity must be positive - otherwise the capacitor would accumulate charge spontaneously. Thus Eq. (17.4) is only valid if f > rjm, so that there is no electronic overlap between the two plates. Similarly the use of a macroscopic dielectric constant in Eq. (17.5) presupposes a plate separation of macroscopic dimensions, and again the total capacity is positive. Only unphysical models or bad mathematical approximations can produce negative interfacial capacities, which enjoyed a brief spell of fame under the name of the Cooper-Harrison catastrophe [2]. 

As can be seen, the ng MO of the tram isomer is lower in energy than the ns MO of the cis isomer, a result consistent only with the presence of strong through space and through bond interaction of the two Cl atoms. This is an important result insofar as it indicates that four electron overlap repulsion is greater for tram than for cis 1,2-disubstituted ethylenes. 

In other papers408, the discussion of conjugative destabilization has been based on an incorrect assumption, L e that the destabilizing interaction of filled orbitals increases as their energy separation decreases, while, as we have seen in Eq. (5 ), four electron overlap repulsions depend not on the energy separation of the two interacting MO s but rather on the sum of them. Thus, situation A is less destabilizing than situation B (constant Sy). 

It is important to remember that the Marcus model refers to a weakly electronically coupled model, as embodied in the term outer-sphere ET. Thus it must be assumed that the electronic overlap between the two reactants is so small that no quantum-chemical effects ensue, yet that there must be enough overlap for the transmission coefficient k of the Eyring equation to be equal to 1 (the reaction must be adiabatic). Usually, this minimum overlap requirement is put at a fairly low level, around 0.1 kcal mol-1, which causes no problems for most reactions involving at least one organic species. 

According to Bockris and Habib, the potential difference at the metal/solution interface at pzc is a result of the contribution of two components the surface potential (electron overlap) of the metal go and solvent dipoles oriented at the electrode surface, go- The value of go cannot be experimentally measured because the absolute value of the electrode potential is not known. However, the value of go can be estimated from the relation... 

As mentioned in Sec. 1.3, the electrochemical potential of electrons in condensed phases corresponds to the Fermi level of electrons in the phases. There are two possible cases of electron ensembles in condensed phases one to which the band model is applicable (in the state of degenera< where the wave functions of electrons overlap), and the other to which the band model cannot apply (in the state of nondegeneracy where no overlap of electron wave functions occurs). In the former case electrons or holes are allowed to move in the bands, while in the latter case electrons are assumed to be individual particles rather than waves and move in accord with a thermal hopping mechanism between the a4jacent sites of localized electron levels. 

Each lobe of the sp orbital containing one-electron overlap head-on carbon atoms and translational repetition of this tetragonal C-C cluster makes diamond. The three tetrahedral arms of orbital can also be terminated by hydrogen atoms that overlap head-on. If terminated by hydrogen, the tetrahedral C-H cluster makes the CH molecule of gas methane (Fig. 4.4). 

Another semiconducting fulleride salt, [Ru(bpy)3](C5o)2 with bpy = 2,2 -bipyridine, crystallizes on the Pt electrode surface out of dichloromethane solutions saturated with [Ru(bpy)3]PF5 within a few minutes [79]. The NIR spectra of benzonitrile solutions of this salt demonstrate that the only fulleride anion present is 55 . The temperature dependence of the conductivity is typical for a semiconductor, with the room temperature conductivity being 0.01 S cm and the activation energy 0.1 kj mol (0.15 eV). It was postulated that there is an electronic overlap between the two ions of this salt leading to a donation of electron density from the 55 to the ligand orbitals in the [Ru(bpy)3] " AI 0.7) [79]. 

Most of the reactivity problems described in Sect. VI C have been treated recently by methods based on the electronic Overlap Population concept as introduced in the Electronic Population analysis of R. S. MuUiken. In fact the studies of the problems of Sect. VI C have established the general usefulness and apphcability of electronic overlap populations as reactivity measures for other excited- and ground-state reactions. The most important advantage of the electronic overlap population method of reactivity analysis is the possibihty provided for relating bond forming reactivity of two initially nonbonded atoms to the strength of their electronic interaction. 

The definition of electronic overlap population, at three different summation levels, is as follows ... 

The electronic overlap populations in all three cases were calculated from the one electron Extended Hiickel MO s. For the photocyclizations of 1,2-difuryl ethylenes very similar results were obtained also from minimal basis set ab-initio wavefunctions l The possibility of obtaining useful reactivity analyses from wave-functions which are easily available even for large systems could prove to be an important practical consideration for further applications of this method. The dependence on Sri sj ill (5) ensures that electronic overlap populations show the desirable physical characteristics for their use as reactivity measures strong falling-off with increasing interatomic distance and proper directional dependence. This last point is of particular significance for bond formation in polyenes. Thus for two C 2 p atomic... 

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