Solute delocalization

Three types of solvent or solute delocalization have now been examined, as summarized in Table III for three different adsorbent types (four, if we distinguish Cig-deactivated silica from silica). The theoretical requirements on the configuration and density of adsorption sites were discussed earlier (Section II,B) for a given type of localization/delocalization to be possible. In each case the nature of adsorption sites is fairly well understood for the four adsorbents of Table III, as disucssed in Ref. / and 17 and shown in Fig. 14. Thus, in the case of alumina, surface hydroxyls do not function as adsorption sites. Although surface oxide atoms are capable of interacting with acidic adsorbate molecules (see below), in most cases the adsorbate will interact with a cationic center (either aluminum atom or lattice defect) in the next layer. As a result, we can say that in most cases adsorption sites on alumina are buried within the surface, rather than being exposed for covalent site-adsorbate interaction. These sites are also rigidly positioned within the surface. Finally, the... 

In the full quantum mechanical picture, the evolving wavepackets are delocalized functions, representing the probability of finding the nuclei at a particular point in space. This representation is unsuitable for direct dynamics as it is necessary to know the potential surface over a region of space at each point in time. Fortunately, there are approximate formulations based on trajectories in phase space, which will be discussed below. These local representations, so-called as only a portion of the FES is examined at each point in time, have a classical flavor. The delocalized and nonlocal nature of the full solution of the Schtddinger equation should, however, be kept in mind. 

There exist a number of d -synthons, which are stabilized by the delocalization of the electron pair into orbitals of hetero atoms, although the nucleophilic centre remains at the carbon atom. From nitroalkanes anions may be formed in aqueous solutions (e.g. CHjNOj pK, = 10.2). Nitromethane and -ethane anions are particularly useful in synthesis. The cyanide anion is also a classical d -synthon (HCN pK = 9.1). 

Kinetic data on acetate displacement from C-3 using a number of sulfur and nitrogen nucleophiles in aqueous solution at near neutral pH demonstrate that the reaction proceeds by an 5 1 mechanism (B-72MI51004). The intermediate in this reaction is depicted as a dipolar allylic carbonium ion (9) with significant charge delocalization. Of particular significance in this regard is the observation that the free carboxylate at C-4 is required since... 

The most easily obtained information from such calculations is the relative orderings of the eneigy levels and the atomic coefficients. Solutions are readily available for a number of frequently encountered delocalized systems, which we will illustrate by referring to some typical examples. Consider, first, linear polyenes of formula C H 2 such as 1,3-butadiene, 1,3,5-hexatriene, and so forth. The energy levels for such compounds are given by the expression... 

The triarylmethyl cations are particularly stable because of the conjugation with the aryl groups, which delocalizes the positive charge. Because of their stability and ease of generation, the triarylmethyl cations have been the subject of studies aimed at determining the effect of substituents on carbocation stability. Many of these studies used the characteristic UV absorption spectra of the cations to determine their concentration. In acidic solution, equilibrium is established between triarylearbinols and the corresponding carbocations. 

The other C=N systems included in Scheme 8.2 are more stable to aqueous hydrolysis than are the imines. For many of these compounds, the equilibrium constants for formation are high, even in aqueous solution. The additional stability can be attributed to the participation of the atom adjacent to the nitrogen in delocalized bonding. This resonance interaction tends to increase electron density at the sp carbon and reduces its reactivity toward nucleophiles. 

It might also be expected that enamines would be less basic than the corresponding saturated tertiary amines as a consequence of the delocalization of the nonbonded electron pair of the nitrogen. The older literature (/—/), which involved measurements in aqueous or partly aqueous solution, led to the opposite conclusion. This unexpected increase in basicity was rationalized in terms of an equilibrium between the enamine and the quaternary iminium hydroxide ... 

The two sets of coefficients result in two sets of Fock matrices (and their associated density matrices), and ultimately to a solution producing two sets of orbitals. These separate orbitals produce proper dissociation to separate atoms, correct delocalized orbitals for resonant systems, and other attributes characteristic of open shell systems. However, the eigenfunctions are not pure spin states, but contain some amount of spin contamination from higher states (for example, doublets are contaminated to some degree by functions corresponding to quartets and higher states). 

Tire fulvalenium salts 35 and 38 react reversibly in aqueous buffer solutions to yield the corresponding triarylcyclopropenols, as evidenced by the well-defined isosbestic points in their UV spectra. Tire pK values derived from spectra are compatible with extensive delocalization of charge in the heterocyclic ring (68TL5541). 

According to its IR spectrum, phospharinane 141 exists in the solid state exclusively as the tautomer 141b possessing the localized electronic structure (Scheme 43) (83UK1761). However, by means of NMR and IR spectroscopy, it was shown that in CDCI3 solution the delocalized structure 141a is also present, although at a low relative concentration. 

The n values were high for all of the ionic liquids investigated (0.97-1.28) when compared to molecular solvents. The n values result from measuring the ability of the solvent to induce a dipole in a variety of solute species, and they will incorporate the Coulombic interactions from the ions as well as dipole-dipole and polarizability effects. This explains the consistently high values for all of the salts in the studies. The values for quaternary ammonium salts are lower than those for the monoalkylammonium salts. This probably arises from the ability of the charge center on the cation to approach the solute more closely for the monoalkylammonium salts. The values for the imidazolium salts are lower still, probably reflecting the delocalization of the charge in the cation. 

The hydrogeh atom bound to the amide nitrogen in 15 is rather acidic and it can be easily removed as a proton in the presence of some competent base. Naturally, such an event would afford a delocalized anion, a nucleophilic species, which could attack the proximal epoxide at position 16 in an intramolecular fashion to give the desired azabicyclo[3.2.1]octanol framework. In the event, when a solution of 15 in benzene is treated with sodium hydride at 100 °C, the processes just outlined do in fact take place and intermediate 14 is obtained after hydrolytic cleavage of the trifluoroacetyl group with potassium hydroxide. The formation of azabi-cyclo[3.2.1]octanol 14 in an overall yield of 43% from enone 16 underscores the efficiency of Overman s route to this heavily functionalized bicycle. 

Unstable dithiocarbamates Au(S2CNR2)2 have been detected in solution by ESR but the square planar Au(S2C2(CN)2)2 has been isolated as a green Bu4N+ salt the gold(II) state appears to be stabilized by delocalization of... 

The Rouse model, as given by the system of Eq, (21), describes the dynamics of a connected body displaying local interactions. In the Zimm model, on the other hand, the interactions among the segments are delocalized due to the inclusion of long range hydrodynamic effects. For this reason, the solution of the system of coupled equations and its transformation into normal mode coordinates are much more laborious than with the Rouse model. In order to uncouple the system of matrix equations, Zimm replaced S2U by its average over the equilibrium distribution function ... 

One common indicator is phenolphthalein (Fig. 11.10). The acid form ol this large molecule (3) is colorless its conjugate base form (4) is pink. The structure of the base form of phenolphthalein allows electrons to be delocalized across all three of the benzenelike rings of carbon atoms, and the increase in delocalization is part of the reason for the change in color. The pFCIn of phenolphthalein is 9.4, and so the end point occurs in slightly basic solution. Litmus, another well-known indicator, has pkln = 6.5 it is red for pH < 5 and blue for pH > 8. 

Structures with a cyclic character (70° a 110°) are less solvated than open cation structures (a < 70° a > 110°) due to a larger charge delocalization in the former. Thus, the alterations of the potential energy surface described above are plausible. There are two possible structures for activated complexes in solution. They... 

Values for c in each method are obtained by solving the equation for various values of each c and choosing the solution of lowest energy. In practice, both methods give similar solutions for molecules that contain only localized electrons, and these are in agreement with the Lewis structures long familiar to the organic chemist. Delocalized systems are considered in Chapter 2. 

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