Delocalization interactions

One of the simplest nonlinear isotherm models is the Langmuir model. Its basic assumption is that adsorbate deposits on the adsorbent surface in the form of the monomolecular layer, owing to the delocalized interactions with the adsorbent snrface. The Langmuir isotherm can be given by the following relationship ... 

A in both complexes, it is thought that the two atoms are kept close together by the delocalized interaction with all metal atoms. 

The r value should be a measure of the positive charge stabilization through the TT-delocalization interaction with the aryl rr-system in the incipient carbocation or the carbocationic transition state and will vary significantly with the a-R-substituents. Mishima et al. (1990c) found that the r values for all these systems [IC" ], ArC R R, can be correlated using (32) in terms of both resonance Act r and inductive polar a° substituent constants of R and R, ... 

The a values estimated from Eq. (7) for 2-, 3-, and 4-pyridyl groups agree well with the mean values for these groups (cf. Table VI, Section II,B,4). A set of a (contiguous) constants was proposed to account for contiguous delocalization interactions between adjacent functionalities X and G in series (5) and (6). This set was shown to overlap with Mine s a set for the majority of substituents, but it provides new values for substituents, including 4-pyridyl, in the Hammett and iso-Hammett series. A duality of the CTr and... 

Generally speaking, the increased electron delocalization interactions on going from the ground to the excited state favor a more planar geometry for excited anilines in nonpolar or weakly polar solvents, even when the anilines are pre-twisted in the ground state92. 

For such an asymmetric structure as dimethoxymethane with one torsion angle fixed at 60 °, additional sine terms are necessary, in order to account for the lack of symmetry about 0 = 180° (see Ref. 94). The individual components V,(0), V2(0), and V3(0) of the total potential function V(0) can be identified with specific physical effects of similar periodicity. For example, the onefold term, V,(0) = 0.5 V ( 1 — cos 0), moves from a maximum v ue to a minimum value as 0 changes by 180 °. The same variation with torsion shows dipolar or steric interactions. The twofold term, V2(0), changes from a maximum to a minimum as 0 changes by 90°. This periodicity frequently corresponds to the change of delocalization interactions. Finally, the threefold term, V3(0), moves from a maximum value to a minimum value as it changes by 60°. This is generally attributed to the intrinsic torsion potential. 

It was established from calculations of substituted dimethyl ether that the largest difference in net charge occurs at the central carbon atom and on its substituent that is, on the atoms where a delocalization interaction occurs. A pronounced enhancement of negative charge on the oxygen atom... 

Hence, the anomeric effect [positive value of AE(AE3)] can appear at a suitable combination of the V and V coefficients. Because the V, term is associated with the dipole-dipole interactions of polar groups, and the V2 term with delocalization interactions of lone-pair orbitals on heteroatoms, it may be concluded that the latter equation also effectively describes a balance... 

The balance of electrostatic and delocalization interactions in an isolated molecule may be perturbed by the influence of the solvent. In calculations based on Eq. 7, the analysis of solvation-energy terms suggested that the electrostatic contribution stabilizing the ap orientation of the acetal s ment is the conformationally dominant term. For example, in 2-methoxyoxane, the difference in energy of the (ap, ap) and (ap, sc) conformers in water, compared to that in the isolated molecule, caused by solute-solvent electrostatic interactions alone, amounts to 4 kJ.mor. Accordingly, the inter-and intra-molecular, electrostatic interactions operate in reverse directions in acetals. Whereas the intramolecular, electrostatic interactions are responsible, together with delocalization interactions, for the aiq)earance of the anomeric, reverse anomeric, and exo-anomeric effects, the solute-solvent electrostatic interactions lessen their im nitude, and may even cancel them. Of course, the solvent may also influence the electron distribution and energy of MO s in a molecule. In this way, the orbital interactions of lone-pairs and delocalization contributions to the anomeric effect may be scaled by the solvent, but this mechanism of the environmental effect is, in most cases, of only minor importance. 

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