Electron-Delocalization Effects

There are several fundamental reasons why the GMH and adiabatic formulations are to be preferred over the traditionally employed diabatic formulation. The definition of the diabatic basis set is straightforward for intermolecular ET reactions when the donor and acceptor units are separated before the reaction and form a donor-acceptor complex in the course of diffusion in a liquid solvent. The diabatic states are then defined as those of separate donor and acceptor units. The current trend in experimental design of donor-acceptor systems, however, has focused more attention on intramolecular reactions where the donor and acceptor units are coupled in one molecule by a bridge.The direct donor-acceptor overlap and the mixing to bridge states both lead to electronic delocalization, with the result that the centers of electronic localization and localized diabatic states are ill-defined. It is then more appropriate to use either the GMH or adiabatic formulation. 

There is an additional, more fundamental, issue involved in applying the standard diabatic formalism. The solvent reorganization energy and the solvent component of the equilibrium free energy gap are bilinear forms of A ab and (Fav (Eqs. [45] and [47]). A unitary transformation of the diabatic basis (Eq. [27]), which should not affect any physical observables, then changes A b and v, affecting the reorganization parameters. The activation parameters of ET consequently depend on transformations of the basis set  

This situation is of course not satisfactory as observable quantities should be invariant with respect to unitary basis transformations. Here, we outline the adiabatic route to a basis-invariant formulation of the theory. 

In the adiabatic gas-phase basis, the number of independent parameters drops to four AF, AE i, and a i, where the superscript ad refers to 

The reaction coordinate is now a projection of the nuclear solvent polarization on the adiabatic differential solute field 

In the adiabatic gas-phase basis, the number of independent parameters drops to four Xad, AEad, AE12, and ai2, where the superscript ad refers to the adiabatic representation in which AE12 is the gas-phase gap between the eigenenergies, Eq. [29]. The equation for the free energy surfaces can then be rewritten in the basis-invariant form 

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Bretta F. King and F. Weinhold, Structure and spectroscopy of (HCN)n clusters Cooperative and electronic delocalization effects in C H N hydrogen bonding. J. Chem. Phys. 103, 333 347 (1995). 

It is prerequisite to define localized, diabatic state wave fimctions, representing specific Lewis resonance configurations, in a VB-like method. Although this can in principle be done using an orbital localization technique, the difficulty is that these localization methods not only include orthorgonalization tails, but also include delocalization tails, which make contribution to the electronic delocalization effect and are not appropriate to describe diabatic potential energy surfaces. We have proposed to construct the locahzed diabatic state, or Lewis resonance structure, using a strictly block-localized wave function (BLW) method, which was developed recently for the study of electronic delocalization within a molecule.(28-3 1)... 

We have recently been examining various inner-sphere adsorbed redox couples with the aim of deducing if such electron delocalization effects are indeed encountered. One type of candidate system is transition-metal cyano complexes. Some representative data for the Fe(CN)63>/1 "couple adsorbed at gold are presented in Figs. 2 and 3. 

Such conclusions are, however, extremely speculative at present. The Fe(CN) 3"/ system suffers from a number of complications, including the possibility of surface reactions to form Prussian Blue-like cyano-bridged chains. Details of these results will be given in a forthcoming publication. (14) This brief summary is included here in order to illustrate how information on electron delocalization effects for adsorbed redox couples might be obtained, at least in principle, by examining potential-dependent SERS frequencies. 

The best characterized species is [Os2(N2)(NH3)10]5+ made as a bromide or as a tosylate from reaction of [0s(H20)(NH3)s]3+ with [Os(N2)(NH3)5]2+ in the presence of zinc amalgam. The stability of the mixed valence system (formally Os111 11) has been ascribed to electronic delocalization effects and an MO scheme proposed,2 0s but it is not clear why it appears to be more stable than its reduction product, [Os(N2)(NH3),0]4+. Magnetic circular dichroism spectra and cyclic voltammetry of the ion have been measured.28011 A number of other mixed homonuclear species are known, viz. [0s2(N2)(NH3)9(H20)]s+, [Os2(N2)(NH3)9C1]4+, [Os2(N2)(NH3)8C12]3+ and... 

Abstract In this chapter we discuss the influence of ir-electron delocalization on the properties of H-bonds. Hence the so-called resonance-assisted hydrogen bonds (RAHBs) are characterized since such systems are mainly classified in the literature as those where TT-electron delocalization plays a very important role. Both the intramolecular and intermolecular RAHBs are described. RAHBs are often indicated as very strong interactions thus, their possible covalent nature is also discussed. Examples of the representative crystal structures as well as the results of the ab initio and DFT calculations are presented. Additionally the RAHB systems, and the other complexes where rr-electron delocalization effects are detectable, are characterized with the use of the QTAIM (Quantum Theory Atoms in Molecules ) method. The decomposition scheme of the interaction energy is applied to expand the knowledge of the nature of the RAHBs. 

A conspicuous example of the electron delocalization effects on the 7° contributions to /(C,H) couplings, rule (c), is given by those corresponding to the bridgehead position in bicyclo[l.l.l]pentane (3). It is interesting to compare them with the corresponding effects in bicyclo[2.2.2]octane (31) the NBO... 

The antioxidant activity of phenolic compounds is related to their structure, in particular the number of hydroxy-substituents in the aromatic ring and the nature of the substituents in the para or ortho position. In particular the addition of a hydroxyl or methoxy group in the ortho position increases the antioxidant activity due to a strong electron delocalizing effect and this helps to... 

The axial conformation in MM4 is stabilized by the anomeric effect, which is represented largely by substantial (-1.85) and V2 (-1.30) torsion potentials (Fig. 7.1). The bond dipoles in the equatorial conformation add up to give a greater dipole moment, and a higher dipole-dipole repulsion energy than in the axial conformation. Thus, increasing the dielectric constant tends to stabilize the equatorial conformation more than it stabilizes the axial, as shown in Table 7.5. The anomeric effect in MM4 is the summation of the electronic delocalization effect included in the torsion potential, plus contributions from torsion-stretch and torsion-bend interactions, plus the electrostatic effect from the interaction of the bond dipoles. 

Scheme 18.1 Cooperative electron delocalization effects between Eu and Fe in EuFeOs perov-skite for total oxidation of toluene. (Reprinted with permission from Ref. [25]. Copyright 2014, Elsevier.)...

The first hyperpolarizability of planar and non-planar 4-[A,A-dimethyl-amino]-4 -nitro stilbene has been calculated at the CPHF level to investigate efficient 7i-electron delocalization effects within a global investigation including vibrational spectroscopies. ... 

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