Four-electron interaction

Steric repulsions come from two orbital-four electron interactions between two occupied orbitals. Facially selective reactions do occur in sterically unbiased systems, and these facial selectivities can be interpreted in terms of unsymmetrical K faces. Particular emphasis has been placed on the dissymmetrization of the orbital extension, i.e., orbital distortions [1, 2]. The orbital distortions are described in (Chapter Orbital Mixing Rules by Inagaki in this volume). Here, we review the effects of unsymmetrization of the orbitals due to phase environment in the vicinity of the reaction centers [3]. 

Such four-electron interactions are sometimes considered to be intrinsically destabilizing but this is an artifact of performing perturbation theory with a non-Hermitian (unphysical) model H<-° as discussed in Section 3.4.2. 

The interaction of C-M bonding orbitals with heteroatom lone-pair orbitals is a two-center-four-electron interaction. This is destabilizing and raises the energy of the HOMO relative to the unperturbed orbitals, and hence lowers the ionization potential of the heteroatom lone-pair electrons. The interaction is qualitatively represented by the molecular orbital interaction diagram shown in Figure 11. The strength of the interactions depends on a number of factors but most importantly on the orientation of the C-M bond with respect to the lone-pair orbital and on the... 

The repulsive two-orbital, four-electron interaction that turns into an attractive bonding force when the electrons, rising in energy, are dumped at the Fermi level is not just a curiosity. I think that it is responsible for observed kinetic barriers to chemisorption and the possible existence of several independent potential energy minima as a molecule approaches a surface. 

Figure 33 Schematic drawing showing how the interactions of levels (bottom) can lead to a potential energy curve (top) which has a substantial barrier to chemisorption. R measures the approach of a molecule, symbolized by a single interacting electron pair, to a surface. At large R repulsive four-electron interactions dominate. At some R (second point from left), die antibonding combination crosses the Fermi level and dumps its electrons. At shorter R there is bonding.

Both of these interactions are primarily of type and (see 54 or 59), four-electron repulsive or two-electron attractive interactions. Actually, the energetic and bonding consequences are a little complicated the z2-rrtt interaction would be destabilizing if the antibonding component of this interaction remained filled, below the Fermi level. In fact, many z2-ir0 antibonding states are pushed above the Fermi level, vacated. This converts a destabilizing, four-electron interaction into a stabilizing two-electron one. 

The first term generates the reference HF and the second all singly excited states. The first parenthesis generates all doubly excited states, which may be considered as connected (T2) or disconnected (Tj). The second parenthesis generates all triply excited states, which again may be either true (T3) or product triples (T2T1, Tj). The quadruply excited states can similarly be viewed as composed of five terms, a true quadruple and four product terms. Physically a connected type such as T4 corresponds to four electrons interacting simultaneously, while a disconnected term such as T2 corresponds to two... 

The instability of the eclipsed form of ethane was originally postulated to result from repulsion of filled hydrogen orbitals. However, state-of-the-art quantum chemical calculations now indicate that two main factors contribute to the preference for the staggered conformation of ethane. First, the eclipsed form is selectively destabilized by unfavorable four-electron interactions between the filled C-H bonding orbitals of... 

Mole- Four electrons interaction cule B slightly unfavourable... 

Another formal treatment of the rearside attack model was proposed by Liotta, Burgess and Eberhardt [31]. These authors extended frontier orbital analysis of the interactions between a nucleophile and a n-electrophile by including the stabilizing two-electron interactions of the nucleophile HOMO with all the unoccupied n and a MO s on the rt-electrophile, as well as the net destabilizing four-electron interactions of the nucleophile HOMO with all the occupied n and a MO s. The analysis... 

In the case of a four-electron interaction (1-21), both the bonding and antibonding orbitals are doubly occupied. Since AE is larger than Air ", the four-electron interaction is destabilizing, and it can be shown that the destabilization is proportional to the square of the overlap,. ... 

If we consider a two-electron interaction between doubly occupied Xi and empty Xz (1-22), the two electrons are stabilized by 2AE . The stahlization associated with a two-electron interaction between two orbitals of different energy is therefore proportional to the square of the overlap and inversely proportional to the energy difference between the two orbitals, that is, proportional to S /Ae. However, a four-electron interaction is destabU-izing, since AE is larger than AE" " (1-23). It can be shovm that this four-electron destabilization is proportional to the square of the overlap,. ... 

In both degenerate and nondcgcncrate orbital interaction cases, a two-orbital-two-electron interaction is stabilizing while a (w o-orbilal-four-electron interaction is destabilizing. 

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