Orbital extension

When the orbitals have been classified with respect to symmetry, they can be arranged according to energy and the correlation lines can be drawn as in Fig. 11.10. From the orbital correlation diagram, it can be concluded that the thermal concerted cycloadditon reaction between butadiene and ethylene is allowed. All bonding levels of the reactants correlate with product ground-state orbitals. Extension of orbital correlation analysis to cycloaddition reactions involving other numbers of n electrons leads to the conclusion that the suprafacial-suprafacial addition is allowed for systems with 4n + 2 n electrons but forbidden for systems with 4n 7t electrons. 

The orbital mixing theory was developed by Inagaki and Fukui [1] to predict the direction of nonequivalent orbital extension of plane-asymmetric olefins and to understand the n facial selectivity. The orbital mixing rules were successfully apphed to understand diverse chemical phenomena [2] and to design n facial selective Diels-Alder reactions [28-34], The applications to the n facial selectivities of Diels-Alder reactions are reviewed by Ishida and Inagaki elesewhere in this volume. Ohwada [26, 27, 35, 36] proposed that the orbital phase relation between the reaction sites and the groups in their environment could control the n facial selectivities and review the orbital phase environments and the selectivities elsewhere in this volume. Here, we review applications of the orbital mixing rules to the n facial selectivities of reactions other than the Diels-Alder reactions. 

The nonequivalent n orbital extension or the higher electron density in the exo face pyramidizes the unsaturated carbons The -H bonds are bent in the endo face. 

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]. 

Deformation of symmetrical orbital extension of carbonyl or olefin compounds was proposed to be the origin of the facial selectivities. We illustrate the unsymmetrical orbital phase environment of % orbitals of carbonyl and olefin groups and facial selectivities in Fig. 1 [3, 4]. There are in-phase and out-of-phase combinations of... 

In some cases half these values are adopted as /r. The absolute value of the LCAO coefficient, [c j, serves as the measure of orbital extension, as well as the square value, 4 . ... 

Although the theory behind BLW is more general, a typical application of the method is the energy calculation of a specific resonance structure in the context of resonance theory. As a resonance structure is, by definition, composed of local bonds plus core and lone pairs, a bond between atoms A and B will be represented as a bonding MO strictly localized on the A and B centers, a lone pair will be an AO localized on a single center, and so on. With these restrictions on orbital extension, the SCF solution can be... 

For transition elements like Pt and Au the linear orbital extension to the LAPW method [43] has been used. We have employed the procedure proposed in [20], in which the 5p-states for Au and Pt are included in the core for total energy calculations, but corresponding local orbitals are also included in the basis for the valence states in order to allow the basis functions for the actual valence electrons to orthogonalize to the extended core states. 

Of great importance is the radial orbital extension difference, Ar = rp — rs, (Table 1 and Figure 1). Due to the orbital behavior described above, Ar for carbon is only —0.2 pm. However, Ar increases successively in a zig-zag fashion (caused by the d-block... 

Fig. 9 The HF/3-21G HOMO and LUMO of the rigid benzoquinone-6-aniline donor acceptor system. The HOMO is associated with the aniline donor and the LUMO with the benzoquinone acceptor. These MOs are the active orbitals involved in optical ET in this molecule (see Fig. lb). Note that the benzoquinone LUMO is not entirely localised within this group, but extends into the bridge, by a hyperconjugation mechanism, the LUMO amplitude decaying exponentially with increasing penetration into the bridge. This type of orbital extension is also observed for the aniline HOMO.

The absence of 1,2-hydride shifts in [331] is in sharp contrast with the behaviour of related systems, e.g. the cyclopentyl cation [49]. This may be explained in terms of both steric and electronic factors. Strain makes the five membered ring planar and lengthens the C(l)-C(2) bond. This prevents a favourable geometry for hydrogen migration to the empty p-orbital. Extensive charge delocalization into the aromatic rings, as shown by the C-nmr spectrum, must also decrease the rate of the 1,2-hydride shift. 

Figure 6-8. Interactions with an adjacent c-orbital causes uneven orbital extension of the LUMO.

The uneven orbital extension is observed by plotting the value of the LUMO coellicicnt at a given distance from the atom onto an electron density surface, as supported by SPARTAN. 

Origin of Ji-facial diastereoselection in carbonyl addition, application of the exterior frontier orbital extension model to l,3-diheteran-5-ones (heteroatom = 0,S) 00H(52)1435. 

Since the denominators involve the difference of state-energies for the functions >pQ and contracted virtual functions >Pq Yi, they are separated widely in energy, since the contracted virtual functions are excited by lifting inactive holes to inactive particles, which have a gap, in between which the active orbitals appear. Thus the denominators are again robust. The same is valid for the corresponding single excitations involving inactive orbitals. Extensivity of our newly developed API-SSMRCC theory will be discussed in the next section. 

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