Overlap-enhanced orbital

CF orbitals Coulson-Fisher-type orbitals. These are semilocalized AOs, also called overlap enhanced orbitals (OEOs) which are localized on a given center, but have small delocalization tails on other centers. Special cases of CF AOs are BDOs (see above). 

Attempts have been made to account for the rate enhancements in intramolecular catalysis on the basis of an effective concentration of 55 M combined with the requirement of very precise alignment of the electronic orbitals of the reacting atoms orbital steering. Although this treatment does have the merit of emphasizing the importance of correct orientation in the enzyme-substrate complex, it overestimates this importance, because, as we now know, the value of 55 M is an extreme underestimate of the contribution of translational entropy to effective concentration. The consensus is that although there are requirements for the satisfactory overlap of orbitals in the transition state, these amount to an accuracy of only 10° or so.23-24 The distortion of even a fully formed carbon-carbon bond... 

The calculations reported so far are based on unconstrained mixing of all valence functions as a result, the optimized orbitals differ greatly from those pictured by Pauling, which - although usually hybrids - were strictly monocentric in character. The optimized forms resemble more closely the Coulson-Fischer orbitals of Sect.2, being distorted AOs which result in considerably increased overlap in the bond regions. In this general context, such AOs have been referred to as overlap-enhanced... 

We overview our valence bond (VB) approach to the ir-electron Pariser-Parr-Pople (PPP) model Hamiltonians referred to sis the PPP-VB method. It is based on the concept of overlap enhanced atomic orbitals (OEAOs) that characterizes modern ab initio VB methods and employs the techniques afforded by the Clifford algebra unitary group approach (CAUGA) to carry out actual computations. We present a sample of previous results, sis well sis some new ones, to illustrate the ability of the PPP-VB method to provide a highly correlated description of the ir-electron PPP model systems, while relying on conceptusilly very simple wave functions that involve only a few covalent structures. 

The van der Waals and hydrogen bond interactions present in AZ-28 force the hapten into a fixed conformation that is cat-alyticaUy unfavorable. In contrast, the antibody combining site of the germline precursor to AZ-28 seems to have much more flexibility, allowing dynamic changes that lead to enhanced orbital overlap and increased rate acceleration. The disparity in catalysis is further supported by molecular dynamics simulation... 

Analyze The size of the band gap depends on the vertical and horizontal positions of the elements in the periodic table. The band gap will increase when either of the following conditions is met (1) The elements are located higher up in the periodic table, where enhanced orbital overlap leads to a larger splitting between bonding and antibonding orbitals, or (2) the horizontal separation between the elements increases, which leads to an increase in the electronegativity difference and bond polarity. 

Figure 5. Bending in of a substituent enhances orbital overlap.

The synclinal conformation (sc) is appropriate for overlap of an oxygen nonbonded pair with the a C—Cl orbital. The preferred ap relationship, requires an antiperiplanar alignment of a lone-pair orbital with the bond to the electronegative substituent. Because of the donor-acceptor nature of the interaction it is enhanced in the order F < O < N for the donor (D) atom and N < O < F for the acceptor (A) atom. 

Lewis acids catalyze Diels-Alder reactions. Do they enhance overlap between diene and dienophile orbitals and/ or do they reduce the HOMO/LUMO energy difference ... 

FIGURE U5 When two ls-orbitals overlap in the same region of space in such a way that their wavefunctions have the same signs in that region, their wavefunctions (red lines) interfere constructively and give rise to a region of enhanced amplitude between the two nuclei (blue line). 

The carhon-carbon double bond in alkenes is more reactive than carbon-carbon single bonds and gives alkenes their characteristic properties. As we saw in Section 3.4, a double bond consists of a a-bond and a 7r-bond. Each carbon atom in a double bond is sp2 hybridized and uses the three hybrid orbitals to form three cr-bonds. The unhvbridized p-orbitals on each carbon atom overlap each other and form a Tr-bond. As we saw in Section 3.7, the carbon-carbon 7r-bond is relatively weak because the overlap responsible for the formation of the 7r-bond is less extensive than that responsible for the formation of the a-bond and the enhanced electron density does not lie directly between the two nuclei. A consequence of this weakness is the reaction most characteristic of alkenes, the replacement of the 77-bond by two new a-bonds, which is discussed in Section 18.6. 

Two reasons may be offered for the enhanced /3-deuterium isotope effect in vinyl cations as compared with carbonium ions (193). As pointed out by Noyce and Schiavelli (21), in the transition state of a vinyl cation, the isotopically substituted C—H bond is ideally suited for overlap with the developing vacant p orbital, as the dihedral angle between the empty p orbital and C—H bonds is zero in the intermediate, as shown in structure 239. Shiner and co-workers (195)... 

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