Phase overlapping

The characteristic feature of valence bond theory is that it pictures a covalent bond between two atoms in terms of an m phase overlap of a half filled orbital of one atom with a half filled orbital of the other illustrated for the case of H2 m Figure 2 3 Two hydrogen atoms each containing an electron m a Is orbital combine so that their orbitals overlap to give a new orbital associated with both of them In phase orbital overlap (con structive interference) increases the probability of finding an electron m the region between the two nuclei where it feels the attractive force of both of them... 

In phase overlap of two Is orbitals gives new orbital encompassing both hydrogen atoms... 

In valence bond theory a covalent bond is described m terms of m phase overlap of a half filled orbital of one atom with a half filled orbital of another When applied to bonding m H2 the orbitals involved are the Is orbitals of two hydrogen atoms and the bond is a ct bond... 

FIGURE 4 11 Combi nation of tert butyl cation and chloride anion to give tert butyl chloride In phase overlap between a vacant p orbital of (CHbIbC and a filled p orbital of Cr gives a C—Cl (T bond... 

Despite the recent efforts for settling operational conditions for metal and metalloid fractionation, conventional batch sequential extraction schemes lack automation and are rather time consuming and laborious. Two additional main problems are the phase overlapping and possible re-adsorption of released elements. 

The first interaction has favorable orbital phase overlap for a concerted (2ns + vizs) reaction. The interaction integral y, Eqs. 3—6, for a concerted process would have a maximum value if the two molecules approached each other so that the reacting orbitals could overlap in the most efficient manner. The best geometry would involve a face-to-face reaction of the two reactant species. The stereochemical consequence of such a reaction would be specific retention of substituent relative geometries. 

Changes in molecular shape which increase the in-phase overlap between two or more AOs in a MO tend to lower the energy of that MO. Conversely, changes in shape which decrease in-phase overlap or increase out-of-phase overlap among AOs in a MO tend to raise the energy of the MO. This can be called the overlap rule. 

The lowest unfilled molecular orbitals in the haloalkanes are formed from the out-of-phase overlap of an sp3 hybrid orbital of the carbon atom... 

Fig. 6.16 Molecular Orbital pictures and qnalilalive energies of linear and bent AB molecules. Open and shaded areas represent differences in sign (+ or ) of the wave functions. Changes in shape which increase in-phase overlap lower the molecular orbital energy- From Gimarc.

Front-side attack, corresponding to an attack on the big lobe of silicon, leads to retention. When unfavorable, out-of-phase overlap between the nucleophile and the orbitals of the leaving group predominates, nucleophilic attack occurs at the rear of the molecule, opposite X, leading to... 

In the case of the p -methoxyphenoxide anion, Taft et al. (77) have shown that the oxygen atom has a high degree of sp3 character. This nucleophile is quite similar to hard alkyl anions from an electronic point of view, i.e., it is a hard nucleophile with contracted valence orbitals around oxygen, unfavorable out-of-phase overlap with the leaving group is minimized (Scheme 9), and a front-side attack leading to retention is therefore possible. The stereochemical data are summarized in Table XI. 

In contrast, sodium p -nitrophenoxide is similar to the allyllithium compounds. The counter cation reduces the p character of the oxygen and prevents the delocalization of the negative charge over the aromatic system. The valence orbitals are centered toward Na+, whereas for the naked anion they are more disposable or, in other words, more diffuse (Scheme 22). Therefore, in the latter case, unfavorable out-of-phase overlap with the leaving group is increased, and rear-side attack of the nucleophile is promoted, leading to inversion (Table XI). 

B3LYP/6-31G(d) calculations were used to predict the stability of possible ortho-fused heterocycles, tf-CAtTS., (where = 1-8). With 0-C6H4S ( = 3, 5, 7) an even number of out-of-phase overlaps was achieved, whereas with 0-C6H4S (x = 2, 4, 6, 8) an odd number of out-of-phase overlaps was achieved (e.g., compare structures A and B) (Figure 7) <2004JOC5483>. 

In the case of we can say that there is positive (in-phase) overlap between the hydrogen Is orbitals, because the product is positive in the internuclear region (the amplitudes of both orbitals are positive) this leads to bonding between the two atoms. In the case of the amplitudes... 

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