Overlap out of phase

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... 

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>. 

An in-phase overlap is bonding and lowers the MO energy, whereas an out-of-phase overlap is antibonding and raises the MO energy. 

This effect has been reproduced in ab initio calculations40 and rationalized.41 The principle of maximum overlap states that the preferred trajectory corresponds to the best molecular overlap between the reaction partners (rule 4). If the nucleophile adopts a perpendicular trajectory, the atomic overlap with the carbon will be maximized. However, a competing out-of-phase overlap between the nucleophile HOMO and the carbonyl LUMO (shown by the wavy line) reduces the overall frontier orbital interaction. If the nucleophile is displaced laterally (arrow), the small diminution in the overlap with C is outweighed by the reduction in the antibonding interaction with O. This increase in the overall overlap explains the preference for attack from an obtuse angle... 

AO is offset by an out-of-phase overlap with the AO of the leaving group. Salem had to resort to numerical calculations before concluding that inversion is favored.147... 

On the contrary, if the crest of one wave overlaps with the trough of the other, then two waves interact in a destructive manner. In other words, this is out of phase overlap or subtraction overlap and the resulting wave is weakened. Such type of subtraction overlap of atomic orbitals with opposite signs leads to the formation of antibonding molecular orbital. 

The mechanisms of chemical reactions and the reactivity properties of the molecules involved started to be elucidated through the analysis of the wave functions defining the quantum state of molecular systems,5-7 for instance the Fukui s frontier molecular orbital (FMO) theory8,9 has been very successful in rationalizing organic reactions basically through the analysis of the in- and out-of-phase overlap between the highest occupied molecular orbital (HOMO) of the nucleophile and the lowest unoccupied molecular... 

Mobius aromaticity A monocyclic array of orbitals in which a single out-of-phase overlap (or, more generally, an odd number of out-of-phase overlaps) reveals the opposite pattern of aromatic character to Hiickel systems with 4n electrons it is stabilized (aromatic), whereas with 4n + 2 it is destabilized (antiaromatic). In the excited state 4n + 2, Mobius pi-electron systems are stabilized, and 4n systems are destabilized. No examples of ground-state Mobius pi systems are known, but the concept has been applied to transition states of PERI-CYCLIC REACTIONS (see AROMATIC [3]). 

The HOMO and LUMO are of particular interest. As seen in Figure 5, the shape of the HOMO is generated by the out-of-phase overlap of the AOs locahzed, on the one... 

---