7i*-orbital

The 7i-orbitals of benzene, C6H6, may be modeled very crudely using the wavefunctions and energies of a particle on a ring. Lets first treat the particle on a ring problem and then extend it to the benzene system. 

For example, in formaldehyde, H2CO, one forms sp hybrids on the C atom on the O atom, either sp hybrids (with one p orbital "reserved" for use in forming the n and 7i orbitals and another p orbital to be used as a non-bonding orbital lying in the plane of the molecule) or sp hybrids (with the remaining p orbital reserved for the n and 7i orbitals) can be used. The H atoms use their 1 s orbitals since hybridization is not feasible for them. The C atom clearly uses its sp2 hybrids to form two CH and one CO a bondingantibonding orbital pairs. 

Hamiltonian contains (fe2/2me r ) 32/3y2 whereas the potential energy part is independent of Y, the energies of the moleeular orbitals depend on the square of the m quantum number. Thus, pairs of orbitals with m= 1 are energetieally degenerate pairs with m= 2 are degenerate, and so on. The absolute value of m, whieh is what the energy depends on, is ealled the X quantum number. Moleeular orbitals with = 0 are ealled a orbitals those with = 1 are 7i orbitals and those with = 2 are 5 orbitals. 

For a 7C% 1 configuration in which two non-equivalent n orbitals (i.e., orbitals whieh are of n symmetry but whieh are not both members of the same degenerate set an example would be the n and 7i orbitals in the B2 moleeule) are oeeupied, the above analysis must be expanded by ineluding determinants of the form 7iia7i ia, ... 

In the olefin example mentioned above, the two non-orthogonal "polarized orbital pairs" involve mixing the n and 7i orbitals to produee two left-right polarized orbitals as depleted below ... 

Lone pairs are not necessarily the highest-energy electrons. In the case of phenylisocyanide, the two highest-energy molecular orbitals are delocalized 7i orbitals. 

Arynes present structural features of some interest. They clearly cannot be acetylenic in the usual sense as this would require enormous deformation of the benzene ring in order to accommodate the 180° bond angle required by the sp1 hybridised carbons in an alkyne (p. 9). It seems more likely that the delocalised 7i orbitals of the aromatic system are left largely untouched (aromatic stability thereby being conserved), and that the two available electrons are accommodated in the original sp2 hybrid orbitals (101) ... 

Concerted cycloaddition reactions provide the most powerful way to stereospecific creations of new chiral centers in organic molecules. In a manner similar to the Diels-Alder reaction, a pair of diastereoisomers, the endo and exo isomers, can be formed (Eq. 8.45). The endo selectivity in the Diels-Alder arises from secondary 7I-orbital interactions, but this interaction is small in 1,3-dipolar cycloaddition. If alkenes, or 1,3-dipoles, contain a chiral center(s), the approach toward one of the faces of the alkene or the 1,3-dipole can be discriminated. Such selectivity is defined as diastereomeric excess (de). 

Clearly, from inspection of Table 4.14, there is a good correlation between the steric bulk of R and L and the non-coincidence angle a. Furthermore, analysis of the hyperfine parameters leads to the conclusion that only about 25% of the electron spin resides in Co orbitals (mainly dxz), and crystal structures of the R = CF3, L = PPh3 and P(OPh)3 complexes do indeed show distortions. The difference between iron and cobalt is just one electron, but this electron occupies a dithiolene 7i orbital, which makes the cobalt complexes much more easily distorted. 

The antibonding 7i orbital is of higher energy, and it is not occupied by electrons when the molecule is in the ground state. 

This analysis confirms that the effect of cyclic constraints is not purely steric but also has an electronic component. Another aspect of this dichotomy is shown in Fig. 11 which illustrates the decrease in the energy gap between the frontier in-plane rc-MOs. The decrease in the C1-C6 distance destabilizes the occupied MO where the interaction between the end orbitals is antibonding and, at the same time, stabilizes the empty MO where the 7i -orbitals overlap constructively. As a result, the efficiency of the photochemical Bergman cyclization should increase and, indeed, the most efficient photo-Bergman cyclizations reported in the literature involve cyclic enediynes.43 Again, the analogy with interrupted [2 + 2] photocycloaddition is instructive. 

Fig. 2 (top) Planar regioregular polymer with directly overlapping pi orbitals vs. twisted backbone with 7i orbitals out-of-plane [1]... 

Scheme 1 Bithiophene crown ether in planar conformation with 7i orbital overlapping in the absence of bound metal. After the chelation of the metal ion, the bithiophene is forced out plane and the 7t orbitals no longer have maximal overlapping [12]...

Fig. 13 Simplified 7i-orbital diagram for metal-allenylidene complexes...

The Catalysis Concept of Iminium Activation In 2000, the MacMillan laboratory disclosed a new strategy for asymmetric synthesis based on the capacity of chiral amines to function as enantioselective catalysts for a range of transformations that traditionally use Lewis acids. This catalytic concept was founded on the mechanistic postulate that the reversible formation of iminium ions from a,p-unsaturated aldehydes and amines [Eq. (11.10)] might emulate the equilibrium dynamics and 7i-orbital electronics that are inherent to Lewis acid catalysis [i.e., lowest unoccupied molecular orbital (LUMO)-lowering activation] [Eq. (11.9)] ... 

Thus 2-ketoquinuclidine 25 gives quinuclidine in good yields [120]. There is no overlap between the a-bond and the carbonyl 7i -orbital to assist simultaneous electron transfer and bond cleavage. 

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