Orbitals alignment

Fladdon R C, Brus L E and Raghavaohari K 1986 Rehybridization and n-orbital alignment the key to the existenoe of spheroidal oarbon olusters Chem. Rhys. Lett. 131 165... 

The 7t-electron delocalization requires proper orbital alignment. As a result, there is a significant barrier to rotation about the carbon-carbon bonds in the allyl cation. The results of 6-31G/MP2 calculations show the perpendicular allyl cation to be 37.8 kcal/mol higher than the planar ion. Related calculations indicate that rotation does not occur but that... 

The deviation from planarity that is present in a structure such as 1 raises the question of how severely a conjugated system can be distorted from the ideal coplanar alignment of p orbitals and still retain aromaticity. This problem has been analyzed by determining the degree of rehybridization necessary to maximize p orbital overlap in 1. It is found that rehybridization to incorporate fractional amounts of s character can improve orbital alignment substantially. Orbitals with about 6% s character are suggested to be involved... 

The importance of specific orbital alignments in the TB propagation of remote stereoelectronic influences can be assessed directly by structure-sensitive spectroscopic techniques. The results of many such studies have been summarized as various effects or rules that express the dependence on geometrical factors, such as the all-trans zig-zag or W pattern of skeletal bridge bonds. Such a W-effect 105... 

The second factor used to support the non-classical position is the high exojendo rate ratio usually found in solvolysis. The high ratios have been taken as evidence for delocalization of the a electrons of the bond between C-1 and C-6 into the rear of a developing p-orbital at C-2 as an ex o-substituent ionizes. Similar delocalization during the ionization of an endo-substituent is not anticipated because of poor orbital alignment. 

Figure 1.28. (a) Infinite periodic linear chain of atoms separated by the distance a, (b) band structure for 1 and p atomic orbitals pointing perpendicularly to the chain direction, (c) band structure for p atomic orbitals aligned along the chain direction and (d) DOS of a ID infinite periodic linear chain. 

Let us now consider the ideal case of the BFS (see Fig. 1.18). In the absence of anions and neglecting sulfur- or selenium-induced lateral molecule-molecule interactions, the organic molecules can be modelled as forming an ideal ID chain with orbitals aligned in the direction of the chain with a lattice constant a given... 

For hydrogen, only the Is orbital is energetically accessible for band formation. For elements of lithium through fluorine, the 2s and, at somewhat higher energy, the three 2p orbitals are available, and, depending on the ways in which the atomic orbitals align with the crystal structure, these may form either a continuous s,p band or a pair of bands with the same... 

Second in frequency of occurrence are concerted cycloadditions and electronic reorganizations of the sigmatropic type. Here, although mutually compatible charge distributions are significant, it is the possibility for correct orbital alignment that is of overriding importance. 

One of the simplest examples of sp hybridization is found in acetylene, H-C = C-H, a colorless gas used in welding. Both carbon atoms in the acetylene molecule have linear geometry and are sp-hybridized. When the two sp-hybridized carbon atoms approach each other with their sp orbitals aligned... 

Doubly bonded carbons are sp2-hybridized. Carbon has three sp2 hybrid orbitals, which lie in a plane and point toward the comers of an equilateral triangle, and one unhybridized p orbital, which is oriented at a 90° angle to the plane of the sp2 hybrids. When two s/r-hybridized carbon atoms approach each other with sp2 orbitals aligned head-on for sigma bonding, the unhybridized p orbitals on each carbon overlap to form a pi bond, resulting in a net carbon-carbon double bond. 

Interestingly, the reverse trend is observed with other oxidizing agents, such as chromic acid. Thus, chromic acid is known to oxidize quicker axial alcohols, which is explained by the release of steric congestion exerted by 1,3-f/rm-diaxial interactions.102 Apparently, a proper orbital alignment plays a greater role in DDQ oxidations than the release of steric congestion. 

Haddon, R. C., Brus, L. E. Raghavachari, K. 19866 Rehybridization and Jt-orbital alignment the key to the existence of spheroidal carbon clusters. Chem. Phys. Lett. 131, 165-169. 

The magnetic quantum number, mf, determines the spatial orientation of the orbital s angular momentum and takes the values - to + . An s orbital ( - 0), being spherical, can only have one orientation in space—it does not point in any one direction and hence it only has one value for me(0). However, a p orbital could point in any direction. For a p orbital ( = 1) there are three values of file -1,0, and +1. These correspond to the p orbitals aligned along the mutually perpendicular x-, y-, and z-axes. These orbitals, designated p, py, and p, are all degenerate. They differ only in their spatial orientations. 

We explained this effect by saying that the Jt of the C-O and the G of C-Cl overlap to form a new, lower-energy (and therefore more reactive) LUMO. What we did not note then, because it was not relevant, is that this overlap can only occur when the C-Cl bond is perpendicular to the C-O bond, because only then are the 7t and G orbitals aligned correctly. 

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