Orbital strain

The cooperative Jahn-Teller type interaction is obtained by the orbital-lattice coupled model [12,13]. Let us consider the Hamiltonian with the Jahn-Teller coupling g, the kinetic energy and the lattice potential for the Jahn-Teller phonon mode, the orbital-strain interaction, and the elastic-strain energy. The Jahn-Teller distortion mode Qi around a metal site i is represented by the Jahn-Teller phonon coordinates k- By introduce the canonical transformation for k, the orbital and lattice degrees of freedom are separated. The final form of the interaction between the inter-site orbitals given by... 

Conformational analysis is far simpler m cyclopropane than m any other cycloalkane Cyclopropane s three carbon atoms are of geometric necessity coplanar and rotation about Its carbon-carbon bonds is impossible You saw m Section 3 4 how angle strain m cyclopropane leads to an abnormally large heat of combustion Let s now look at cyclopropane m more detail to see how our orbital hybridization bonding model may be adapted to molecules of unusual geometry... 

In cyclic systems such as 1, the dominant conformation is the one with the maximum anomeric effect. In the case of 1, only conformation lA provides the preferred antiperiplanar geometry for both oxygens. Antiperiplanar relationships are indicated by including lone pairs in the oxygen orbitals. Other effects, such as torsional strain and nonbonded repulsion, contribute to the conformational equilibrium, of course. Normally, a value of about 1.5 kcal/mol is assigned to the stabilization due to an optimum anomeric interaction in an acetal. 

This stereoelectronic requirement would lead to a large distortion of the normal geometry of a five-membered ring and introduce strain. It is this distortion and strain that disfavor the 5-endo-trig cyclization. In contrast, 5-endo-dig cychzation is feasible because the acetylenic system provides an orbital that is available for a nearly planar mode of approach. 

There have been several representations of the bonding in benzyne. The one most generally used pictures benzyne as being similar to benzene but with an additional weak bond in the plane of the ring, formed by overlap of the two sp orbitals. Comparison of the NMR characteristies with MO ealeulations indieate that the eonjugation is maintained and that benzyne is a strained but aromatie moleeule. ... 

This compound is less stable than 5 and reverts to benzene with a half-life of about 2 days at 25°C, with AH = 23 kcal/mol. The observed kinetic stability of Dewar benzene is surprisingly high when one considers that its conversion to benzene is exothermic by 71 kcal/mol. The stability of Dewar benzene is intimately related to the orbital symmetry requirements for concerted electrocyclic transformations. The concerted thermal pathway should be conrotatory, since the reaction is the ring opening of a cyclobutene and therefore leads not to benzene, but to a highly strained Z,Z, -cyclohexatriene. A disrotatory process, which would lead directly to benzene, is forbidden. ... 

It is important to note here that both of the 5-exo radical cyclizations (133—>132—>131, Scheme 27) must proceed in a cis fashion the transition state leading to a strained mms-fused bicy-clo[3.3.0]octane does not permit efficient overlap between the singly occupied molecular orbital (SOMO) of the radical and the lowest unoccupied molecular orbital (LUMO) of the alkene. The relative orientation of the two side chains in the monocyclic radical precursor 134 is thus very significant because it dictates the relationship between the two outer rings (i. e. syn or anti) in the tricyclic product. The cis-anti-cis ring fusion stereochemistry of hirsutene would arise naturally from a cyclization precursor with trans-disposed side chain appendages (see 134). 

One hypothesis proposes a destabilizing, repulsive interaction between two occupied orbitals. The equatorial transition state is destabilized compared to the axial transition state by torsional strain which is introduced by bond eclipsing of the incipient bond with the axial C-2 and C-6 carbon-hydrogen bonds. This Felkin model33 37 relies on the assumption that an incipient bond, even if it is only partially formed, suffers from severe repulsion in the case of eclipsing vicinal tr-bonds. 

Radicals with very polar substituents e.g. trifluoromethyl radical 2), and radicals that arc part of strained ring systems (e.g. cydopropyl radical 3) arc ct-radicals. They have a pyramidal structure and are depicted with the free spin resident in an spJ hybrid orbital. nr-Radicals with appropriate substitution are potentially chiral, however, barriers to inversion are typically low with respect to the activation energy for reaction. 

Table 9 shows the PP MO results for this interesting series of highly strained three-membered cyclic molecules. Here a detailed comparison is possible with the best results of an all-electron study, including d functions10 (also reported in Table 9). An analysis of this table reveals how all trends in population analysis, both in charges and overlap populations, are the same in the AE + d and in the simple PP calculations, with very few and very minor exceptions. PP predicts a charge donation to the aliphatic groups, while AE predicts a withdrawal, mainly due to the availability of d orbitals on sulphur, which can allocate extra electronic charge. As outlined in the general notes on population analysis (Section III.D) comparisons should be carried out on a relative basis and,...

Clearly, there exists a good agreement between theoretical predictions (and calculations) based on the participation of sulfur 3d-orbitals and available experimental results. Thus, the important role of the sulfur d-orbitals in determining the structure and, consequently, the chemistry of sulfones and sulfoxides in general, and of strained smallring sulfones and sulfoxides in particular, has been established. 

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