Sigma symmetrical

When a cyclic polyene is large enough, it can exist in both cis- and iraws-forms. Our approach to polyene cyclization has tacitly assumed an all cis -n chain in the form of a band or ribbon that would slip smoothly on to the surface of a cylinder of appropriate diameter. Should the orbitals of the two polyenes in (36) have a mismatch in their orbital symmetries, a single twist in the tt band of one of them could remedy this (Fig. 10c). Cycloaddition would now be allowed and the reaction would proceed, provided other factors were favorable. Such cases of Mobius (Zimmerman, 1966), anti (Fukui and Fujimoto, 1966b) or axisymmetric (Lemal and McGregor, 1966), as opposed to Hiickel, syn, or sigma-symmetric ring closure are unknown (or, at least, rare). A Mobius form has, however, been proposed as the key intermediate in the photochemical transformations of benzene (Farenhorst, 1966) in (48) in place of the disrotatory cyclization proposed by van Tamelen (1965). 

A bond m which the orbitals overlap along a line connecting the atoms (the inter nuclear axis) is called a sigma (a) bond The electron distribution m a ct bond is cylm drically symmetric were we to slice through a ct bond perpendicular to the mternuclear axis Its cross section would appear as a circle Another way to see the shape of the elec tron distribution is to view the molecule end on... 

The electron density in both molecular orbitals is symmetrical about the axis between the two nuclei. This means that both of these are sigma orbitals. In MO notation, the Is bonding orbital is designated as eru. The antibonding orbital is given the symbol An asterisk designates an antibonding orbital... 

In the bond framework in Figure 10-18. all the bonds form from end-on overlap of orbitals directed toward each other. As illustrated by the three examples in Figure 10-20. this type of overlap gives high electron density distributed symmetrically along the intemuclear axis. A bond of this type is called a sigma (cr) bond, and a bonding orbital that describes a cr bond is a (7 orbital. 

The Lewis dot formalism shows any halogen in a molecule surrounded by three electron lone pairs. An unfortunate consequence of this perspective is that it is natural to assume that these electrons are equivalent and symmetrically distributed (i.e., that the iodine is sp3 hybridized). Even simple quantum mechanical calculations, however, show that this is not the case [148]. Consider the diiodine molecule in the gas phase (Fig. 3). There is a region directly opposite the I-I sigma bond where the nucleus is poorly shielded by the atoms electron cloud. Allen described this as polar flattening , where the effective atomic radius is shorter at this point than it is perpendicular to the I-I bond [149]. Politzer and coworkers simply call it a sigma hole [150,151]. This area of positive electrostatic potential also coincides with the LUMO of the molecule (Fig. 4). 

The inhibited unimolecular decomposition of symmetrically di-substituted benzoyl peroxides into radicals also obeys the Hammett rho-sigma relationship. Unfortunately, no extensive activation parameter data are available. The effect of the substituent changes on the rates at the single temperature has been explained in terms of dipole-dipole repulsion in the peroxide.122... 

This means that the ionization and rearrangement need not be concerted and that symmetrical protonated ethylene can not be a major intermediate in the reaction. A similar experiment with isobutylamine and nitrous acid in heavy water gave products that contained no carbon-deuterium bonds. Since it is known that the -complex formed from isobutylene and acid is in rapid equilibrium with protons from the solvent, none of this can be formed in the nitrous acid induced deamination. This in turn makes it probable that the transition state for the hydrogen migration is of the sigma rather than the -bonded type.261... 

Fig.4 (see p. 74/75) shows all localized orbitals for the ground state of the BH molecule and the 12 excited state of B2.37) These are again rotationally symmetric orbitals, i.e., sigma type orbitals, and the complete contour surfaces can be obtained by spinning around the indicated axis. In all orbitals shown the outermost contour corresponds to a wavefunction value of 0.025 Bohr-3/2. For all valence shell orbitals the increment from one contour to another is 0.025 Bohr-3/2. For the inner shells the increment is again 0.2 Bohr 3/2, but only three contours and the wavefunction values at the nuclear positions are shown. 

In any bond between two atoms, you can imagine an imagin iry line (the bond axis) that connects the center of one atom to the center of the other atom. Sigma bonds are perfectly symmetric about this line you can imc ine the sigma bond as a kind of tube that wraps ciround the bond axis. 

However, it is not invariant under reflection into any of the three ov symmetry planes. It thus does not have the full symmetry required for an A state, and it is only fully symmetric in the C31, subgroup of the D31, molecular point group. The energy lies a further O.lOeV below that of the all-sigma three-configuration solution (see Table 4). 

Sigma (s) Orbital A molecular orbital which is symmetrical about a line joining the two nuclei (the bond axis) is called a sigma (s) orbital. It may be bonding or antibonding molecular orbital. 

This is a view down the internuclear axis, perpendicular to the plane that cuts through the MO. In this view it can easily be seen that the intersection of the plane with the MO is symmetrical. Therefore, this is classified as a sigma bond. 

Sigma (a) bond (Section 3.2) A bond formed by overlap of orbitals that point direedy toward each other so that its MO is symmetric about the inter-nuclcar axis. 

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