Controlling symmetry properties

A complete mechanistic description of these reactions must explain not only their high degree of stereospecificity, but also why four-ir-electron systems undergo conrotatory reactions whereas six-Ji-electron systems undergo disrotatory reactions. Woodward and Hoifinann proposed that the stereochemistry of the reactions is controlled by the symmetry properties of the HOMO of the reacting system. The idea that the HOMO should control the course of the reaction is an example of frontier orbital theory, which holds that it is the electrons of highest energy, i.e., those in the HOMO, that are of prime importance. The symmetry characteristics of the occupied orbitals of 1,3-butadiene are shown in Fig. 11.1. 

Symmetry dictates that the representations of the direct product of the factors in the integral (3 /T Hso 1 l/s2) transform under the group operations according to the totally symmetric representation, Aj. The spin part of the Hso spin-orbit operator converts triplet spin to singlet spin wavefunctions and singlet functions to triplet wavefunctions. As such, the spin function does not have a bearing on the symmetry properties of Hso- Rather, the control is embedded in the orbital part. The components of the orbital angular momentum, (Lx, Ly, and Lz) of Hso have symmetry properties of rotations about the x, y, and z symmetry axes, Rx, Ry, and Rz. Thus, from Table 2.1, the possible symmetry... 

To show that this is the case we simplify the discussion of the optical excitation of the B — A — B molecule by focusing upon transitions between electronic states of the same representations, e.g., A to A or A" to A" (where A denotes the symmetric representation and A" the antisymmetric representation of the Cs group). We further assume that the ground vibronic state belongs to the A representation. To obtain control we choose the intermediate state E2) to be symmetric, and the intermediate state E ) to be antisymmetric, with respect to reflection in the a hyperplane. Hence we must first demonstrate that it is possible optically to excite, simultaneously, both the-symmetric E2) and antisymmetric E ) states from the ground state Eg). This requires the existence of both a symmetric dipole component, denoted ds, and an antisymmetric component, denoted da, with respect to reflection in the a hyperplane, because, by the symmetry properties of E2) and 1 ),... 

Contrary to systems possessing an inversion center in which the interference between a one-photon and a two-photon process can only lead to phase control of differential properties, e.g., current directionality [29,54,95,96], we have shown that the CPT process of broken symmetry systems allows us to control integral properties as well, a prime example of which is the control of the excited states population of two enantiomers. 

A complete mechanistic description of these reactions must explain not only their high degree of stereospecificity, but also why four-tt-electron systems undergo conrotatory reactions, while six-tt-electron systems undergo disrotatory reactions. Woodward and Hoffmann suggested that the stereochemistry of these reactions is controlled by the symmetry properties of the highest occupied molecular orbital... 

Recently, Woodward and Hoffmann (1965, 1968, 1969), Longuet-Higgins and Abrahamson (1965), and Fukui (1971) have suggested that the stereochemical courses of these reactions are controlled by the symmetry properties of the orbitals of the reactants and products. Two approaches are employed, the frontier orbital method, and the correlation diagram method. The first approach requires a knowledge of the molecular orbitals of unsaturated hydrocarbons and consideration of the way in which they can interact. 

The lower symmetry of nanorods (in comparison to nanoshells) allows additional flexibility in terms of the tunability of their optical extinction properties. Not only can the properties be tuned by control of aspect ratio (Figure 7.4a) but there is also an effect of particle volume (Figure 7.4b), end cap profile (Figure 7.4c), convexity of waist (Figure 7.4d), convexity of ends (Figure 7.4e) and loss of rotational symmetry (Figure 7.4f). 

Properties of nickel poly(pyrazol-l-yl)borate complexes such as solubility, coordination geometry, etc., can be controlled by appropriate substituent groups on the pyrazol rings, in particular in the 3- and 5-positions. Typical complexes are those of octahedral C symmetry (192)°02-604 and tetrahedral species (193). In the former case, two different tris(pyrazolyl)borate ligands may be involved to give heteroleptic compounds.602,603 Substituents in the 5-position mainly provide protection of the BH group. Only few representative examples are discussed here. 

This idea is elegant for its simplicity and also for its usefulness. While often in phenomenological theories of materials, control of parameters with molecular structure would provide useful properties, but the parameters are not related in any obvious way to controllable molecular structural features. Meyer s idea, however, is just the opposite. Chemists have the ability to control enantiomeric purity and thus can easily create an LC phase lacking reflection symmetry. In the case of the SmC, the macroscopic polar symmetry of this fluid phase can lead to a macroscopic electric dipole, and such a dipole was indeed detected by Meyer and his collaborators in a SmC material, as reported in 1975.2... 

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