Analysis in Maximum Symmetry

Halevi s method to determine whether a chemical reaction is allowed or forbidden considers both the electronic and vibrational changes in the molecule. Of course, its high degree of rigor may render its application more complicated as compared with the methods which focus only upon changes in the electronic structure. The approaches introduced by Fukui and Woodward and Hoffmann seem to have received more widespread acceptance and utilization. 

The interaction of two ethylene molecules will be considered in two geometrical arrangements. The two molecules adopt a mutually parallel approach in one arrangement and a mutually perpendicular approach in the other. Applications of various methods will be considered briefly. 

Since cr and cr are maintained throughout the reaction, there must be a continuous correlation of orbitals of the same symmetry type. Therefore, orbitals of like symmetry correlate with one another and they can be connected. This, the crucial idea of the Woodward-Hoffmann method, is shown in the central part of the diagram. 

Inspection of this correlation diagram immediately reveals that there is a problem. One of the bonding orbitals at the left correlates with an antibonding orbital on the product side. Consequently, if orbital symmetry is to be conserved, two ground state ethylene molecules cannot combine via face-to-face approach to give a ground-state cyclobutane, or vice versa. This concerted reaction is symmetry forbidden.  

Character under Orbital occupation Character under  

Halevi s method to determine whether a chemical reaction is allowed or 

The rules for the state correlation diagrams are the same as for the orbital correlation diagrams only states that possess the same symmetry can be connected. In order to determine the symmetries of the states, first the symmetries of the MOs must be determined. These are given for the face-to-face dimerization of ethylene in Table 7-1. The character table (Table 7-2) shows that the two crucial symmetry elements are the symmetry planes ct(x ) and cr (yz). The MOs are all symmetric with respect to the third plane, a ixz) (vide supra). The corresponding three symmetry operations will unambiguously determine the symmetry of the MOs. Another possibility is to take the simplest subgroup of which already contains the two crucial symmetry 

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E. A. Halevi, Orbital Correspondence Analysis in Maximum Symmetry. Helv. Chim. Acta 1975, 58, 2136-2151. 

An analysis of the dimerization of silacyclopropene was carried out by Orbital Correspondence Analysis in Maximum Symmetry (OCAMS). This analysis showed that the dimerization of silacyclopropene follows an allowed pathway <82JOM(240)129>. 

Huisgen s mechanism was also discussed on the basis of the principle of orbital correspondence analysis in maximum symmetry (OCAMS) by Halevi (1992, p. 168). 

OCAMS orbital correspondence analysis in maximum symmetry... 

Theoretical Aspects, Calculations, and Physical Data.—The basis of orbital-corre-pondence analysis in maximum symmetry has been described in terms of the familiar A and S notation, and the relationship to the Woodward-Hoffmann and Longuet-Higgins-Abrahamson analyses of pericyclic reactions discussed. In a useful and... 

In their now classic monograph [1], Wooodward and Hoffmann concentrate on three basic types of no mechanism reaction Electrocyclic reactions -notably polyene cyclizations, cycloadditions, and sigmatropic rearrangements. These three reaction types will be taken up in this and the next two chapters from the viewpoint of Orbital Correspondence Analysis in Maximum Symmetry (OCAMS) [2, 3, 4], the formalism of which follows naturally from that developed in Chapter 4. The similarities to the original WH-LHA approach [5, 6], and the points at which OCAMS departs from it, will be illustrated. In addition, a few related concepts, such as allowedness and forbiddenness , global vs. local symmetry, and concertedness and synchronicity , will be taken up where appropriate. 

Professor Halevi has set out to correct the situation by making available a rigorously written text. He relies on a particularly well thought-through formulation, referred to as Orbital Correspondence Analysis in Maximum Symmetry (OCAMS). The playful reference to the medieval scholar, Occam, whose fabled razor all students are told about, is well chosen this is a text of high intellectual and scholarly standards. 

My object in writing this book is to present a coherent set of operational rules for the analysis of reaction mechanism in terms of symmetry, and to explore their scope and reliability. It is written from the viewpoint of Orbital Correspondence Analysis in Maximum Symmetry - OCAMS for short, hence its subtitle, but not with the intention of touting a homemade prodct The procedural details of OCAMS are of secondary importance its advantage lies in the provision of a coherent overview of the relation between symmetry and mechanism it allows us to see the forest without losing sight of the trees. For reasons of self-consistency, the book remains within the framework of molecular orbital theory reformulation of the OCAMS approach in valence-bond terms has not been attempted. 

The thermal stresses were computed by the finite element code ANSYS [29], taking full advantage of the axial symmetry of the filter see Fig. 16. Both the temperature-dependent physical properties of the EX-54 filter (Section V) and the time-dependent thermocouple data were used as inputs to stress analysis. The maximum stresses in the axial and tangential directions at the midsection are summarized in Table 14. It should be noted in Table 14 that the radial temperature gradient is the major contributor to thermal stresses those due to axial gradient are less than 20%. 

A guiding principle in the following analysis is the principle of maximum symmetry which states that ... 

The experimental diffraction data were analyzed by a combined technique involving Rietveld analysis, the maximum entropy method (MEM), and MEM-based pattern fitting (MPF) [10-15]. Rietveld analysis, which is used to refine the crystal structure from the powder diffraction data by a least squares method, was carried out using the RIETAN-2000 program [27], which yields structure factors and their errors after structural refinement. It is known that MEM can be used to obtain a nuclear density distribution map based on neutron structure factors and their errors [5, 6, 8, 10-15, 26-29] any type of complicated nuclear density distribution is allowed so long as it satisfies the symmetry requirements. MEM calculations were carried out using the PRIMA program [29]. To reduce the bias imposed by the simple structural model in the Rietveld refinement, an iterative procedure known as the REMEDY cycle [29] was applied after MEM analysis (Fig. 6.3). In this procedure, structure factors... 

In the early discussions of hybrid orbitals4,5 it was pointed out that the maximum strength (the maximum value in the bond direction) of a bond orbital formed from completed subshells of orbitals is associated with cylindrical symmetry of the orbital. In order to simplify the analysis of spd hybridization Hultgren5 decided to discuss only orbitals with cylindrical symmetry. He pointed out that no more than three d orbitals with cylindrical symmetry can be formed in a set of five d orbitals, and that each of these three is equivalent to the function d2 (see Table 1), except in orientation. 

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