The stereochemistry of reactions can also be treated by permutation group theory for reactions that involve the transformation of an sp carbon atom center into an sp carbon atom center, as in additions to C=C bonds, in elimination reactions, or in eIcctrocycHc reactions such as the one shown in Figure 3-21. Details have been published 3l]. [Pg.199]

The stereochemistry of reactions can be treated by means of permutation group theory. [Pg.200]

A. Cayley was also the creator of the matrix theory he made an essential contribution to the development of the group theory, i.e. those branches of mathematics which were later extensively used in physics and mathematics. Moreover, Cayley was the first to indicate the relationship between the point groups of symmetry and the permutation groups (see Chapter 6). [Pg.128]

Figure 3-22. The treatment of the stereochemistry of an 5,j2 reaction by permutation group theory, |

Further arguments of Menshutkin can be easily interpreted in terms of the permutation group theory. Here the number of cycles in the permutation (40) is equal to the number of disubstituted derivatives, i.e. 3 (ortho-, meta-, and para-), and the digits combined in one cycle indicate the numbers of equivalent positions in a monosubstituted derivative. [Pg.141]

Figure 3-23. The treatment ofthe stereochemistry ofa further S,y2 reaction by permutation group theory. |

The stereochemistry of reactions has to be handled in any detailed modeling of chemical reactions. Section 2.7 showed how permutation group theory can be used to represent the stereochemistry of molecular structures. We will now extend this approach to handle the stereochemistry of reactions also [31]. [Pg.197]

Thus, valuable information concerning the possible nature of permutation isomerism reactions was obtained only by the methods of the graph theory and group theory, without analysis of electronic and nuclear densities. [Pg.137]

The use of the conventional spin formulation in conjunction with a spin-free Hamiltonian HSF merely assures symmetry adaptation to a given spin-free permutational symmetry [Asp] without recourse to group theory. In fact, one may symmetry adapt to a given spin-free permutational symmetry without recourse to spin. This is the motivation behind the Spin-Free Quantum Chemistry series.107-116 In this spin-free formulation one uses a spatial electronic ket which is symmetry adapted to a given spin-free permutational symmetry by the application of an appropriate projector. The Pauli-allowed partitions are given by eq. (2-12) and the correspondence with spin by eqs. (2-14) and (2-15). Finally, since in this formulation [Asp] is the only type of permutational symmetry involved, we suppress the superscript SF on [Asp], [Pg.8]

The transformed (permuted) state is necessarily in the same polyad as the nontransformed one. This means that permutation operators act by changing the order of the basis states in a given polyad. This is very important because it allows one to obtain the transformed eigenvector explicitly (i.e., the linear combination of local modes) in terms of a simple linear (permutation) transformation. By applying the well-known formula of discrete group theory for the calculation of the character, we can schematically write [Pg.643]

For the two-spin system the only symmetry operation is the interchange of the two nuclei, and the correct linear combinations, and could be constructed by inspection. When three or more symmetrically equivalent nuclei are present, the symmetry operations consist of various permutations of the nuclei. The correct symmetrized functions can be determined systematically only by application of results from group theory. We shall not present the details of this procedure. [Pg.163]

© 2019 chempedia.info