Chemical reactions symmetry-allowed

Orbital symmetry rules for predicting thermally and photo-chemically driven symmetry-allowed and symmetry-forbidden concerted reactions. 

Let us now examine the Diels-Alder cycloaddition from a molecular orbital perspective Chemical experience such as the observation that the substituents that increase the reac tivity of a dienophile tend to be those that attract electrons suggests that electrons flow from the diene to the dienophile during the reaction Thus the orbitals to be considered are the HOMO of the diene and the LUMO of the dienophile As shown m Figure 10 11 for the case of ethylene and 1 3 butadiene the symmetry properties of the HOMO of the diene and the LUMO of the dienophile permit bond formation between the ends of the diene system and the two carbons of the dienophile double bond because the necessary orbitals overlap m phase with each other Cycloaddition of a diene and an alkene is said to be a symmetry allowed reaction... 

The chemical reactions through cyclic transition states are controlled by the symmetry of the frontier orbitals [11]. At the symmetrical (Cs) six-membered ring transition state of Diels-Alder reaction between butadiene and ethylene, the HOMO of butadiene and the LUMO of ethylene (Scheme 18) are antisymmetric with respect to the reflection in the mirror plane (Scheme 24). The symmetry allows the frontier orbitals to have the same signs of the overlap integrals between the p-or-bital components at both reaction sites. The simultaneous interactions at the both sites promotes the frontier orbital interaction more than the interaction at one site of an acyclic transition state. This is also the case with interaction between the HOMO of ethylene and the LUMO of butadiene. The Diels-Alder reactions occur through the cyclic transition states in a concerted and stereospecific manner with retention of configuration of the reactants. 

A pericyclic reaction is allowed if orbital symmetry is conserved. In such reactions there is conversion of the ground (electronic) state of reactant into the ground state of the product. Such reactions are said to be thermally allowed, or there is the conversion of the first excited state of the reactant into the first excited state of the product. There are photo-chemically allowed reactions. 

Symmetry has for many years played a vital role in the elucidation of molecular structure although apart from some special situations it was not thought to have a dominant influence on the structure or chemical properties of molecules. In recent years however it has played a large part in the interpretation of many organic reactions through the work of Woodward and Hoffman, and the concept of symmetry allowed or forbidden reaction is now an important part of mechanistic organic chemistry. 

Everything that counts in chemistry is related to the electronic structure of atoms and molecules. The formation of molecules from atoms, their behavior and reactivity all depend on the electronic structure. What is the role of symmetry in all this In various aspects of the electronic structure, symmetry can tell us a good deal why certain bonds can form and others cannot, why certain electronic transitions are allowed and others are not, and why certain chemical reactions occur and others do not. Our discussion of these points is based primarily on some monographs listed in References [2-8],... 

The statement a chemical reaction is symmetry allowed or symmetry forbidden, should not be taken literally. When a reaction is symmetry allowed, it means that it has a low activation energy. This makes it possible for the given reaction to occur, though it does not mean that it always will. There are other factors which can impose a substantial activation barrier. Such factors may be steric repulsions, difficulties in approach, and unfavorable relative energies of orbitals. Similarly, symmetry forbidden means that the reaction, as a concerted one, would have a high activation barrier. However, various factors may make the reaction still possible for example, it may happen as a stepwise reaction through intermediates. In this case, of course, it is no longer a concerted reaction. 

Possible Role of BrCOOH. The possibility that the nearby Br atom plays a role chemically through an interaction involving all species seems reasonable, but at this point is speculative. Since the photolysis of HBr involves n—a electronic excitation, the biradical HBr can interact with the CO2 n orbitals to form bromoformic acid in a symmetry-allowed, concerted way. This can result in a short-lived, highly excited bromoformic acid intermediate, as shown schematically in Figure 30. The term bromoformic acid is used here to indicate an electronic interaction that may assist the overall chemical transformation leading to OH. The nuclei are initially very far from their BrCOOH equilibrium positions, and may even avoid the equilibrium structure completely in the reaction. 

In chemical reactions, a Lewis base HOMO (donor) must combine with a Lewis acid LUMO (acceptor) with electron density flowing from the HOMO to the LUMO. The orbitals must have the same symmetry with respect to the bond axis as above so that they can overlap in some way (linear, angular, etc.) according to the principles of MOT as described by Pearson (1976) (see also Appendix I). The major principles to remember are listed below. If all of these criteria are met, then a reaction is termed symmetry-allowed ... 

Symmetry and stability analysis. The semi-empirical unrestricted Hartree-Fock (UHF) method was used for symmetry and stability analysis of chemical reactions at early stage of our theoretical studies.1,2 The BS MOs for CT diradicals are also expanded in terms of composite donor and acceptor MOs to obtain the Mulliken CT theoretical explanations of their electronic structures. Instability in chemical bonds followed by the BS ab initio calculations is one of the useful approaches for elucidating electronic structures of active reaction intermediates and transition structures.2 The concept is also useful to characterize chemical reaction mechanisms in combination with the Woodward-Hoffman (WH) orbital symmetry criterion,3 as illustrated in Figure 1. According to the Woodward-Hoffmann rule,3 there are two types of organic reactions orbital-symmetry allowed and forbidden. On the other hand, the orbital instability condition is the other criterion for distinguishing between nonradical and diradical cases.2 The combination of the two criteria provides four different cases (i) allowed nonradical (AN), (ii) allowed radical (AR), (iii) forbidden nonradical (FN), and (iv) forbidden radical (FR). The charge and spin density populations obtained by the ab initio BS MO calculations are responsible for the above classifications as shown in Fig. 1. 

Hence, from the standpoint of invariance, any chemical reaction including polymerization is characterized by a set of observables (e.g., the elements of symmetry with operators commuting with the Hamiltonian of the reaction) A. The processes during which all the combination of properties of the reacting system (formally characterized by a set of eigenvalues a ) remains invariant are allowed in the sense of symmetry. This is the nature of both physical and chemical kinetic selection rules including the Woodward-Hoffmann principle. Hence, the specific feature of all selection rules is the fact that they allow much less than forbid . In other words, each of them exhibits a kind of veto right on the occurrence of chemical reactions. At the same time, the processes allowed with respect to symmetry may be forbidden by thermodynamic or steric factors. 

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