Allowedness and Forbiddenness

It is clear from the two examples just given that all of the mechanistic information obtainable from an analysis in local symmetry can be deduced from correlation or correspondence diagrams formulated in the global symmetry of the reactant and product. As we will see in the following sections, the converse is not true the arbitrary separation of a molecular system into moieties with different local symmetries can be misleading. 

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The real breakthrough in recognizing the role that symmetry plays in determining the course of chemical reactions has occurred only recently, mainly through the activities of Woodward and Hoffmann [5, 6], Fukui [7, 8], Bader [9, 10], Pearson [11], Halevi [12, 13], and others. The main idea in their work is that symmetry phenomena may play as important a role in chemical reactions as they do in the construction of molecular orbitals or in molecular spectroscopy. It is even possible to make certain symmetry based selection rules for the allowedness and forbiddenness of a chemical reaction, just as is done for spectroscopic transitions. 

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. 

The allowedness and forbiddenness of a pericyclic reaction toward heat or light depends on this symmetry property. Usually two types of element of symmetry. 

The symmetries of the initial and the final wave functions and of the electromagnetic radiation operator determine the allowedness or forbiddenness of an electronic transition. The transition moment integrand must be totally symmetric for an allowed transition such that Mmn V0. 

An approach very closely related to that of Woodward and Hoffmann is the so-called Hiickel-Mobius approach 35> based on the rule An +2 electron systems prefer Hiickel geometries and An electron systems prefer Mobius geometries 36>. When no symmetry exists and there is no cyclic orbital array the allowedness or forbiddenness of a reaction can be determined by following the form of the MO s during the reaction 37>. A detailed quantum mechanical study of the stereochemistry of thermal and photo cyclo-addition reactions has been reported38), and a quantum mechanical discussion of the applicability of the Woodward-Hoffmann rules can be found in a paper by George and Ross 39>. 

We saw earlier that the probability of electric dipole absorption is related to the transition dipole moment. However, there are a variety of terms commonly used to describe the strength or probability of absorption. The allowedness or forbiddenness of the transition, and oscillator strength, /, are useful ideas where the relative, rather than absolute value, of the strength of coupling is required. These terms are factors used to describe how likely absorption is by reference to the ideal oscillator of a free electron where the transition is fully allowed and both the allowedness and oscillator strength are unity. 

This quantity was computed by De Proft et al. along the initial stages of the model reaction coordinate of a series of allowed and forbidden pericyclic reactions the sign of this quantity was shown to predict the allowedness of the reaction in agreement with the famous Woodward-Hoffmann rules for... 

The choice of phase indication in the molecular orbital is arbitrary and it is equally valid to choose to rotate together the unshaded orbitals in Equation 5.14, that is, 90° clockwise rotation at C-2 paired with 90° counterclockwise rotationatC-6. Both choices are equally valid for consideration of allowedness and both indicate disrotatory motion, but each may lead to different stereoisomeric products. Two allowed motions should be considered in all pericyclic reactions. Which of the two disrotatory motions occurs will be determined in most cases by steric or electronic effects among the substituents, or both may occur. Conrotation, in which both orbitals rotate in the same direction, is forbidden for this reaction because it leads to antibonding overlap at one end. 

Infrared spectroscopy is not as inherently informative with regard to metal interactions in highly symmetrical metal-metal bound dimers as is Raman spectroscopy, since the totally symmetric metal-metal stretch is a forbidden absorption in the infrared experiment. Oldham and Ketteringham have prepared mixed-halide dimers of the type Re2ClxBr 2xto lower the symmetry and hence introduce some infrared allowedness into the Re-Re stretching mode (206). Indeed, the appearance of a medium-intensity band at 274 cm 1 in the infrared spectrum of the mixed-halo species was considered to be the result of absorption by the metal—metal stretching vibration, which was also observed in the Raman spectrum at 274 cm ". ... 

According to Zimmermann [101] and Dewar [102], the allowedness of a concerted pericyclic reaction can be predicted in the following way A cyclic array of orbitals belongs to the Hiickel system if it has zero or an even-number phase inversions. For such a system, a transition state with An+ 2 electrons will be thermally allowed due to aromaticity, while the transition state with An electrons will be thermally forbidden due to antiaromaticity. 

An important consequence of the pseudopericyclic mechanism is that the planar (or nearly planar) transition states preclude orbital overlap between the a- and Jt-orbitals. This implies that all pseudopericyclic reactions are allowed. Therefore, Jt-electron count, which dictates whether a pericyclic reaction will be allowed or forbidden, disrotatory, or conrotatory, is inconsequential when it comes to pseudopericyclic reactions. Bimey demonstrated this allowedness for all pseudopericyclic reactions in the study of the electrocyclic reactions 4.11-4.14. 

Both of these dienes are conformationally flexible as regards the adoption of an s-cis conformation, but the former apparently has a somewhat higher s-cis content and might therefore be expected to preferentially adopt the dienic role. However, the product corresponds to the use of 2,3-dimethyl-l,3-butadiene in the dienic role. Since this latter diene is by far the more difficult to ionize of the two dienes, the observed reaction must be of the allowed [4-1-1] type. The possibility that this empirically observed sense of role selectivity has its origin in orbital symmetry allowedness/forbiddenness was tested in the maimer shown in Scheme 25. 

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