Conservation of orbital symmetry

According to orbital symmetry theory, in any concerted process the reactant orbitals must be transformed into product orbitals of the same symmetry. Thus, the symmetry of the orbitals of the reactants must be conserved as they are transformed into the orbitals of the product. 

The original explanation of Woodward and Hoffmann involved construction of an orbital correlation diagram for the reaction under consideration, and then carrying out the reaction in such a manner so that the symmetries of the reactant and product orbitals matched exactly. If the correlation diagram indicates that the reaction may occur without encountering a symmetry-imposed barrier, it is termed symmetry-allowed. If a symmetry is present, the reaction is designated symmetry-forbidden. 

Before we move on, it is worthwhile to clarify the implications of the words allowed and forbidden. An allowed reaction is simply one with a low activation energy relative to some other pathway, while a forbidden reaction is a process for which there is a significant activation energy. 

The term orbital correlation diagram describes the theoretical device that Woodward and Hoffmann developed to interpret pericyclic reactions. The Woodward-Hoffmann method for correlating reactant orbitals with product orbitals includes the following  

Select an appropriate symmetry element, e.g. mirror plane (m) or rotation axis (C2), which passes through at least one bond that is breaking or forming in order to give useful information. 

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The Woodward-Hoffmann method [52], which assumes conservation of orbital symmetry, is another variant of the same idea. In it, the emphasis is put on the symmetries of molecular orbitals. Longuet-Higgins and Abramson [53] noted the necessity of state-to-state correlation, rather than the orbital correlation, which is not rigorously justified (see also, [30,44]). However, the orbital symmetry conservation rules appear to be very useful for most themial reactions. 

Conservation of orbital symmetry is a general principle that requires orbitals of the same phase (sign) to match up in a chemical reaction. For example, if terminal orbitals are to combine with one another in a cyclixation reaction as in pattern. A, they must rotate in the same dii ection (conrotatory ovei lap). but if they combine according to pattern H. they must rotate in opposite directions (disrotatory). In each case, rotation takes place so that overlap is between lobes of the it orbitals that are of the same sign. 

Woodward, R.B. and Hoffmann, R. Conservation of Orbital Symmetry Verlag Chemie, Weinheim, ERG, 1970. 

R. B. Woodward and R. Hotfmai Ji, The Conservation of Orbital Symmetry, Verlag Chemie, Weinheim, 1970. 

Cycloaddition involves the combination of two molecules in such a way that a new ring is formed. The principles of conservation of orbital symmetry also apply to concerted cycloaddition reactions and to the reverse, concerted fragmentation of one molecule into two or more smaller components (cycloreversion). The most important cycloaddition reaction from the point of view of synthesis is the Diels-Alder reaction. This reaction has been the object of extensive theoretical and mechanistic study, as well as synthetic application. The Diels-Alder reaction is the addition of an alkene to a diene to form a cyclohexene. It is called a [47t + 27c]-cycloaddition reaction because four tc electrons from the diene and the two n electrons from the alkene (which is called the dienophile) are directly involved in the bonding change. For most systems, the reactivity pattern, regioselectivity, and stereoselectivity are consistent with describing the reaction as a concerted process. In particular, the reaction is a stereospecific syn (suprafacial) addition with respect to both the alkene and the diene. This stereospecificity has been demonstrated with many substituted dienes and alkenes and also holds for the simplest possible example of the reaction, that of ethylene with butadiene ... 

Prior to the delineation of the concept of conservation of orbital symmetry by Woodward and Hoffmann, Bachmann and Deno reported that all Diels-Alder reactions... 

See, e.g. (a) Woodward, R. B. Hoffmann, R. The Conservation of Orbital Symmetry, Verlag Chemie 1970 (b) Flfm-ING, L. Frontier Orbitals and Organic Chemical Reactions, John Wiley and Sons, London, 1977. 

An explanation for the finding that concerted [4 -I- 2] cycloadditions take place thermally, while concerted [2 + 2] cycloadditions occur under photochemical conditions, is given through the principle of conservation of orbital symmetry. According to the Woodw ard-Hofmann rules derived thereof, a concerted, pericyclic [4 -I- 2] cycloaddition reaction from the ground state is symmetry-allowed. 

The names for these mechanisms vary throughout the literature. For example, the Sgi mechanism has also been called the Sp2, the Se2 (closed), and the Se2 (cyclic) mechanism. The original designations, Se 1, Se2, and so on, were devised by the Hughes-Ingold school. It has been contended that the SeI mechanism violates the principle of conservation of orbital symmetry (p. 1068), and that the Se2 (back) mechanism partially violates it Slack, D.A. Baird, M.C. J. Am. Chem. Soc., 1976, 98, 5539. 

It must be emphasized once again that the rules apply only to cycloaddition reactions that take place by cyclic mechanisms, that is, where two s bonds are formed (or broken) at about the same time. The rule does not apply to cases where one bond is clearly formed (or broken) before the other. It must further be emphasized that the fact that the thermal Diels-Alder reaction (mechanism a) is allowed by the principle of conservation of orbital symmetry does not constitute proof that any given Diels-Alder reaction proceeds by this mechanism. The principle merely says the mechanism is allowed, not that it must go by this pathway. However, the principle does say that thermal 2 + 2 cycloadditions in which the molecules assume a face-to-face geometry cannot take place by a cyclic mechanism because their activation energies would be too high (however, see below). As we shall see (15-49), such reactions largely occur by two-step mechanisms. Similarly. 2 + 4 photochemical cycloadditions are also known, but the fact that they are not stereospecific indicates that they also take place by the two-step diradical mechanism (mechanism... 

In 15-58, we used the principle of conservation of orbital symmetry to explain why certain reactions take place readily and others do not. The orbital symmetry principle can also explain why certain molecules are stable though highly strained. For example, quadricyclane and hexamethylprismane are thermodynamically much less stable (because much more strained) than their corresponding isomeric dienes, norbomadiene and hexamethylbicyclo[2.2.0]hexadiene (108). Yet the... 

Woodward, R.B. Hoffmann, R. The Conservation of Orbital Symmetry Academic Press NY, 1970 p. 114. 

Hoffmann R, Woodward RB (1970) The conservation of orbital symmetry, Verlag Chimie/ Academic, New York... 

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