~ e i - w e iShen' California State University LOS Angeles, 90032
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I
The realization of the importance of orbital symmetry to the feasibility of concerted chemical reactions must be considered one giant breakthrough of the fascinating developments in organic chemistry in the 1960's. The definitive rules developed by Woodward and Hoffmann (I) based on the cooservati~nof orbital symmetry are of great interest to organic chemists for they not only explain the ljresently known reactions, but also show great predictive power on the hitherto unstudied reactions. T o predict whether a chemical reaction is symmetry allowed or disallowed, one requires a knowledge of symmetry properties of the molecular orbitals of the reactants and products, and also their relative energies to construct a correlation diagram (1, 2). For complicatbd systems, i t requires a considerable familiarity of extended Hiickel calculation to assert the relative energies of the MO's. Based on the Huckel-Mobius concent (vide infra). Zimmerman has advanced another approach for p i e d k i n g allowedness and disallowedness of a concerted reaction (3). (Dewar has arrived a t a similar conclusion by his molecular orbital theoretical approach ( 4 ) . ) The simplicity of applying this concept on concerted reactions prompts us to introduce it into the undergraduate cirriculum in organic chemistry. Theoretical Considerations Hiickel's rule (5) tells us that if there are 4n + 2 electrons (where n is an integer) in a cyclic polyene, this compound will have aromatic, or closed shell, stability. On the other hand, systems which have 4n electrons are said to be antiaromatic and to be very unstable. This generalization regarding stability seems to hold quite well (6). In 1964, Heilbronner (7) showed that if one twisted the cyclic oolvene once to form the so-called "Mobius strip,"2 the system with 4n electrons would have aromatic stability, whereas those with 4n + 2 electrons would be antiaromatic. With this idea in mind, let us examine a cyclic array of basis set p-orbitals (i.e., a collection of p-orbitals prior to MO calculation) such as Figure 1. It is obvious to note that there is no sign inversion3 (positive-minus overlap) among the neighboring p-orbitals. In the Mobius system (Fig. 2), however, there is one sign inversion. Thus, it can be generalized and shown that a cyclic array of orbitals with odd number of sign inversions belongs to the Mobius system, and those with zero or even number sign inversions belongs to the Huckel system. Zimmerman applied this concept to cyclic transition states in concerted reactions. Thus. a Huckel tvoe transition state with 4n 2 electrons should be a th&ally allowed (energetically favorable) Drocess due to the aromaticitv. and those with 4n electrons' should he antiaromatic, and thermally disal-
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'Address correspondence to US. Borax Research Carp., h a heim, Calif. 92801. 2Mbhius Strip: A continuous, one sided surface farmed by twisting one end of a rectangular strip thmugh 180" about the longitudinal axis of the strip and attaching this end to the other, named after August Ferdinand Mobius, German mathematician (1790-1868). 3Dewar called the positive negative overlap as "phase dislocation," and the Mobius system as "anti-Hockel systems-see ref. (4).
'Far definitionof these symbols see ref. (I), p. 72 and ref. (2c) 238
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Journal of Chemical Education
KkkckeI-M*dbh~Concept in Concerted ~ e a c t i o k
Figure 1. Huckel system. For convenience. wb choose signs so that ail neighboring p-orbitals have same sign above (and below) the nodal plane, i.e.. overlap in phase.
Figure 2. Mobiussystem. Note thesign inversion in the front
Rules for Aromaticity and Antiaromaticity
No.of Sign Inversion
System
Odd Even or Zero
Mbhius Hfickel
Ammatic"
Antiaromatie*
4n
4n+2
4n
+2
4n
'Thermally allowed process. Photolytically allowed process. lowed. For Mobius type transition states, those with 4n electrons should be thermally allowed, and those with 4n 2 electrons thermally disallowed. These rules for predicting the allowedness of a concerted pericyclic reaction 'are summarized in the table. The above discussion is limited to ground state thermal reactions. For concerted photochemical reactions, the rules should be exactly opposite to those corresponding to thermal ones (8).
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Examples Cycloaddition and Cycloreversion Reactions Let us first see how to apply this concept to the dimerization of ethylene. The basis set orbitals of the two ethylenes are shown on the left in eqn. (1). The cyclic array of orbitals as shown by the dotted line in the transition state have zero sign inversion; thus, it belongs to the Huckel system. However, there are only 4n
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02$ 62s] reaction eqn. (5) (121, are also expected and found to be thermally allowed due to the aromatic stahilization of the transition state.
positive sign
0 Negative
sign
NO. or eign i n v ~ l s i o n= 0 Hiickel System 4" + 2 C 4 d e c t r o n s Thermally d i d l o v e d
= 4 electrons in these orbitals. So, one may conclude that this [x2s a2sI3 dimerization is thermally forbidden, Instead, it is a photochemically allowed reaction. One example (9) of such a photochemically allowed process is shown in eqn. (2).
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No. or sign in" HGckel System
0
=
I n + 2 = 6
(4)
Thwmally allowed
+ TCNE
A
aC (5)
CN
It is very important to note that the relative orientation of the positive and negative lobes in the reactants are irrelevant. The same conclusion can be reached by having the other relative orientation as shown in eqn. (3).
No. Of sign i n " = ? Hdekel Syatrm 4 " + 1 = B
Thermally allowed
No. or sign in". = 2 HGckel system 4"+2%
