D. J. Sardella Boston College Chestnut Hill. Massachusetts 02167
I
Where Does Resonance Energy Come From?
II
A nonmathematical approach to the theory of aromaticity
The contrast hetween the chemical and o h w i d oro~erties of aromatic systems and those ofconjugatkdicyc~iEpdlyenea is so striking that it forms one of the ereat natural divisions of organic &emistry. Contemporary organic texts invariably devote a chapter or a lengthy section to a discussion of aromaticity which typically inciudes a review of chemical, thermochemical, and structural data intended to highlight the apparently anomalous properties of aromatic systems, followed hy a description of the resonance and molecular orbital formuliltions for henzene, and often a statement of the Huckel 4n 2 rule, along with illustrations of its applicability. I have long feltthat while the discussions of experimental data and the operational definition of aromaticity (the what) are generally presented clearly, the theoretical discussions shed virtually no light on the reason for the enhanced stabilities of aromatic svstems (the whv). In fact. the onlvooint which both models, &presented in host texts, are cap&e of ex~lainina - is bond leneth - euualization in aromatic svstems (a feature of secondary importance). However, in my view, neither model conveys any energy information. I t is not clear to a student unfamiliar with the variational theorem why molecules for which two or more canonical structures can be drawn should he more stable than tbcae for which only one can he drawn.' Neither is it clear why a cyclic array of overlapping p-orbitals should lead to an especially stable (or, in the case of cyclobutadiene, an especially unstable) system. Both approaches amount, as f a r as students' understanding is concerned, to renaming aromaticity. The genesis of the4n t 2 rule is usuallv totallv unclear.and students oftenemolov it likea magic formula, devoid of understanding. In an attemot to confront the central issue of whv aromatic systems are aromatic, a t a level which students with no quantum mechanical background and with only basic verbal ideas of orbitals and bonds can appreciate, I have used the followine which is essentiallv a verbal a~olication - aooroacb, .. .. of perturbational molecular orbital theory.2 It is assumed that the student is familiar with the idea that molecular orbitals are formed by combining atomic orbitals, and that the number of molecular orbitals euuals the number of atomic orbitals from which they are consiructed. Furthermore, the student is assumed to know that combination of two AO's in phase (i.e., additively) leads u)formation of a hooding MO which is lower in energy than either of the AO's, and that combination out of phase (subtractively) gives an antibonding MO higher in energy than either AO. The discussion of aromaticitv oroceeds as follows. lmaeine the MO's of benzene t o be formed from those of 1,3,5-hkatriene by simply allowing thep-orbitals on carbons 1and 6 to overlap. What happens to the energy of the system? The students are told that for oolvenes 1) the MO's are svmmetrically disposed about the' z&o of energy3 (the energy of an electron in a 20 AO): .. 2). that the lowest enerev MO is bondine everywhere (i.e., no out-of-phase relationships, hence sym-
metrical about its midpoint): and 3) that the MO symmetries alternate with increasing energy (an analogy can be made t o the vibrational modes of a string with clamped ends, or by the rule that the number of modes in a wavefunction increases with increasing energy). If the ends of a symmetrical orbital are ioined. a new bonding interaction is added. and the orbital's energy falls, whereas joining the ends of an antisymmetric MO introduces an antibonding interaction which raises
-
+
Figure I. Orbital miation diagram fw the process 1.3.5-hexahiene zene.
-
be*
..
--
Figwe 2. Orbital conelation diagram tor t k process pentadiene anion dopentadieneanion.
-
cy-
-
Or, considering the instability of cyclobutadiene, for which two canonical structurescan be written, even when this will be true. Wewar, M. J. S.. "The Molecular Orbital Theory of Organic Chemistrv." McCraw-Hill. New York. 1969.. Cham . 6. Ref. (i), p. 200. 'Coulson, C. A., "Valence," 2nd Ed., Oxford University Press, London, 1961, pp. 12-85.
Figure 3. Orbital -elation
diagram for lbprocess butadiene
--+
cyciobuie-
dim.
Volume 54, Number 4, April 1977 1 217
its enerw. If the number of electrons in symmetrical MO's exceedsthat in antisymmetric onesvcycl
