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Encyclopedia of Physical Science and Technology EN012G-576 July 28, 2001 12:44

Physical Organic Chemistry 237

˚
gas-phase ion was computed to be 2.38 A. It does not cle of atomic orbitals, each overlapping with two neigh-
change if the ion is embedded in a continuum whose di- bors. Electrons are delocalized over those cycles since
electric constant is equal to that of chloroform or water. they are in bonds that are forming and breaking. In 130
An alternative approach to solvation is to simulate the there are six delocalized electrons, and in 131 there are
motions of the ion and of discrete solvent molecules, as four. Therefore transition state 130 is aromatic and 131
governed by their forces of interaction. Interaction with is antiaromatic. These reflect stabilization or destabiliza-
chloroform molecules does not change d O O , but if the ion tion universally associated with cyclic systems containing
also interacts with K , it becomes asymmetric. In water 4n + 2(n = 0, 1, 2,...)or4n (n = 1, 2,...) delocalized
+
˚
d O O increases to 2.46 A and the structure again becomes electrons. Accordingly, 130 represents a low-energy tran-
asymmetric because of the entropy associated with hy- sition state, corresponding to a fast reaction, whereas 131
drogen bonding by water to the ion. These results are in is of high energy and corresponds to a slow reaction. The
agreement with some experimental data. conclusion that 125 can undergo this reaction whereas 127
cannot is a distinction not accessible from resonance the-
O H ··· O O ··· H O. (49) ory. It does follow from molecular orbital theory but it re-

quires a generalization to transition states of the concept of
aromaticity.

B. Pericyclic Reactions
The Woodward–Hoffmann rules are a triumph of the ap-
plication of molecular orbital theory to reactivity. They
are concerned with pericyclic reactions, reactions where There are two alternatives whereby 127 can react. To
electrons reorganize around a cycle of nuclei, with simul- account for these it is necessary to generalize aromaticity
taneous bond breaking and bond making, as in 67. There even further, to excited states and to a different topol-
are three classes of pericyclic reactions: (1) electrocyclic ogy. According to molecular orbital calculations, the ex-
reactions, where a new single bond is made across the cited electronic states of cyclic systems containing 4n
ends of a pi system, as well as the reverse of such a reac- delocalized electrons are stabilized (relative to acyclic
tion, (2) sigmatropic rearrangements, where a group mi- comparisons), whereas those with 4n + 2 are destabi-
grates across a pi system, and (3) cycloaddition reactions, lized. Thus aromaticity and antiaromaticity reverse in an
where one pi system adds across another, as well as the excited state. For example, the excited electronic state
reverse, a cycloreversion reaction. The full treatment of of transition state 131 becomes stabilized, and 127 can
the Woodward–Hoffmann rules involves consideration of be transformed rapidly into 128 under photochemical
the symmetry of the molecular orbitals, but there is a sim- conditions.
pler approach that that focuses on aromaticity of transition
states.
The electrocyclizations of 1,3,5-hexatriene (125)to
1,3-cyclohexadiene (126) and of 1,3-butadiene (127)to
cyclobutene (128) offer a revealing comparison. From The alternative topology arises by rotating the outer-
the initially planar triene (125), rotation about the out- most pi bonds of 127 in the same direction. This is called
ermost pi bonds allows overlap between the p atomic or- conrotatory motion, in distinction to the previous disro-
bitals on carbons 1 and 6, to form 129. If those carbons tatory motion, where the bonds rotated in opposite direc-
3
also rehybridize toward sp , the transition state (130)is tions. This now leads to transition state 132, where the top
reached. Eventually those carbons form a sigma bond and lobe of the rehybridizing orbital on carbon 1 overlaps with
the product (126) results. Similarly, the planar butadiene the bottom lobe of the orbital on carbon 4. It would seem as
(127) rotates and rehybridizes to create transition state though this is an antibonding interaction because a nodal
131, which proceeds to form the sigma bond of the prod- surface is created between these atomic orbitals. However,
uct (128). Unlike the acyclic reactants or the products, according to molecular orbital calculations, this leads to
where the sigma bonds do not overlap with the pi or- a stabilization. Indeed, this is a general result for cyclic
bitals, the transition states may be characterized by a cy- systems containing 4n delocalized electrons but subject to