16
Chemistry 1981
the nitrogen lone-pair so as not to disturb the
π conjugation will evidently be
more advantageous than the addition to higher occupied
π orbitals which may
intercept the
π conjugation. Thus, the reason why proton dare not add to the
positions of large amplitude of
π HOMO in this case will easily be understood.
It is not completely satisfactory to dispose of a disagreement between the
HOMO-LUMO argument and the experimental fact formally as an exception to
the theory. A so-called exception does possess its own reason. To investigate
what the reason is will possibly yield a novel finding.
The HOMO-LUMO interaction argument was recently pointed out
44
to be
in an auxiliary sense useful for the interpretation of the sign of a reaction
constant and the scale of a substituent constant in the Hammett rule
45
which
has made an immeasurable contribution to the study of the substituent effect in
chemical reactivity. In the cyclic addition, like Diels-Alder reactions and 1,3-
dipolar additions, the relative easiness of occurrence of reactions, various
subsidiary effects, and interesting phenomena like regioselection and periselec-
tion were interpreted with considerable success simply by the knowledge of the
height of the energy level of HOMO and LUMO, the mode of their extension,
their nodal structure, etc.
46
- I defined these in a mass: the "orbital pattern".
Other topics that have been discussed in terms of HOMO-LUMO interac-
tions are thermal formation of excited states,
47
singlet-triplet selectivity,
48
the
chemical property of biradicals and excited molecules,
49
the interaction of the
central atom and ligands in transition metal complexes,
50
the interaction of
three or more orbitals
51
and so forth. Inagaki et al. included in the theory the
polarization effect in HOMO and LUMO due to the mixing in of other orbitals
and gave an elucidation for a number of organic chemical problems which were
not always easy to explain. The unique stereoselection in the transannular
cross-bond formation, the lone-pair effect, the d orbital effect, and the orbital
polarization effect due to substituents were the cases.
52
As was partly discussed above, the method of orbital interaction was applied
not only to the ground electronic state but to the excited states, giving an
explanation of the path of even complicated photochemical isomerizations.
13
21
In a majority of ca ses the HOMO and the LUMO of the ground-state
molecule were also found to be the essential orbitals. Even the ground-state
reaction of a strong electron acceptor (or donor) causes a mixing in of an
ionized electron configuration or an excited electron configuration in another
molecule. In consequence, a partial HOMO-HOMO or LUMO-LUMO inter-
action, which would be trivial if there were no influence of the acceptor (or
donor), becomes important in stabilizing the interacting system.*’
The problems so far discussed have been limited to chemical reactions.
However, the HOMO-LUMO interaction must come into relation also with
other chemical phenomena in almost the same mechanism - with the exception
of one different point that they usually do not bring about so remarkable a
change in the nuclear configuration as in the case of chemical reactions.
N
OW
let us examine the possibility of applying the theory to so-called “aromati-
city”- one of the simplest, but the hardest-to-interpret problems. There seem
to be few problems so annoying to theoreticians as the explanation of this
K. Fukui
17
chemically classical concept. I greatly appreciate the contribution of Dewar’s
theory
53, 54
based on a quantitative energy values argument. Here, however, I
want to give a quality comment through a totally different way of consider-
ation.
It is easily ascertained
55
in Fig. 4 that in benzene, naphthalene, phenan-
threne, etc., any virtual division of the molecule into two always produces the
parts in which their HOMO and LUMO overlap in-phase at the two junctions.
Fig. 4. The HOMO-LUMO phase relationship in virtual division of aromatic hydrocarbons.
(SOMO: a singly occupied MO of a radical)
18
Chemistry 1981
But these circumstances are not seen in anthracene which is usually looked
upon as one of the typical representatives of aromatic compounds. Hosoya
55
pointed out from the comparison with phenanthrene indicated in Fig. 4, that
the ring growth of type (II) was less stable than that of (I),
It is well known that anthracene occasionally exhibits a reactivity of olefin-like
additions.
In view of so-called Hückel’s (4n+2)-rule mentioned above, an anthracene
molecule has
14π electrons and fulfils the stability condition for “aromaticity.”
Actually, if one considers a molecule of anthracene with the two inside bonds
deleted,
it is really seen that the HOMO and the LUMO of the two parts overlap in an
in-phase manner at both of the junctions:
In this way, it is understood that the two bonds which were deleted above
exerted a certain unfavourable influence for aromaticity. Such an influence
bears a close resemblance to that of impurity scattering in the wave of a free
electron moving in a metal crystal.
This discussion seems to be a digression but, as a matter of fact, it relates to
the essential question as to how an electron in a molecule can delocalize. As will
be mentioned later, Anderson
56
solved the question how an electron in a