14
Chemistry 1981
Fig. 3. The mode of interaction between orbitals of two molecules
case, where it was controlled by the electrostatic interaction of charges. This
classification was conveniently used by many people. In this context the review
articles of Herndon
29
and of Hudson
30
appeared to be very useful. The names
of Coulson
4
and Dewar
31
should also be noted here as those who contributed
to the development of reactivity theories.
Returning to the subject again, let us assume that two molecules approach
each other and orbital overlapping takes place. The perturbation theory
32
of
this sort of interaction indicates that, the larger the orbital overlapping is and
the smaller the level separation of two overlapping orbitals is, the larger is the
contribution of the orbital pair to the stabilization of an interacting system.
Accordingly, at least at the beginning, a reaction will proceed with a mutual
nuclear configuration which is most favourable for the HOMO-LUMO over-
lapping.
Now let us suppose an electron flow from the HOMO of molecule I to the
LUMO of molecule II. In each molecule the bonds between the reaction
centre - the place at which the orbitals overlap with those of the other mole-
cule - and the remaining part of the molecule are weakened. On this occasion,
in molecule I the bonds which are bonding in HOMO are weakened and those
K. Fukui
15
antibonding in HOMO are strengthened, while in molecule II the bonds which
are antibonding in LUMO are weakened and those bonding in LUMO are
strengthened. Consequently, the HOMO of molecule I particularly destabi-
lizes as compared with the other occupied orbitals, and the LUMO of molecule
II discriminatively stabilizes among unoccupied orbitals, so that the HOMO-
LUMO level separation between the two molecules is decreased. Such a
circumstance is clearly understandable in Fig. 3.
The following tendency is further stressed. When the bond weakenings
specified above have arisen, the HOMO and the LUMO tend to become more
localized at these weakened bonds in each molecule. Besides, the weakening of
the bonds between the reaction centre and the remaining part causes an
increase of the amplitudes of HOMO and LUMO at the reaction centres,
resulting in a larger overlapping of HOMO and LUMO.
33
Such a trend of the
characteristic change in the orbital pattern is made numerically certain by
actual calculations. The role of interaction between HOMO and LUMO turns
out in this way to become more and more important as the reaction proceeds.
A series of studies on chemical interactions were attempted in which the
interaction of reactants was divided into the Coulomb, the exchange, the
polarization, and the delocalization interactions, and their magnitude of contri-
bution to the interaction energy was quantitatively discussed
.32,34
The inter-
actions discussed by this method were the dimerization
35
and the addition to
ethylene
36
of methylene and the dimerization of BH
3
,
37
and also several
donor-acceptor interactions-BH
3
- N H
3
,
38
B H
3
- C O ,
39
N H
3
- H F ,
40
etc. The
method was applied also to reactions of radicals, such as the abstraction of a
methane hydrogen by methyl radical, the addition of methyl radical to ethyl-
ene
41
and recombinations, disproportionations, and self-reactions of two radi-
cals.
42
In these calculations, the configuration analysis proposed originally by
Baba
43
was also utilized conveniently. We could show numerically the mode of
increase of the electron delocalization from HOMO to LUMO along with the
proceeding of reaction, the increasing weight of contribution of such a delocali-
zation to the stabilization of the reacting system, the driving force of the
reaction in terms of orbital interactions, and so on.
The question “Why HOMO and LUMO solely determine the reaction
path?” was one which I very frequently received from the audiences in my
lectures given in the past in different places. The discussion so far made here is
thought to correspond, at least partly, to that answer. But one may not adhere
so strictly to the HOMO and LUMO. In one-centre reactions like substitu-
tions, which the orbital symmetry has nothing to do with, any occupied orbitals
which are very close to HOMO should properly be taken into account.
12
In
large paraffin molecules a number of HOMO’s (high-lying occupied MO’s),
and furthermore as will shortly be referred to later, in metal crystals, even
“HOMO-band” must be taken along the line of reactivity argument. If
HOMO or LUMO happens to be inadequate owing to its extension, the
symmetry, or the nodal property, the next orbital should be sought for. One of
the simplest examples of such an instance is the protonation of pyridine. In this
case, the nitrogen lone-pair orbital is not HOMO, but the addition of proton to