Chemistry Reference
In-Depth Information
outer electrons results in decrease of total number of the sextets
(Figs. 3(b)→3(c)). Energy difference between before and after the
pairing of the electrons on the zigzag edges should be smaller in
3-3
than
in
3-1
, since the pairing in
3-3
causes the destruction of two sextets;
leading to propensity of electrons to more localize in separated places in
3-3
.
8
For larger polyperiacenes of anthracene such as
3-5
and
3-7
, the
difference in the number of the sextet between the biradical and Kekulé
structures increase with increment of molecular size; three for
3-5
and
four for
3-7
(Fig. 4). More sextets in the biradical structures would result
in more dominant contribution of biradical electron configuration to the
ground state. Two unpaired electrons localize at the zigzag-edge regions
so as to gain Π-bonding energy in the inner pairs of electrons, as was
seen in Figs. 3(a)→3(b).
2.2.
Quantum chemical method
The singlet open-shell character was estimated using the index defined
by Yamaguchi
9
coupled to the symmetry-broken UBHandHLYP/6-31G*
calculation.
10
The degree of the singlet open-shell character,
Y
i
, can
be determined from the following equations:
Y
i
= 1 − 2
T
i
/ (1 +
T
i
2
),
T
i
= (
N
HOMO-i
-
N
LUMO+i
) / 2, where
N
HOMO-i
and
N
LUMO+i
represent natural
orbital occupation numbers of HOMO-i and LUMO+i, respectively.
The index
Y
0
which are determined from the HOMO-LUMO pair are
related to a Π-bond cleavage and vary continuously from zero to unity.
A perfect biradical molecule has
Y
0
of unity. Table 1 shows
Y
0
of
polyacenes and polyperiacenes. The series of polyperinathalene
2-B
,
which have been extensively studied by Müllen and co-workers,
11
has no
appreciable
Y
0
, although theoretical calculation for larger systems has
predicted a small HOMO-LUMO energy gap.
12
Actually even
2-7
shows
high stability. On the other hand, bisanthene
3-3
has a small but non-
negligible value of
Y
0
, suggesting that
3-3
is basically classified into a
closed-shell molecule with potential biradical character. High reactivity
toward oxygen of
3-3
supports this idea.
13
Larger homolog
3-5
and
3-7
give large values of
Y
0
, clearly indicating their appreciable biradical
character. It is noteworthy that apparent biradical character is recognized
