Chemistry Reference
In-Depth Information
number of nonbonding state
N
is given as the difference in the
n
N
−=
,
where the carbon sites belonging to a given subgroup (starred) are
directly bonded to the sites belonging to another subgroup (unstarred).
This implies that Kekulé molecules (Fig. 1(a)), in which
N
N
numbers of the starred (
N
) and unstarred (
) sites:
N
un
*
n
*
un
*
N
is always
equal to
u
N
, have no nonbonding state and are nonmagnetic. In contrast,
the triangle-shaped molecules consisting of 3, 6 and 10 benzene rings
have 1, 2 and 3 nonbonding states and are ferromagnetic with S=1/2, 1
and 3/2, respectively, since the electrons occupying these degenerate
nonbonding states at
E
F
obey the Hund rule with the parallel spin
arrangement as shown in Figs. 1(b)-(d).
It should be noted here that the nonbonding Π-electron states are
populated around the peripheral zigzag shaped region of the molecules as
illustrated in Fig. 1(e) for triangulene consisting of 6 benzene rings. This
indicates that the nonbonding Π-electron state is the small molecule
version of the edge state. Indeed, an extrapolation of the electronic state
to nano-sized graphene demonstrates the presence of the nonbonding
state when a nanographene sheet is zigzag edged, in contrast to the
absence of such a state in the armchair-edged sheet. Figure 2 presents the
spatial distribution of the HOMO level for armchair-edged and zigzag-
edged nanographene sheets.
7
The armchair-edged nanographene sheet
has a uniform distribution of the HOMO state. On the contrary, the
zigzag-edged nanographene sheet has a large local-density-of-states,
which is assigned to the edge state, around the zigzag edge region.
*
Fig. 2. The spatial distribution of the HOMO level in (a) armchair-edged and (b) zigzag-
edged nanographene sheets. The HOMO level is assigned to the edge state in the zigzag-
edged nanographene sheet. (Ref. 7)
