15 Molecular Theory of Graphene
265
The peculiarity of the graphene edges had been a topic for intense discussions
from the very beginning of the graphene science [51] when they were disclosed
by using the tight-binding band calculation within the Hückel approximation [52].
However, they have not been attributed to the effectively unpaired electrons and have
been discussed in the context of the graphene spin system peculiarity with respect
to the expected magnetic behavior of the sample. In this context, it is worthwhile
to refer to one more quote from the Hoffmann ‘informal reflection’ [1]: “There is a
special problem that theory has with unterminated structures—ribbons cut off on the
sides, polymers lacking ends. If passivation is not chosen as a strategy, then the radical lobes of the unterminated carbon atoms, or undercoordinated transition metals,
will generate states that are roughly in the middle energetically, above filled levels,
below empty levels in a typical molecule that has a substantial gap between filled
and unfilled levels. If such levels—states, the physicists call them—are not identified as “intruder” states, not really real, but arising from the artifact of termination,
they may be mistaken for real states in the band gap, important electronically. And
if electrons are placed in them, there is no end to the trouble one can get into. These
band gap states are, of course, the origin of the reactivity of the terminated but not
passivated point, line, or plane. But they have little to do with the fundamental electronic structure of the material”. Supporting the said above, depicted in Fig. 15.4a
presents the reactivity image of the graphene molecule. As seen in the figure, not
only edge, but basal-plane carbon atoms are chemically active, albeit with different efficacy. Important to note, that the reactivity is distributed over atoms rather
inhomogeneously. The recent atom-resolved graphene images convincingly witness
this inhomogeneity as can be seen in Figs. 15.4b and c. Therefore, the effectively
unpaired electrons of the sp 2 molecules are a physical reality and are assuming their
leading place in the molecular theory of graphene.
In the singlet state, the N DA values are identical to the atom free valences [13]
and thus exhibit the atomic chemical susceptibility (ACS) [55, 56]. The N DA distribution over atoms plots a ‘chemical portrait’ of the studied molecule, whose analysis allows for making the definite choice of the target atom with the highest N DA
value to be subjected to the chemical attack by an external addend. Therefore, we
have come to Answer 5 claiming that peculiarities of the graphene chemistry can be
exhibited at the quantitative level, much as this has been done for fullerenes [5].
Answer 5 Computational strategy of the chemical modification of graphene.
The typical chemical portrait of graphene fragment in Fig. 15.4a highlights edge
atoms as those with the highest chemical activities, besides rather irregular, while
exhibiting additionally the basal atoms ACS comparable with that one of fullerene
C 60 [28, 57]. This circumstance is the main consequence of the odd electron correlation in graphene in regard to its chemical modification. Ignoring the correlation has
resulted in a common conclusion about chemical inertness of the graphene atoms
with the only exclusion concerning the edge ones. Having this general indication
only, a computationist is still in the dark concerning the place of both the first and
265
The peculiarity of the graphene edges had been a topic for intense discussions
from the very beginning of the graphene science [51] when they were disclosed
by using the tight-binding band calculation within the Hückel approximation [52].
However, they have not been attributed to the effectively unpaired electrons and have
been discussed in the context of the graphene spin system peculiarity with respect
to the expected magnetic behavior of the sample. In this context, it is worthwhile
to refer to one more quote from the Hoffmann ‘informal reflection’ [1]: “There is a
special problem that theory has with unterminated structures—ribbons cut off on the
sides, polymers lacking ends. If passivation is not chosen as a strategy, then the radical lobes of the unterminated carbon atoms, or undercoordinated transition metals,
will generate states that are roughly in the middle energetically, above filled levels,
below empty levels in a typical molecule that has a substantial gap between filled
and unfilled levels. If such levels—states, the physicists call them—are not identified as “intruder” states, not really real, but arising from the artifact of termination,
they may be mistaken for real states in the band gap, important electronically. And
if electrons are placed in them, there is no end to the trouble one can get into. These
band gap states are, of course, the origin of the reactivity of the terminated but not
passivated point, line, or plane. But they have little to do with the fundamental electronic structure of the material”. Supporting the said above, depicted in Fig. 15.4a
presents the reactivity image of the graphene molecule. As seen in the figure, not
only edge, but basal-plane carbon atoms are chemically active, albeit with different efficacy. Important to note, that the reactivity is distributed over atoms rather
inhomogeneously. The recent atom-resolved graphene images convincingly witness
this inhomogeneity as can be seen in Figs. 15.4b and c. Therefore, the effectively
unpaired electrons of the sp 2 molecules are a physical reality and are assuming their
leading place in the molecular theory of graphene.
In the singlet state, the N DA values are identical to the atom free valences [13]
and thus exhibit the atomic chemical susceptibility (ACS) [55, 56]. The N DA distribution over atoms plots a ‘chemical portrait’ of the studied molecule, whose analysis allows for making the definite choice of the target atom with the highest N DA
value to be subjected to the chemical attack by an external addend. Therefore, we
have come to Answer 5 claiming that peculiarities of the graphene chemistry can be
exhibited at the quantitative level, much as this has been done for fullerenes [5].
Answer 5 Computational strategy of the chemical modification of graphene.
The typical chemical portrait of graphene fragment in Fig. 15.4a highlights edge
atoms as those with the highest chemical activities, besides rather irregular, while
exhibiting additionally the basal atoms ACS comparable with that one of fullerene
C 60 [28, 57]. This circumstance is the main consequence of the odd electron correlation in graphene in regard to its chemical modification. Ignoring the correlation has
resulted in a common conclusion about chemical inertness of the graphene atoms
with the only exclusion concerning the edge ones. Having this general indication
only, a computationist is still in the dark concerning the place of both the first and