250
E.F. Sheka
It goes without saying that theory is really of value when it is
used to perform numerical experiments that capture a trend.
Not numbers, but a trend.
Roald Hoffmann, 2013.
15.1 Introduction
For more than ten years, I have been immersed in an absorbing world of quantum chemistry of sp 2 nanocarbons, a world full of mysteries, hidden obstacles, and
wonderful discoveries. My first travelling was stimulated by a wish to find the answer to a very simple question: why is there no fullerene Si 60 while fullerene C 60
does exist? A widely spread standard statement “silicon does not like sp 2 configuration” just postulated the fact but did not explain the reason. Moreover, computations,
available by that time, showed that Si 60 molecule could exist. A comparative examination of C 60 and Si 60 showed a strange feature in the high-spin states behavior of
the molecules. As occurred, a sequence of spin-varying states (singlet (RHF)-tripletquintet) formed a progressively growing series by energy for the C 60 molecule while
for the Si 60 one energy of the triplet and quintet states turned out to drop drastically
with respect to the RHF singlet. Due to a crucial controversy with the reality, a natural question arose: what is wrong with the molecule singlet state? I will not touch
here on the frequent claim that the semiempirical approach is bad. It is not the case,
in general, and is absolutely not relevant to carbonaceous and siliceous species due
to superior parameterization of both atoms. Actually, all the next stories have shown
that the matter was not due to the wrong approximation but was provided by an
inherent peculiarity of both molecules. At that time, in 2003, it was shown that the
singlet state of the Si 60 molecule took its correct place below the triplet one if it
only is calculated by using the open-shell unrestricted Hartree-Fock (UHF) approximation [4, 6, 7]. Since then, in more than eight dozen papers that followed, I and
my colleagues have convinced ourselves and have tried to convince others that UHF
approach touches very intimate properties of sp 2 nanocarbons that select them from
other carbonaceous species and put them in a particular place. The properties are
the result of a significant weakening of the interaction between the odd electrons of
the species in comparison with, say, that one in the benzene molecule.
During these investigations we obtained (i) the answer to the initial question concerning the absence of Si 60 molecule [4], (ii) disclosed regulations that
govern chemistry, magnetism, biomedical and photonic behavior of carbonaceous
fullerenes [5], (iii) showed a tight similarity in the description of the properties of
fullerenes, carbon nanotubes, and graphene molecules [5, 8]. Little by little an applied molecular theory of sp 2 nanocarbons became sharply defined, which revealed
itself in the most vivid way in case of graphene. However, graphene, which is a famous nobeliated 2D solid, and molecular theory—if there is no controversy between
these subjects?
The answer lies on a surface and follows from a well known definition of
graphene: ‘Graphene is an allotrope of carbon, whose structure is one-atom-thick
E.F. Sheka
It goes without saying that theory is really of value when it is
used to perform numerical experiments that capture a trend.
Not numbers, but a trend.
Roald Hoffmann, 2013.
15.1 Introduction
For more than ten years, I have been immersed in an absorbing world of quantum chemistry of sp 2 nanocarbons, a world full of mysteries, hidden obstacles, and
wonderful discoveries. My first travelling was stimulated by a wish to find the answer to a very simple question: why is there no fullerene Si 60 while fullerene C 60
does exist? A widely spread standard statement “silicon does not like sp 2 configuration” just postulated the fact but did not explain the reason. Moreover, computations,
available by that time, showed that Si 60 molecule could exist. A comparative examination of C 60 and Si 60 showed a strange feature in the high-spin states behavior of
the molecules. As occurred, a sequence of spin-varying states (singlet (RHF)-tripletquintet) formed a progressively growing series by energy for the C 60 molecule while
for the Si 60 one energy of the triplet and quintet states turned out to drop drastically
with respect to the RHF singlet. Due to a crucial controversy with the reality, a natural question arose: what is wrong with the molecule singlet state? I will not touch
here on the frequent claim that the semiempirical approach is bad. It is not the case,
in general, and is absolutely not relevant to carbonaceous and siliceous species due
to superior parameterization of both atoms. Actually, all the next stories have shown
that the matter was not due to the wrong approximation but was provided by an
inherent peculiarity of both molecules. At that time, in 2003, it was shown that the
singlet state of the Si 60 molecule took its correct place below the triplet one if it
only is calculated by using the open-shell unrestricted Hartree-Fock (UHF) approximation [4, 6, 7]. Since then, in more than eight dozen papers that followed, I and
my colleagues have convinced ourselves and have tried to convince others that UHF
approach touches very intimate properties of sp 2 nanocarbons that select them from
other carbonaceous species and put them in a particular place. The properties are
the result of a significant weakening of the interaction between the odd electrons of
the species in comparison with, say, that one in the benzene molecule.
During these investigations we obtained (i) the answer to the initial question concerning the absence of Si 60 molecule [4], (ii) disclosed regulations that
govern chemistry, magnetism, biomedical and photonic behavior of carbonaceous
fullerenes [5], (iii) showed a tight similarity in the description of the properties of
fullerenes, carbon nanotubes, and graphene molecules [5, 8]. Little by little an applied molecular theory of sp 2 nanocarbons became sharply defined, which revealed
itself in the most vivid way in case of graphene. However, graphene, which is a famous nobeliated 2D solid, and molecular theory—if there is no controversy between
these subjects?
The answer lies on a surface and follows from a well known definition of
graphene: ‘Graphene is an allotrope of carbon, whose structure is one-atom-thick