Chapter 15
Molecular Theory of Graphene
E.F. Sheka
Abstract Odd electrons of benzenoid units and the correlation of these electrons
having different spins are the main concepts of the molecular theory of graphene.
In contrast to the theory of aromaticity, the molecular theory is based on the fact
that odd electrons with different spins occupy different places in the space so that
the configuration interaction becomes the central point of the theory. Consequently,
a multi-determinant presentation of the wave function of the system of weakly interacting odd electrons is utterly mandatory on the way of the theory realization
at the computational level. However, the efficacy of the available CI computational
techniques is quite restricted in regard to large polyatomic systems, which does not
allow performing extensive computational experiments. Facing the problem, computationists have addressed standard single-determinant ones albeit not often being
aware of the correctness of the obtained results. The current chapter presents the
molecular theory of graphene in terms of single-determinant computational schemes
and discloses how reliable information about the electron-correlated system can be
obtained by using either UHF or UDFT computational schemes.
When the paper was written, a splendid conceptually profound ‘informal reflection’
of Roald Hoffmann appeared in the first issue of the Angewandte Chemie (International edition) that celebrates its 125-year anniversary [1]. Hoffmann’s “Small but
Strong Lessons from Chemistry for Nanoscience” turned out to be remarkably concordant to the main ideas discussed in the current chapter. This should be expected
since the Hoffmann concepts on stabilizing singlet states of biradicals in organic
chemistry (see [2] and references therein) and dimeric molecular magnets [3] have
laid the foundation of the molecular theory of fullerenes [4, 5], application of which
to graphene science is discussed below. These problems are on a knife-edge today
that is why, once in full agreement with Hoffmann’s answers to the question ‘What
you can trust about theory?’. I would like to preface the presentation of the text of a
quote from the ‘informal reflection’, placing it as the epigraph
E.F. Sheka (B)
Peoples’ Friendship University of Russia, Miklukho-Maklay, 6, Moscow 117198, Russia
e-mail: sheka@icp.ac.ru
M. Hotokka et al. (eds.), Advances in Quantum Methods and Applications in
Chemistry, Physics, and Biology, Progress in Theoretical Chemistry and Physics 27,
DOI 10.1007/978-3-319-01529-3_15,
© Springer International Publishing Switzerland 2013
249
Molecular Theory of Graphene
E.F. Sheka
Abstract Odd electrons of benzenoid units and the correlation of these electrons
having different spins are the main concepts of the molecular theory of graphene.
In contrast to the theory of aromaticity, the molecular theory is based on the fact
that odd electrons with different spins occupy different places in the space so that
the configuration interaction becomes the central point of the theory. Consequently,
a multi-determinant presentation of the wave function of the system of weakly interacting odd electrons is utterly mandatory on the way of the theory realization
at the computational level. However, the efficacy of the available CI computational
techniques is quite restricted in regard to large polyatomic systems, which does not
allow performing extensive computational experiments. Facing the problem, computationists have addressed standard single-determinant ones albeit not often being
aware of the correctness of the obtained results. The current chapter presents the
molecular theory of graphene in terms of single-determinant computational schemes
and discloses how reliable information about the electron-correlated system can be
obtained by using either UHF or UDFT computational schemes.
When the paper was written, a splendid conceptually profound ‘informal reflection’
of Roald Hoffmann appeared in the first issue of the Angewandte Chemie (International edition) that celebrates its 125-year anniversary [1]. Hoffmann’s “Small but
Strong Lessons from Chemistry for Nanoscience” turned out to be remarkably concordant to the main ideas discussed in the current chapter. This should be expected
since the Hoffmann concepts on stabilizing singlet states of biradicals in organic
chemistry (see [2] and references therein) and dimeric molecular magnets [3] have
laid the foundation of the molecular theory of fullerenes [4, 5], application of which
to graphene science is discussed below. These problems are on a knife-edge today
that is why, once in full agreement with Hoffmann’s answers to the question ‘What
you can trust about theory?’. I would like to preface the presentation of the text of a
quote from the ‘informal reflection’, placing it as the epigraph
E.F. Sheka (B)
Peoples’ Friendship University of Russia, Miklukho-Maklay, 6, Moscow 117198, Russia
e-mail: sheka@icp.ac.ru
M. Hotokka et al. (eds.), Advances in Quantum Methods and Applications in
Chemistry, Physics, and Biology, Progress in Theoretical Chemistry and Physics 27,
DOI 10.1007/978-3-319-01529-3_15,
© Springer International Publishing Switzerland 2013
249