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E.F. Sheka
The current chapter is concentrated at the molecular essence of graphene considered from the viewpoint of the molecular theory of sp 2 nanocarbons. The theory is
based on two main concepts, which involve the odd-electron origin of the graphene
electron system and these electrons correlation. The latter turns out to play the governing role. As will be shown below, such an approach occurs very efficient in describing chemical, magnetic, mechanical, and optical properties of graphene.
15.2 Odd Electrons Correlation
In spite of formally two-atomic unit cell of crystalline graphene, its properties are
evidently governed by the behaviour of odd electrons of the hexagonal benzenoid
units. The only thing that we know about the behaviour for sure is that the interaction between odd electrons is weak; nevertheless, how weak is it? Is it enough to
provide a tight covalent pairing when two electrons with different spins occupy the
same place in space or, oppositely, is it too weak for this and the two electrons are
located in different spaces thus becoming spin correlated? This supremely influential molecular aspect of graphene can be visualised on the platform of the molecular
quantum theory.
To exhibit a trend, a system computational experiment must be carried out meaning that a vast number of computations are to be performed as well as a great number
of atoms are to be considered. When speaking about electron correlation, one should
address the problem to the configuration interaction (CI). However, neither full CI
nor any its truncated version, clear and transparent conceptually, can be applied for
the computational experiments, valuable for graphene nanoscience. Owing to this,
techniques based on single unrestricted open-shell determinants becomes the only
alternative. Unrestricted Hartree-Fock (UHF) and unrestricted DFT (spin polarized,
UDFT) approaches form the techniques ground and are both sensitive to the electron correlation, but differently due to different dependence of their algorithms on
electron spins [10, 11]. The approach application raises two questions: (1) what are
criteria that show the electron correlation in the studied system and (2) how much
are the solutions of single-determinant approaches informative for a system of correlated electrons.
Answering the first question, three criteria, which highlight the electron correlation at the single-determinant level of theory, can be suggested. Those concern the
following characteristic parameters:
Criterion 1
E
RU
≥ 0,
where,
E
RU
= E
R
− E
U
(15.1)
presents a misalignment of energy. Here, E R and E U are the total energies calculated by using the restricted and unrestricted versions of the software in use.
E.F. Sheka
The current chapter is concentrated at the molecular essence of graphene considered from the viewpoint of the molecular theory of sp 2 nanocarbons. The theory is
based on two main concepts, which involve the odd-electron origin of the graphene
electron system and these electrons correlation. The latter turns out to play the governing role. As will be shown below, such an approach occurs very efficient in describing chemical, magnetic, mechanical, and optical properties of graphene.
15.2 Odd Electrons Correlation
In spite of formally two-atomic unit cell of crystalline graphene, its properties are
evidently governed by the behaviour of odd electrons of the hexagonal benzenoid
units. The only thing that we know about the behaviour for sure is that the interaction between odd electrons is weak; nevertheless, how weak is it? Is it enough to
provide a tight covalent pairing when two electrons with different spins occupy the
same place in space or, oppositely, is it too weak for this and the two electrons are
located in different spaces thus becoming spin correlated? This supremely influential molecular aspect of graphene can be visualised on the platform of the molecular
quantum theory.
To exhibit a trend, a system computational experiment must be carried out meaning that a vast number of computations are to be performed as well as a great number
of atoms are to be considered. When speaking about electron correlation, one should
address the problem to the configuration interaction (CI). However, neither full CI
nor any its truncated version, clear and transparent conceptually, can be applied for
the computational experiments, valuable for graphene nanoscience. Owing to this,
techniques based on single unrestricted open-shell determinants becomes the only
alternative. Unrestricted Hartree-Fock (UHF) and unrestricted DFT (spin polarized,
UDFT) approaches form the techniques ground and are both sensitive to the electron correlation, but differently due to different dependence of their algorithms on
electron spins [10, 11]. The approach application raises two questions: (1) what are
criteria that show the electron correlation in the studied system and (2) how much
are the solutions of single-determinant approaches informative for a system of correlated electrons.
Answering the first question, three criteria, which highlight the electron correlation at the single-determinant level of theory, can be suggested. Those concern the
following characteristic parameters:
Criterion 1
E
RU
≥ 0,
where,
E
RU
= E
R
− E
U
(15.1)
presents a misalignment of energy. Here, E R and E U are the total energies calculated by using the restricted and unrestricted versions of the software in use.