15 Molecular Theory of Graphene
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subordinate to the theory of aromaticity. In the case of graphene, the values are not
zero, which manifests a considerable correlation of its odd electrons. Studying the
graphene odd electrons system by using the unrestricted broken symmetry approach,
one can obtain the following answers concerning the issue mentioned above.
Answer 1 states that application of both UHF and UDFT techniques in the framework of the broken symmetry approach [20] allows determining the energies of pure
spin states quite correctly.
Answer 2 concerns the quantitative description of the graphene magnetism and
shows that the broken symmetry approaches provide the exact determination of the
magnetic constant. The value is size-dependent and steadily decreases by absolute
value when the graphene molecule size increases. The molecules with linear dimension of a few nm can provide the constant small enough for the magnetism of the
singlet graphene to be recorded. However, when the size exceeds the electron mean
free pass, the magnetism disappears due to quantizing electronic states and coming
back to the crystalline graphene unit cell that is diamagnetic.
Answer 3 is related to the graphene characteristic that controls the odd electrons
correlation. As shown, this is the C–C bond length that exceeds the critical value
R crit = 1.395 Å. Above this value two adjacent odd electrons become effectively
unpaired, firstly, partially radicalized and then completely radicalized as the C–C
distance grows.
Answer 4 addresses the definite physical reality of the effectively unpaired electrons. So far there had been only one case when UBS HF computational results
were compared with those obtained by using one of the CI schemes in the form
of either CASSCF or MRCI approach [38]. The two techniques were applied to
the description of diradical character of the Cope rearrangement transition state.
CASSCF, MRCI, and UBS HF calculations have revealed effectively unpaired electrons N D at the level of 1.05, 1.55, and 1.45 e, respectively, just highlighting that
the feature is a characteristic for the electron correlation but not the proximity of
the UBS HF approach. Recent successes in the atomic force microscopy with unprecedented high accuracy have allowed seeing the unpaired electrons directly. The
recorded molecular images for the pentacene, olympicene, and graphene molecules
are in full consent with those calculated in the UBS HF approximation.
Answer 5 concerns the basic grounds of the chemical modification of graphene.
As shown, the fractional number of the effectively unpaired electrons related to a
given atom N DA is the quantitative indicator of the atom chemical activity (atomic
chemical susceptibility) that can be used as a reliable pointer of the target atom
entering the reaction. A large scale stepwise reaction can be considered computationally, which leads to the formation of different polyderivatives of graphene. On
the example of hydrogenation and oxidation of graphene, was obtained a general
view of graphene polyhydrides and polyoxides that well fit the experimental reality.
Answer 6 testifies that molecular theory is quite efficient when considering mechanical behavior of graphene. Leaving outside the theory application to the consideration of the deformational process as such [81–83], the current chapter is concentrated on the consequences, related to the odd electros correlation, that are caused by
stretching and rupture of the C–C bonds in the graphene molecules in due course of
279
subordinate to the theory of aromaticity. In the case of graphene, the values are not
zero, which manifests a considerable correlation of its odd electrons. Studying the
graphene odd electrons system by using the unrestricted broken symmetry approach,
one can obtain the following answers concerning the issue mentioned above.
Answer 1 states that application of both UHF and UDFT techniques in the framework of the broken symmetry approach [20] allows determining the energies of pure
spin states quite correctly.
Answer 2 concerns the quantitative description of the graphene magnetism and
shows that the broken symmetry approaches provide the exact determination of the
magnetic constant. The value is size-dependent and steadily decreases by absolute
value when the graphene molecule size increases. The molecules with linear dimension of a few nm can provide the constant small enough for the magnetism of the
singlet graphene to be recorded. However, when the size exceeds the electron mean
free pass, the magnetism disappears due to quantizing electronic states and coming
back to the crystalline graphene unit cell that is diamagnetic.
Answer 3 is related to the graphene characteristic that controls the odd electrons
correlation. As shown, this is the C–C bond length that exceeds the critical value
R crit = 1.395 Å. Above this value two adjacent odd electrons become effectively
unpaired, firstly, partially radicalized and then completely radicalized as the C–C
distance grows.
Answer 4 addresses the definite physical reality of the effectively unpaired electrons. So far there had been only one case when UBS HF computational results
were compared with those obtained by using one of the CI schemes in the form
of either CASSCF or MRCI approach [38]. The two techniques were applied to
the description of diradical character of the Cope rearrangement transition state.
CASSCF, MRCI, and UBS HF calculations have revealed effectively unpaired electrons N D at the level of 1.05, 1.55, and 1.45 e, respectively, just highlighting that
the feature is a characteristic for the electron correlation but not the proximity of
the UBS HF approach. Recent successes in the atomic force microscopy with unprecedented high accuracy have allowed seeing the unpaired electrons directly. The
recorded molecular images for the pentacene, olympicene, and graphene molecules
are in full consent with those calculated in the UBS HF approximation.
Answer 5 concerns the basic grounds of the chemical modification of graphene.
As shown, the fractional number of the effectively unpaired electrons related to a
given atom N DA is the quantitative indicator of the atom chemical activity (atomic
chemical susceptibility) that can be used as a reliable pointer of the target atom
entering the reaction. A large scale stepwise reaction can be considered computationally, which leads to the formation of different polyderivatives of graphene. On
the example of hydrogenation and oxidation of graphene, was obtained a general
view of graphene polyhydrides and polyoxides that well fit the experimental reality.
Answer 6 testifies that molecular theory is quite efficient when considering mechanical behavior of graphene. Leaving outside the theory application to the consideration of the deformational process as such [81–83], the current chapter is concentrated on the consequences, related to the odd electros correlation, that are caused by
stretching and rupture of the C–C bonds in the graphene molecules in due course of