The correlation of odd electrons in graphene turns out to be significant so
that the species should be attributed to correlated ones. This finding
profoundly influences the computational strategy addressing it to
multireference computational schemes. Owing to serious problems related to the
schemes realization, a compromise can be suggested by using single-determinant
approaches based on either Hartree-Fock or Density-Functional theory in the
form of unrestricted open-shell presentation. Both computational schemes enable
to fix the electron correlation, while only the Hartree-Fock theory suggests a
set of quantities to be calculated that can quantitatively characterize the
electron correlation and be used for a quantitative description of such
graphene properties as magnetism, chemical reactivity, and mechanical response.
The paper presents concepts and algorithms of the unrestricted Hartree-Fock
theory applied for the consideration of magnetic properties of nanographenes,
their chemical modification by the example of stepwise hydrogenation, as well
as a possible governing the electron correlation by the carbon skeleton
deformation.Comment: 17 pages, 11 figures, 3 table

Allouche

Benard

Boeker

Cohen

Davidson

Dewar

Elias

Enoki

Geim

Georgiou

Illas

Kahn

Kaplan

Kitagawa

Koenig

Komolov

Koshino

Lain

Levy

Lobayan

Mayer

Meyer

Nair

Noodleman

Schmidt

Seach

Sheka

Shibayama

Staroverov

Tada

Takatsuka

Van Fleck

Wang

Zayets

Zhogolev

Zvezdin

English

arXiv

The correlation of odd electrons in graphene turns out to be significant so that the species should be 
attributed to correlated ones. This finding profoundly influences the computational strategy addressing it 
to configuration-interaction computational schemes. Owing to serious problems related to the schemes 
realization, a compromise can be suggested by using single-determinant approaches based on either 
Hartree-Fock or Density-Functional Theory in the form of unrestricted open-shell presentation. Both 
computational schemes enable to fix the electron correlation, while only the Hartree-Fock theory suggests 
a set of quantities to be calculated that can quantitatively characterize the electron correlation and can be 
used for a quantitative description of such graphene properties as magnetism, chemical reactivity, and 
mechanical response. The paper presents concepts and algorithms of the unrestricted Hartree-Fock theory 
applied for the consideration of magnetic properties of nanographenes, their chemical modification by the 
example of stepwise hydrogenation, as well as a possible governing the electron correlation by the carbon 
skeleton deformation.
When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3502

Sheka, E.F.

Electronic Sumy State University Institutional Repository

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE NANOMATERIALS: APPLICATIONS AND PROPERTIES Vol. 1 No 1, 01NDLCN01 (3pp) (2012)   2304-1862/2012/1(1)01NDLCN01(3) 01NDLCN01-1  2012 Sumy State University Computational Strategy for Graphene: Insight from Odd Electrons Correlation  E.F. Sheka*  Peoples’ Friendship University of Russia, 6, Miklukho-Maklay Str., 117198 Moscow, Russia  (Received 15 February 2012; published online 15 August 2012)  The correlation of odd electrons in graphene turns out to be significant so that the species should be attributed to correlated ones. This finding profoundly influences the computational strategy addressing it to configuration-interaction computational schemes. Owing to serious problems related to the schemes realization, a compromise can be suggested by using single-determinant approaches based on either Hartree-Fock or Density-Functional Theory in the form of unrestricted open-shell presentation. Both computational schemes enable to fix the electron correlation, while only the Hartree-Fock theory suggests a set of quantities to be calculated that can quantitatively characterize the electron correlation and can be used for a quantitative description of such graphene properties as magnetism, chemical reactivity, and mechanical response. The paper presents concepts and algorithms of the unrestricted Hartree-Fock theory applied for the consideration of magnetic properties of nanographenes, their chemical modification by the example of stepwise hydrogenation, as well as a possible governing the electron correlation by the carbon skeleton deformation.   Keywords: Odd Electrons, Electron Correlation, Effectively Unpaired Electrons, Graphene, Magnetism, Chemical Modification, Deformation.    PACS number: 31.15.V –                                                            * sheka@icp.ac.ru 1. INTRODUCTION   According to Wikipedia, ‘Graphene is an allotrope of carbon, whose structure is one-atom-thick planar sheets of sp2-bonded carbon atoms that are densely packed in a honeycomb crystal lattice’ [1]. The definition clearly exhibits a molecular-crystal duality of this extraordinary substance. The peculiar duality is embodied in the computational strategy of graphene, as well.  On one hand, the solid state microscopic theory of quasiparticles in 2D space forms the ground for the description of graphene crystal. On the other hand, quantum molecular theory creates the image of the graphene molecule. However, as earlier, the two seemingly different concepts are tightly interconnected at computational level. Thus, the solid state quasiparticles are usually described in the approach based on a unit cell and/or supercell followed with periodic boundary conditions; besides, the unit cell is described at the molecular theory level. Therefore, the latter lays the foundation of both approaches, whilst rather differently. It is connected with the different origin of the molecular object under study. In the case of solid state approach, the cell and/or supercell should be chosen as a known crystalline motive. When graphene is considered as a molecule, no structural restrictions are introduced in advance. In both cases, it becomes necessary to understand which molecular theory is applicable for the graphene to be studied in the best way. The current paper concerns peculiarities of the molecular theory of graphene. The latter are obviously connected with both the odd-electron origin of the graphene electron system and these electrons correlation that turns out to play the governing role.   2. ODD ELECTRONS CORRELATION  In spite of formally monatomic crystalline structure of graphene, its properties are evidently governed by the behaviour of odd electrons of 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 visualized on the platform of molecular quantum theory.  When speaking about electron correlation, one must address the problem to the configuration interaction (CI). However, neither full CI nor any its truncated versions, clear and transparent conceptually, can be applied for computations valuable for graphene nanoscience that requires a vast number of computations to be performed as well as a great number of atoms to be considered [2, 3]. 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 [4, 5]. Application of the approaches 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:   0RUE ,   E.F. SHEKA PROC. NAP 1, 01NDLCN01 (2012)   01NDLCN01-2 where RU R UE E E'    presents a misalignment of energy. Here, RE and UE are total energies calculated by using restricted and unrestricted versions of the program in use. Criterion 2:   0DN z ,    where DN  is the total number of effectively unpaired electrons and is determined as     0DN trD r rc z  and AD AN D ¦ .   Here,  D r rc  [6] and AD  [7]  present  the  total  and  atom-fractioned spin density caused by the spin asymmetry due to the location of electrons with different spins in different spaces. Criterion 3:    2ˆ 0S' t ,   where 2 2ˆ ˆ( 1)US S S S'     presents the misalignment of  squared  spin.  Here,  2ˆUS  is the squared spin calculated within the applied unrestricted technique while S(S+1) presents the exact value of 2ˆS . Criterion 1 follows from a well known fact that the electron correlation, if available, lowers the total energy. Criterion 2 highlights the fact that the electron correlation is accompanied with the appearance of effectively unpaired electrons that provide the molecule radicalization [6-8]. These electrons total number depends on interatomic distance: when the latter is under a critical value covcritR , two adjacent electrons are covalently bound and ND   0. However, when the distance exceeds covcritR , the two electrons become unpaired, ND t 0,  the  more,  the  larger  is  the  interatomic spacing. In the case of the sp2 C-C bonds, covcritR =1.395 Å. Criterion 3 is the manifestation of the spin contamination of unrestricted single-determinant solutions [6-8]; the stronger electron correlation, the bigger spin contamination of the studied spin state.  Table 1 presents sets of the three parameters evaluated  for  a  number  of  right-angled  (na, nz) fragments of graphene (na and nz count the numbers of benzenoid units along armchair and zigzag edges of the fragment), nanographenes, NGrs below, by using AM1 version of semiempirical UHF approach implemented in the CLUSTER-Z1 codes. To our knowledge, only these codes allow for computing all the above three parameters simultaneously.  The data convincingly evidence that the electron correlation in graphene is significant. In view of the correlation, one can answer the second question put above suggesting quantitative explanation of peculiarities of the graphene magnetism, chemistry, and mechanics, much as this has been done for fullerenes [3].    Table 1 – Identifying parameters of the odd electron correlation in right-angle nanographenes  Fragment  ,a zn n  Odd electrons oddN  RUE' 1 kcal/mol RUEG  % 2 DN , e- DNG , % 2 2ˆUS'  (5, 5) 88 307 17 31 35 15.5 (7, 7) 150 376 15 52.6 35 26.3 (9, 9) 228 641 19 76.2 35 38.1 (11, 10) 296 760 19 94.5 32 47.24 (11, 12) 346 901 20 107.4 31 53.7 (15, 12) 456 1038 19 139 31 69.5 1 Presented energy values are rounded off to an integer 2 The percentage values are related to / (0)RU RU RE E EG  ' and /D D oddN N NG  , respectively      3. CONCLUSIVE REMARKS  Data  presented  in  the  current  paper  have  shown  that the correlation of odd electrons in graphene is significant so that the species should be attributed to correlated ones. This finding considerably complicates the computational strategy addressing it to CI computational schemes. Owing to serious problems related to the realization of such schemes in practice, a compromise can be suggested by using single-determinant approaches based on either Hartree-Fock or density-functional theory in the form of unrestricted open-shell presentation. Both computational schemes can fix the electron correlation, while only the Hartree-Fock theory suggests a set of quantities to be calculated that can quantitatively characterize the electron correlation and be used for a quantitative description of such graphene properties as magnetism, chemical reactivity, and mechanical response.  Magnetic constant J , the inverse value of which directly characterizes the strength of the electron correlation [9], lays the foundation of the description of magnetic properties of graphene. As shown, the constant is ~-16 kcal/mol for a graphene regular crystal, which is too much for the magnetism to be observable. In contrast to crystalline graphene, nondeformed and nondestructured nanographenes can be magnetic, since the magnetic constant rough-inversely depends on the NGr size. The latter determines the correlation zone and provides a recordable magnetization if J  is  from  a  few  units  to  tens nanometers. Small enough J values  can  be  provided as well by magnetic nanostructuring of rather large graphene pieces caused by the introduction of  COMPUTATIONAL STRATEGY FOR GRAPHENE: INSIGHT PROC. NAP 1, 01NDLCN01 (2012)   01NDLCN01-3 half-spin impurities or defects into the graphene body. Additionally, the odd number of the latter may change the singlet spin multiplicity of the ground state. Both scenarios find their verification in practice.  The correlated-electron algorithm-in-action has been applied in the current paper to the chemical modification of (5, 5) NGr by the example of its algorithmic stepwise hydrogenation [10]. As shown, both the hydrogenation of NGr itself and the final hydrides depend on several external factors, namely: 1) the state of the fixation of graphene substrate; 2) the accessibility of the substrate sides to hydrogen; and 3) molecular or atomic composition of the hydrogen vapor. These circumstances make both computational consideration and technology of the graphene hydrogenation multimode with the number of variants not less than eight if only molecular and atomic adsorption does not occur simultaneously. Thus, in full agreement with experimental evidence, a regular chair-like cyclohexanoid structure known as graphane can be obtained only for fixed membranes accessible to hydrogen atoms from both sides. Oppositely, one-side hydrogenation of the membrane results in irregular quasi-amorphous structure. A detailed consideration of all variants should be mandatory included in any serious project aimed at application of the hydrogen-graphene-based nanomaterials in general and for hydrogen-stored fuel cells, in particular.  The electron correlation is highly sensitive to the graphene deformation since the interatomic spacing is the main regulator of the former. Both static and dynamic deformation may influence the action. Static deformation, considered in the paper, is caused by one-side hydrogenation of the pristine sample [9]. When hydrogen atoms are removed, the carbon skeleton keeps its concave, either a canopy-like or basket-like, shape supported by stretched C-C bonds. The stretching stimulates both a significant increasing of the number of effectively unpaired electrons and a remarkable decreasing the magnetic constant absolute value. The former changes the electron-density image of the sample and evidence the enhancement of its chemical reactivity. The latter may result in the deformation-stimulated magnetization of the sample.  In view of these findings, an alternative, correlated-electron explanation of peculiarities related to the density images of the graphene bubbles found on different substrates [11] has been suggested [9].  The dynamic deformation is illustrated by the example  of  the  (5,  5)  NGr uniaxial  tension.  As  shown,  the strengthening of the electron correlation accompanies each step of the deformation [12]. This is followed by both enhancement of chemical reactivity and magnetic ability. In spite of predominantly plastic character of the graphene deformation, the latter can be applied to regulate both abilities of the sample.  The odd electron correlation is not a prerogative of graphene only. Similar phenomenon is characteristic for all sp2 nanocarbons, including both fullerenes and nanotubes [3]. The only preference of graphene consists in much larger variety of cases when this inherent characteristic of the class can be visualized.    REFERENCES  1. A.K.  Geim, K. S.Novoselov, Nature Mat. 6, 183 (2007). 2. E.R. Davidson, A.E. Clark, Phys Chem. Chem. Phys.   9, 1881 (2007). 3. E.F. Sheka, Fullerenes: Nanochemistry, Nanomagnetism, Nanomedicine, Nanophotonics (Boca Raton: CRC Press, Taylor and Francis Group: 2011). 4. E.R. Davidson, Int. J. Quant. Chem. 69, 214 (1998). 5. I.G. Kaplan, Int. J. Quant. Chem. 107, 2595 (2007). 6. K. Takatsuka, T. Fueno, K. Yamaguchi, Theor. Chim. Acta  48, 175 (1978). 7. V.N. Staroverov, E.R. Davidson, Chem. Phys. Lett. 330, 161 (2000). 8. L. Lain, A. Torre, D.R. Alcoba, R.C. Bochicchio, Theor. Chem. Acc. 128, 405 (2011). 9. E.F.Sheka, arXiv1201.5388v1[cond-mat.mtrl-sci]. 10. E.F. Sheka, N.A. Popova, J. Mol. Mod. doi: 10.1007/s00894-012-1356-9 (2012). 11. T. Georgiou, L. Britnell, P. Blake, R.V. Gorbachev, A. Gholinia, A.K. Geim, C. Casiraghi, K.S. Novoselov, Appl. Phys. Lett. 99, 093103 (2011). 12. E.F. Sheka, N.A. Popova, V.A. Popova, E. Nikitina, L. Shaymardanova, J. Mol. Mod. 17, 1121 (2011).   

Computational Strategy for Graphene: Insight from Odd Electrons Correlation

SocioEconomic Challenges Journal (Sumy State University)

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE NANOMATERIALS: APPLICATIONS AND PROPERTIES 
Vol. 1 No 1, 01NDLCN01 (3pp) (2012) 
 
 
2304-1862/2012/1(1)01NDLCN01(3) 01NDLCN01-1  2012 Sumy State University 
Computational Strategy for Graphene: Insight from Odd Electrons Correlation 
 
E.F. Sheka* 
 
Peoples’ Friendship University of Russia, 6, Miklukho-Maklay Str., 117198 Moscow, Russia 
 
(Received 15 February 2012; published online 15 August 2012) 
 
The correlation of odd electrons in graphene turns out to be significant so that the species should be 
attributed to correlated ones. This finding profoundly influences the computational strategy addressing it 
to configuration-interaction computational schemes. Owing to serious problems related to the schemes 
realization, a compromise can be suggested by using single-determinant approaches based on either 
Hartree-Fock or Density-Functional Theory in the form of unrestricted open-shell presentation. Both 
computational schemes enable to fix the electron correlation, while only the Hartree-Fock theory suggests 
a set of quantities to be calculated that can quantitatively characterize the electron correlation and can be 
used for a quantitative description of such graphene properties as magnetism, chemical reactivity, and 
mechanical response. The paper presents concepts and algorithms of the unrestricted Hartree-Fock theory 
applied for the consideration of magnetic properties of nanographenes, their chemical modification by the 
example of stepwise hydrogenation, as well as a possible governing the electron correlation by the carbon 
skeleton deformation.  
 
Keywords: Odd Electrons, Electron Correlation, Effectively Unpaired Electrons, Graphene, Magnetism, 
Chemical Modification, Deformation.  
 
 PACS number: 31.15.V – 
 
                                                          
* sheka@icp.ac.ru 
1. INTRODUCTION  
 
According to Wikipedia, ‘Graphene is an allotrope of 
carbon, whose structure is one-atom-thick planar 
sheets of sp2-bonded carbon atoms that are densely 
packed in a honeycomb crystal lattice’ [1]. The 
definition clearly exhibits a molecular-crystal duality of 
this extraordinary substance. The peculiar duality is 
embodied in the computational strategy of graphene, as 
well.  On one hand, the solid state microscopic theory of 
quasiparticles in 2D space forms the ground for the 
description of graphene crystal. On the other hand, 
quantum molecular theory creates the image of the 
graphene molecule. However, as earlier, the two 
seemingly different concepts are tightly interconnected 
at computational level. Thus, the solid state 
quasiparticles are usually described in the approach 
based on a unit cell and/or supercell followed with 
periodic boundary conditions; besides, the unit cell is 
described at the molecular theory level. Therefore, the 
latter lays the foundation of both approaches, whilst 
rather differently. It is connected with the different 
origin of the molecular object under study. In the case 
of solid state approach, the cell and/or supercell should 
be chosen as a known crystalline motive. When 
graphene is considered as a molecule, no structural 
restrictions are introduced in advance. In both cases, it 
becomes necessary to understand which molecular 
theory is applicable for the graphene to be studied in 
the best way. The current paper concerns peculiarities 
of the molecular theory of graphene. The latter are 
obviously connected with both the odd-electron origin of 
the graphene electron system and these electrons 
correlation that turns out to play the governing role.  
 
2. ODD ELECTRONS CORRELATION 
 
In spite of formally monatomic crystalline structure 
of graphene, its properties are evidently governed by 
the behaviour of odd electrons of 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 visualized on the platform of 
molecular quantum theory.  
When speaking about electron correlation, one must 
address the problem to the configuration interaction 
(CI). However, neither full CI nor any its truncated 
versions, clear and transparent conceptually, can be 
applied for computations valuable for graphene 
nanoscience that requires a vast number of 
computations to be performed as well as a great 
number of atoms to be considered [2, 3]. 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 [4, 5]. 
Application of the approaches 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: 
 
 0RUE ,  
 
E.F. SHEKA PROC. NAP 1, 01NDLCN01 (2012) 
 
 
01NDLCN01-2 
where RU R UE E E'    presents a misalignment of 
energy. Here, RE and UE are total energies calculated 
by using restricted and unrestricted versions of the 
program in use. 
Criterion 2: 
 
 0DN z ,   
 
where DN  is the total number of effectively unpaired 
electrons and is determined as 
 
   0DN trD r rc z  and AD AN D ¦ .  
 
Here,  D r rc  [6] and AD  [7]  present  the  total  and  
atom-fractioned spin density caused by the spin 
asymmetry due to the location of electrons with 
different spins in different spaces. 
Criterion 3:  
 
 2ˆ 0S' t ,  
 
where 2 2
ˆ ˆ
( 1)US S S S'     presents the misalignment 
of  squared  spin.  Here,  2ˆUS  is the squared spin 
calculated within the applied unrestricted technique 
while S(S+1) presents the exact value of 2ˆS . 
Criterion 1 follows from a well known fact that the 
electron correlation, if available, lowers the total 
energy. Criterion 2 highlights the fact that the electron 
correlation is accompanied with the appearance of 
effectively unpaired electrons that provide the molecule 
radicalization [6-8]. These electrons total number 
depends on interatomic distance: when the latter is 
under a critical value covcritR , two adjacent electrons are 
covalently bound and ND   0. However, when the 
distance exceeds covcritR , the two electrons become 
unpaired, ND t 0,  the  more,  the  larger  is  the  
interatomic spacing. In the case of the sp2 C-C bonds, 
cov
critR =1.395 Å. Criterion 3 is the manifestation of the 
spin contamination of unrestricted single-determinant 
solutions [6-8]; the stronger electron correlation, the 
bigger spin contamination of the studied spin state.  
Table 1 presents sets of the three parameters 
evaluated  for  a  number  of  right-angled  (na, nz) 
fragments of graphene (na and nz count the numbers of 
benzenoid units along armchair and zigzag edges of the 
fragment), nanographenes, NGrs below, by using AM1 
version of semiempirical UHF approach implemented 
in the CLUSTER-Z1 codes. To our knowledge, only 
these codes allow for computing all the above three 
parameters simultaneously.  
The data convincingly evidence that the electron 
correlation in graphene is significant. In view of the 
correlation, one can answer the second question put 
above suggesting quantitative explanation of 
peculiarities of the graphene magnetism, chemistry, 
and mechanics, much as this has been done for 
fullerenes [3].  
 
 
Table 1 – Identifying parameters of the odd electron correlation in right-angle nanographenes 
 
Fragment 
 ,a zn n  
Odd electrons 
oddN  
RUE' 1 
kcal/mol 
RUEG  % 2 DN , e- DNG , % 2 2ˆUS'  
(5, 5) 88 307 17 31 35 15.5 
(7, 7) 150 376 15 52.6 35 26.3 
(9, 9) 228 641 19 76.2 35 38.1 
(11, 10) 296 760 19 94.5 32 47.24 
(11, 12) 346 901 20 107.4 31 53.7 
(15, 12) 456 1038 19 139 31 69.5 
1 Presented energy values are rounded off to an integer 
2 The percentage values are related to / (0)RU RU RE E EG  ' and /D D oddN N NG  , respectively 
 
 
 
 
 
3. CONCLUSIVE REMARKS 
 
Data  presented  in  the  current  paper  have  shown  
that the correlation of odd electrons in graphene is 
significant so that the species should be attributed to 
correlated ones. This finding considerably complicates 
the computational strategy addressing it to CI 
computational schemes. Owing to serious problems 
related to the realization of such schemes in practice, a 
compromise can be suggested by using single-
determinant approaches based on either Hartree-Fock 
or density-functional theory in the form of unrestricted 
open-shell presentation. Both computational schemes 
can fix the electron correlation, while only the Hartree-
Fock theory suggests a set of quantities to be calculated 
that can quantitatively characterize the electron 
correlation and be used for a quantitative description of 
such graphene properties as magnetism, chemical 
reactivity, and mechanical response.  
Magnetic constant J , the inverse value of which 
directly characterizes the strength of the electron 
correlation [9], lays the foundation of the description of 
magnetic properties of graphene. As shown, the 
constant is ~-16 kcal/mol for a graphene regular 
crystal, which is too much for the magnetism to be 
observable. In contrast to crystalline graphene, 
nondeformed and nondestructured nanographenes can 
be magnetic, since the magnetic constant rough-
inversely depends on the NGr size. The latter 
determines the correlation zone and provides a 
recordable magnetization if J  is  from  a  few  units  to  
tens nanometers. Small enough J values  can  be  
provided as well by magnetic nanostructuring of rather 
large graphene pieces caused by the introduction of 
 
COMPUTATIONAL STRATEGY FOR GRAPHENE: INSIGHT PROC. NAP 1, 01NDLCN01 (2012) 
 
 
01NDLCN01-3 
half-spin impurities or defects into the graphene body. 
Additionally, the odd number of the latter may change 
the singlet spin multiplicity of the ground state. Both 
scenarios find their verification in practice.  
The correlated-electron algorithm-in-action has 
been applied in the current paper to the chemical 
modification of (5, 5) NGr by the example of its 
algorithmic stepwise hydrogenation [10]. As shown, 
both the hydrogenation of NGr itself and the final 
hydrides depend on several external factors, namely: 1) 
the state of the fixation of graphene substrate; 2) the 
accessibility of the substrate sides to hydrogen; and 3) 
molecular or atomic composition of the hydrogen vapor. 
These circumstances make both computational 
consideration and technology of the graphene 
hydrogenation multimode with the number of variants 
not less than eight if only molecular and atomic 
adsorption does not occur simultaneously. Thus, in full 
agreement with experimental evidence, a regular chair-
like cyclohexanoid structure known as graphane can be 
obtained only for fixed membranes accessible to 
hydrogen atoms from both sides. Oppositely, one-side 
hydrogenation of the membrane results in irregular 
quasi-amorphous structure. A detailed consideration of 
all variants should be mandatory included in any 
serious project aimed at application of the hydrogen-
graphene-based nanomaterials in general and for 
hydrogen-stored fuel cells, in particular.  
The electron correlation is highly sensitive to the 
graphene deformation since the interatomic spacing is 
the main regulator of the former. Both static and 
dynamic deformation may influence the action. Static 
deformation, considered in the paper, is caused by one-
side hydrogenation of the pristine sample [9]. When 
hydrogen atoms are removed, the carbon skeleton 
keeps its concave, either a canopy-like or basket-like, 
shape supported by stretched C-C bonds. The 
stretching stimulates both a significant increasing of 
the number of effectively unpaired electrons and a 
remarkable decreasing the magnetic constant absolute 
value. The former changes the electron-density image 
of the sample and evidence the enhancement of its 
chemical reactivity. The latter may result in the 
deformation-stimulated magnetization of the sample.  
In view of these findings, an alternative, correlated-
electron explanation of peculiarities related to the 
density images of the graphene bubbles found on 
different substrates [11] has been suggested [9].  
The dynamic deformation is illustrated by the 
example  of  the  (5,  5)  NGr uniaxial  tension.  As  shown,  
the strengthening of the electron correlation 
accompanies each step of the deformation [12]. This is 
followed by both enhancement of chemical reactivity 
and magnetic ability. In spite of predominantly plastic 
character of the graphene deformation, the latter can 
be applied to regulate both abilities of the sample.  
The odd electron correlation is not a prerogative of 
graphene only. Similar phenomenon is characteristic 
for all sp2 nanocarbons, including both fullerenes and 
nanotubes [3]. The only preference of graphene consists 
in much larger variety of cases when this inherent 
characteristic of the class can be visualized. 
 
 
 
REFERENCES 
 
1. A.K.  Geim, K. S.Novoselov, Nature Mat. 6, 183 (2007). 
2. E.R. Davidson, A.E. Clark, Phys Chem. Chem. Phys.   9, 
1881 (2007). 
3. E.F. Sheka, Fullerenes: Nanochemistry, Nanomagnetism, 
Nanomedicine, Nanophotonics (Boca Raton: CRC Press, 
Taylor and Francis Group: 2011). 
4. E.R. Davidson, Int. J. Quant. Chem. 69, 214 (1998). 
5. I.G. Kaplan, Int. J. Quant. Chem. 107, 2595 (2007). 
6. K. Takatsuka, T. Fueno, K. Yamaguchi, Theor. Chim. 
Acta  48, 175 (1978). 
7. V.N. Staroverov, E.R. Davidson, Chem. Phys. Lett. 330, 
161 (2000). 
8. L. Lain, A. Torre, D.R. Alcoba, R.C. Bochicchio, Theor. 
Chem. Acc. 128, 405 (2011). 
9. E.F.Sheka, arXiv1201.5388v1[cond-mat.mtrl-sci]. 
10. E.F. Sheka, N.A. Popova, J. Mol. Mod. doi: 
10.1007/s00894-012-1356-9 (2012). 
11. T. Georgiou, L. Britnell, P. Blake, R.V. Gorbachev, 
A. Gholinia, A.K. Geim, C. Casiraghi, K.S. Novoselov, 
Appl. Phys. Lett. 99, 093103 (2011). 
12. E.F. Sheka, N.A. Popova, V.A. Popova, E. Nikitina, 
L. Shaymardanova, J. Mol. Mod. 17, 1121 (2011). 
 
 


Computational Strategy for Graphene: Insight from Odd Electrons Correlation

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