15 Molecular Theory of Graphene
281
8. Sheka E (2009) Nanocarbons through computations: fullerenes, nanotubes, and graphene. In:
The UNESCO-EOLSS encyclopedia nanoscience and nanotechnology. UNESCO, Moscow,
pp 415–444
9. Geim AK, Novoselov KS (2007) The rise of graphene. Nat Mater 6:183–191
10. Davidson E (1998) How robust is present-day DFT? Int J Quant Chem 69:214–245
11. Kaplan I (2007) Problems in DFT with the total spin and degenerate states. Int J Quant Chem
107:2595–2603
12. Takatsuka K, Fueno T, Yamaguchi K (1978) Distribution of odd electrons in ground-state
molecules. Theor Chim Acta 48:175–183
13. Staroverov VN, Davidson ER (2000) Distribution of effectively unpaired electrons. Chem
Phys Lett 330:161–168
14. Benard MJ (1979) A study of Hartree–Fock instabilities in Cr 2 (O 2 CH) 4 and Mo 2 (O 2 CH) 4 .
J Chem Phys 71:2546–2556
15. Lain L, Torre A, Alcoba DR et al (2011) A study of the relationships between unpaired electron density, spin-density and cumulant matrices. Theor Chem Acc 128:405–410
16. Sheka EF, Chernozatonskii LA (2007) Bond length effect on odd electrons behavior in singlewalled carbon nanotubes. J Phys Chem A 111:10771–10780
17. Sheka EF (2012) Computational strategy for graphene: insight from odd electrons correlation.
Int J Quant Chem 112:3076–3090
18. Zayets VA (1990) CLUSTER-Z1: quantum-chemical software for calculations in the s, pbasis. Institute of Surface Chemistry Nat Ac Sci of Ukraine, Kiev
19. Gao X, Zhou Z, Zhao Y et al (2008) Comparative study of carbon and BN nanographenes:
ground electronic states and energy gap engineering. J Phys Chem A 112:12677–12682
20. Noodleman L (1981) Valence bond description of antiferromagnetic coupling in transition
metal dimers. J Chem Phys 74:5737–5742
21. Illas F, de Moreira IPR, de Graaf C, Barone V (2000) Magnetic coupling in biradicals, binuclear complexes and wide-gap insolators; a survey of ab initio function and density functional
theory approaches. Theor Chem Acc 104:265–272
22. Zvezdin AK, Matveev VM, Mukhin AA et al (1985) Redkozemeljnyje iony v magnitouporjadochennykh kristallakh (Rear Earth ions in magnetically ordered crystals). Nauka,
Moskva
23. Van Fleck JH (1932) The theory of electric and magnetic susceptibilities. Oxford at the Clarendon Press, Oxford
24. Kahn O (1993) Molecular magnetism. VCH, New York
25. Koshino M, Ando T (2007) Diamagnetism in disordered graphene. Phys Rev B 75:235333.
(8 pp)
26. Nair RR, Sepioni M, Tsai I-L et al (2012) Spin-half paramagnetism in graphene induced by
point defects. Nat Phys 8:199–202
27. Sheka EF, Chernozatonskii LA (2010) Chemical reactivity and magnetism of graphene. Int J
Quant Chem 110:1938–1946
28. Sheka EF, Chernozatonskii LA (2010) Broken spin symmetry approach to chemical susceptibility and magnetism of graphenium species. J Exp Theor Phys 110:121–132
29. Shibayama Y, Sato H, Enoki T, Endo M (2000) Phys Rev Lett 84:1744
30. Enoki T, Kobayashi Y (2005) J Mater Chem 15:3999
31. Tada K, Haruyama J, Yang HX et al (2011) Graphene magnet realized by hydrogenated
graphene nanopore arrays. Appl Phys Lett 99:183111. (3 pp)
32. Tada K, Haruyama J, Yang HX et al (2011) Ferromagnetism in hydrogenated graphene
nanopore arrays. Phys Rev Lett 107:217203. (5 pp)
33. Sheka EF, Zayets VA, Ginzburg IYa (2006) Nanostructural magnetism of polymeric fullerene
crystals. J Exp Theor Phys 103:728–739
34. Boeker GF (1933) The diamagnetism of carbon tetrachloride, benzene and toluene at different
temperatures. Phys Rev 43:756–760
35. Seach MP, Dench WA (1979) Quantitative electron spectroscopy of surfaces: a standard data
base for electron inelastic mean free paths in solids. Surf Interface Anal 1:2–11
281
8. Sheka E (2009) Nanocarbons through computations: fullerenes, nanotubes, and graphene. In:
The UNESCO-EOLSS encyclopedia nanoscience and nanotechnology. UNESCO, Moscow,
pp 415–444
9. Geim AK, Novoselov KS (2007) The rise of graphene. Nat Mater 6:183–191
10. Davidson E (1998) How robust is present-day DFT? Int J Quant Chem 69:214–245
11. Kaplan I (2007) Problems in DFT with the total spin and degenerate states. Int J Quant Chem
107:2595–2603
12. Takatsuka K, Fueno T, Yamaguchi K (1978) Distribution of odd electrons in ground-state
molecules. Theor Chim Acta 48:175–183
13. Staroverov VN, Davidson ER (2000) Distribution of effectively unpaired electrons. Chem
Phys Lett 330:161–168
14. Benard MJ (1979) A study of Hartree–Fock instabilities in Cr 2 (O 2 CH) 4 and Mo 2 (O 2 CH) 4 .
J Chem Phys 71:2546–2556
15. Lain L, Torre A, Alcoba DR et al (2011) A study of the relationships between unpaired electron density, spin-density and cumulant matrices. Theor Chem Acc 128:405–410
16. Sheka EF, Chernozatonskii LA (2007) Bond length effect on odd electrons behavior in singlewalled carbon nanotubes. J Phys Chem A 111:10771–10780
17. Sheka EF (2012) Computational strategy for graphene: insight from odd electrons correlation.
Int J Quant Chem 112:3076–3090
18. Zayets VA (1990) CLUSTER-Z1: quantum-chemical software for calculations in the s, pbasis. Institute of Surface Chemistry Nat Ac Sci of Ukraine, Kiev
19. Gao X, Zhou Z, Zhao Y et al (2008) Comparative study of carbon and BN nanographenes:
ground electronic states and energy gap engineering. J Phys Chem A 112:12677–12682
20. Noodleman L (1981) Valence bond description of antiferromagnetic coupling in transition
metal dimers. J Chem Phys 74:5737–5742
21. Illas F, de Moreira IPR, de Graaf C, Barone V (2000) Magnetic coupling in biradicals, binuclear complexes and wide-gap insolators; a survey of ab initio function and density functional
theory approaches. Theor Chem Acc 104:265–272
22. Zvezdin AK, Matveev VM, Mukhin AA et al (1985) Redkozemeljnyje iony v magnitouporjadochennykh kristallakh (Rear Earth ions in magnetically ordered crystals). Nauka,
Moskva
23. Van Fleck JH (1932) The theory of electric and magnetic susceptibilities. Oxford at the Clarendon Press, Oxford
24. Kahn O (1993) Molecular magnetism. VCH, New York
25. Koshino M, Ando T (2007) Diamagnetism in disordered graphene. Phys Rev B 75:235333.
(8 pp)
26. Nair RR, Sepioni M, Tsai I-L et al (2012) Spin-half paramagnetism in graphene induced by
point defects. Nat Phys 8:199–202
27. Sheka EF, Chernozatonskii LA (2010) Chemical reactivity and magnetism of graphene. Int J
Quant Chem 110:1938–1946
28. Sheka EF, Chernozatonskii LA (2010) Broken spin symmetry approach to chemical susceptibility and magnetism of graphenium species. J Exp Theor Phys 110:121–132
29. Shibayama Y, Sato H, Enoki T, Endo M (2000) Phys Rev Lett 84:1744
30. Enoki T, Kobayashi Y (2005) J Mater Chem 15:3999
31. Tada K, Haruyama J, Yang HX et al (2011) Graphene magnet realized by hydrogenated
graphene nanopore arrays. Appl Phys Lett 99:183111. (3 pp)
32. Tada K, Haruyama J, Yang HX et al (2011) Ferromagnetism in hydrogenated graphene
nanopore arrays. Phys Rev Lett 107:217203. (5 pp)
33. Sheka EF, Zayets VA, Ginzburg IYa (2006) Nanostructural magnetism of polymeric fullerene
crystals. J Exp Theor Phys 103:728–739
34. Boeker GF (1933) The diamagnetism of carbon tetrachloride, benzene and toluene at different
temperatures. Phys Rev 43:756–760
35. Seach MP, Dench WA (1979) Quantitative electron spectroscopy of surfaces: a standard data
base for electron inelastic mean free paths in solids. Surf Interface Anal 1:2–11