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Physics and chemistry of graphene. Emergentness, magnetism, mechanophysics and mechanochemistry

, ,
Peoples' Friendship University of Russia, ul. Miklukho-Maklaya, 6, Moscow, 117198, Russian Federation

Graphene is considered as a specific object whose electronic structural features are presented in the light of the general concept of emergent phenomena that arise as a result of a quantum phase transition caused by the breaking of a continuous symmetry. This review starts by examining the spin symmetry breaking of the graphene electronic system caused by the correlation of its odd pz electrons that depends on the distance between these electrons and becomes noticeable when the shortest distance, determined by the C=C bond length, exceeds the critical value Rcr=1,395 Å. The symmetry breaking is reliably predicted by universal Hartree—Fock (UHF) formalism that provides a sufficient level of quantitative self-consistent description for the problem. Empirical support has been given to and reliable certification obtained for UHF emergents such as (i) open-shell electron spin-orbitals; (ii) splitting and/or spin polarization of electron spectra; (iii) spin-mixed ground state and, as a consequence, violation of the exact spin multiplicity of electronic states; (iv) existence of local spins at zero total spin density. Using this approach greatly expands our understanding of the ground state of graphene and other sp2 nanocarbons and not only gives a clear insight into the spin features of graphene chemistry, accentuating its emergent character, but also expectedly predicts the occurrence of new graphene physics related emergents. In the latter case, symmetry breaking is relevant not only for spin systems but also for time reversal and imposes to graphene special physical properties such as ferromagnetism, superconductivity and topological nontriviality. This review shows, for the first time, that not only the ferromagnetism but also the mechanical properties of graphene are essentially emergent, extending this feature to the entire physics of graphene.

Fulltext is available at IOP
Keywords: graphene, graphane, open-shell molecules, emergent phenomena, spin symmetry breaking, universal Hartree—Fock (UHF) quantum-chemical approach, Dirac quasi-relativistic approach, hexagonal honeycomb structure, Dirac fermions, spin-orbital coupling, local spins, time reversal symmetry breaking, topological nontriviality, high temperature ferromagnetism, interfacial superconductivity, mechanical properties, static deformation, dynamic deformation, covalent bonds
PACS: 62.25.−g, 68.65.Pq, 73.22.Pr (all)
DOI: 10.3367/UFNe.2017.11.038233
URL: https://ufn.ru/en/articles/2018/7/b/
Citation: Sheka E F, Popova N A, Popova V A "Physics and chemistry of graphene. Emergentness, magnetism, mechanophysics and mechanochemistry" Phys. Usp. 61 645–691 (2018)
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Received: 16th, May 2017, revised: 6th, November 2017, 10th, November 2017

Оригинал: Шека Е Ф, Попова Н А, Попова В А «Физика и химия графена. Эмерджентность, магнетизм, механофизика и механохимия» УФН 188 720–772 (2018); DOI: 10.3367/UFNr.2017.11.038233

References (240) ↓ Cited by (8) Similar articles (20)

  1. Anderson P W Science 177 393 (1972)
  2. Laughlin R B Rev. Mod. Phys. 71 863 (1999); Laflin R B Usp. Fiz. Nauk 170 292 (2000)
  3. Laughlin R B, Pines D Proc. Natl. Acad. Sci. USA 97 28 (2000)
  4. Yannouleas C, Landman U Rep. Prog. Phys. 70 2067 (2007)
  5. Pavarini E, Koch E, Schollwöck U (Eds) Emergent Phenomena in Correlated Matter, Autumn School, Jülich, 23-27 September 2013 Vol. 3 (Jülich: Forschungszentrum Jülich and the German Research School for Simulation Sciences, 2013)
  6. Putz M V et al. Distance, Symmetry, And Topology In Carbon Nanomaterials Carbon Materials (Carbon Materials: Chemistry and Physics) Vol. 9 (Eds A R Ashrafi, M V Diudea) (New York: Springer, 2016) p. 345
  7. Hempel C, Oppenheim P Emergence: Contemporary Readings In Philosophy And Science (Eds M A Bedau, P Humphreys) (Cambridge, Mass.: MIT Press, 2008) p. 61; originally published in, Hempel C Aspects Of Scientific Explanation, And Other Essays In The Philosophy Of Science (New York: Free Press, 1965) p. 61
  8. Earman J Symmetries In Physics: Philosophical Reflections (Eds K Brading, E Castellani) (Cambridge: Cambridge Univ. Press, 2003) p. 335
  9. Butterfield J Found. Phys. 41 1065 (2011)
  10. Putz M V, Ori O Chem. Phys. Lett. 548 95 (2012)
  11. Jalbout A F, Ortiz Y P, Seligman T H Chem. Phys. Lett. 564 69 (2013)
  12. Löwdin P-O Adv. Chem. Phys. 2 207 (1959)
  13. Kitagawa Y et al. J. Phys. Chem. A 113 15041 (2009)
  14. Coe J P, Paterson M J Int. J. Quantum Chem. 116 1772 (2016)
  15. Cui Y et al. J. Chem. Phys. 139 154107 (2013)
  16. Novoselov K S et al. Nature 490 192 (2012)
  17. Sheka E Adv. Quantum Chem. 70 111 (2015)
  18. Sheka E Fullerenes: Nanochemistry, Nanomagnetism, Nanomedicine, Nanophotonics (Boca Raton, FL: CRC Press, 2011)
  19. Sheka E Spin Chemical Physics Of Graphene (Singapore: Pan Stanford, 2017)
  20. Blanquart G Int. J. Quantum Chem. 115 796 (2015)
  21. Kaplan I G Int. J. Quantum Chem. 107 2595 (2007)
  22. Jacob C R, Reiher M Int. J. Quantum Chem. 112 3661 (2012)
  23. Fucutome H Int. J. Quantum Chem. 20 5955 (1981)
  24. Takatsuka K, Fueno T, Yamaguchi K Theor. Chim. Acta 48 175 (1978)
  25. Staroverov V N, Davidson E R Chem. Phys. Lett. 330 161 (2000)
  26. Sheka E F, Zaets V A Zhurn. Fiz. Khim. 79 2250 (2005); Sheka E F, Zayets V A Russ. J. Phys. Chem. 79 2009 (2005)
  27. NWChem. Release66, http://www.nwchem-sw.org/index.php/Release66:Density_Functional_Theory_for_Molecules#ODFT_and_MULT_-
  28. Gaussian 03 Online Manual. Stable, http://www.lct.jussieu.fr/manuels/Gaussian03/g_ur/k_stable.htm
  29. Sheka E F Int. J. Quantum Chem. 114 1079 (2014)
  30. Gross L et al. Science 337 1326 (2012)
  31. Pavliček N et al. Nature Nanotechnol. 12 308 (2017)
  32. Mönig H et al. Nature Nanotechnol. 13 371 (2018)
  33. Sheka E F unpublished UHF data (2018)
  34. Van der Lit J et al. Nature Commun. 4 2023 (2013)
  35. Sheka E F Int. J. Quantum Chem. 112 3076 (2012)
  36. Sheka E F Int. J. Quantum Chem. 107 2803 (2007)
  37. Sheka E F Zhurn. Strukt. Khim. 47 613 (2006); Sheka E F J. Struct. Chem. 47 593 (2006)
  38. Warner J H et al. Nano Lett. 14 6155 (2014)
  39. Nakada K et al. Phys. Rev. B 54 17954 (1996)
  40. Barnard A S, Snook I K Modelling Simulat. Mater. Sci. Eng. 19 054001 (2011)
  41. Acik M, Chabal Y J Jpn. J. Appl. Phys. 50 070101 (2011)
  42. Mishra P C, Yadav A Chem. Phys. 402 56 (2012)
  43. Ang L S, Sulaiman S, Mohamed-Ibrahim M I Monatsh. Chem. Chem. Monthly 144 1271 (2013)
  44. Hoffmann R Angew. Chem. Int. Ed. 52 93 (2013)
  45. Mayer I Int. J. Quantum Chem. 29 73 (1986)
  46. Sheka E F, Popova N A J. Mol. Model. 18 3751 (2012)
  47. Sheka E F, Popova N A Phys. Chem. Chem. Phys. 15 5304 (2013)
  48. Elias D C et al. Science 323 610 (2009)
  49. Sofo J O, Chaudhari A S, Barber G D Phys. Rev. B 75 153401 (2007)
  50. Chuo C K, Pumera M Chem. Soc. Rev. 43 291 (2014)
  51. Liu W Mol. Phys. 108 1679 (2010)
  52. Dyall K, Faegri K Introduction To Relativistic Quantum Chemistry (New York: Oxford Univ. Press, 2007)
  53. Reiher M, Wolf A Relativistic Quantum Chemistry: The Fundamental Theory Of Molecular Science (New York: John Wiley and Sons, 2014)
  54. Löwdin P-O, Mayer I Adv. Quantum Chem. 24 79 (1992)
  55. Marian C M Reviews In Computational Chemistry Vol. 17 (Eds K B Lipkowitz, D B Boyd) (New York: John Wiley and Sons, 2001) p. 99
  56. Kim Y S et al. Int. J. Quantum Chem. 66 98 (1996)
  57. Nakano M, Seino J, Nakai H Int. J. Quantum Chem. 25356 (2017)
  58. Bučinský L et al. Comput. Theor. Chem. 1065 27 (2015)
  59. Wallace P R Phys. Rev. 71 622 (1947)
  60. Slonczewski J C, Weiss P R Phys. Rev. 109 272 (1958)
  61. Kane C L, Mele E J Phys. Rev. Lett. 95 226801 (2005)
  62. Katsnelson M I Mater. Today 10 (1 - 2) 20 (2007)
  63. Geim A K, Novoselov K S Nature Mater. 6 183 (2007)
  64. Kim P "Graphene and relativistic quantum physics" Matière De Dirac, Séminaire Poincaré XVIII (Paris: Institut Henri Poincaré, 2014) p. 1
  65. Hwang C et al. Sci. Rep. 2 590 (2012)
  66. Kara A et al. Surf. Sci. Rep. 67 1 (2012)
  67. Sheka E F Nanosyst. Phys. Chem. Math. 7 983 (2016)
  68. Zhang R et al. Phys. Chem. Chem. Phys. 18 28134 (2016)
  69. Gomes K K et al. Nature 483 306 (2012)
  70. Bhimanapati G R et al. ACS Nano 9 11509 (2015)
  71. Xu L-C, Du A, Kou L Phys. Chem. Chem. Phys. 18 27284 (2016)
  72. Wang C et al. AIP Adv. 6 035204 (2016)
  73. Li W et al. Sci. Bull. 63 282 (2018)
  74. Shao Y et al. Nano Lett. 18 2133 (2018)
  75. Wang A, Zhang X, Zhao M Nanoscale 6 11157 (2014)
  76. Zhang X, Wang A, Zhao M Carbon 84 1 (2015)
  77. Wei L, Zhang X, Zhao M Phys. Chem. Chem. Phys. 18 8059 (2016)
  78. Zhang H et al. Nano Lett. 16 6124 (2016)
  79. Si C et al. Nano Lett. 16 6584 (2016)
  80. Wang J et al. Natl. Sci. Rev. 2 22 (2015)
  81. Tsipas P et al. ACS Nano 12 1696 (2018)
  82. Kochat V et al. Sci. Adv. 1701373 (2018)
  83. Mounet N et al. Nature Nanotechnol. 13 246 (2018)
  84. Sheka E F, Orlenko E V Fullerenes Nanotubes Carbon Nanostruct. 25 289 (2017)
  85. Hohenadler M, Assaad F F J. Phys. Condens. Matter 25 143201 (2013)
  86. Mayorov A S et al. Nano Lett. 12 4629 (2012)
  87. Ortmann F et al. (Eds) Topological Insulators: Fundamentals And Perspectives (Chichester: Wiley, 2015)
  88. Schüler M et al. Phys. Rev. Lett. 111 036601 (2013)
  89. Bach V, Lieb E H, Solovej J P J. Stat. Phys. 76 3 (1994)
  90. Zheng D, Zhang G-M, Wu C Phys. Rev. B 84 205121 (2011)
  91. Lu G et al. Nanoscale 5 1353 (2013)
  92. Chernozatonskii L A i dr. Pis’ma ZhETF 85 84 (2007); Chernozatonskii L A et al. JETP Lett. 85 77 (2007)
  93. Lu N et al. J. Chem. Phys. 133 034502 (2010)
  94. Pan S, Aksay I A ACS Nano 5 4073 (2011)
  95. Nebogatikova N A et al. Phys. Chem. Chem. Phys. 17 13257 (2015)
  96. Wang X, Bai H, Shi G J. Am. Chem. Soc. 133 6338 (2011)
  97. Kang J H et al. Chem. Mater. 28 756 (2016)
  98. Balog R et al. Nature Mater. 9 315 (2010)
  99. Jørgensen J H et al. ACS Nano 10 10798 (2016)
  100. Batzill M Surf. Sci. Rep. 67 83 (2012)
  101. Vlassiouk I V et al. Nature Mater. 17 318 (2018)
  102. Edmonds M T et al. Science Adv. 3 eaao6661 (2017)
  103. Sepkhanov R A et al. Phys. Rev. A 75 063813 (2007)
  104. Haldane F D M, Raghu S Phys. Rev. Lett. 100 013904 (2008)
  105. Ling L, Joannopoulos J D, Soljačić M Nature Photon. 8 821 (2014)
  106. Tarruell L et al. Nature 483 302 (2012)
  107. Graß T et al. 2D Mater. 4 015039 (2016)
  108. Jacqmin T et al. Phys. Rev. Lett. 112 116402 (2014)
  109. Wang S et al. Nature Nanotechnol. 13 29 (2018)
  110. Hubač I, Čársky P Int. J. Quantum Chem. 24 141 (1983)
  111. Yazyev O V Rep. Prog. Phys. 73 056501 (2010)
  112. Esquinazi P et al. Phys. Rev. Lett. 91 227201 (2003)
  113. Sepioni M et al. Phys. Rev. Lett. 105 207205 (2010)
  114. Nair R R et al. Nature Phys. 8 199 (2012)
  115. Eng A Y S et al. ACS Nano 7 5930 (2013)
  116. Nair R R et al. Nature Commun. 4 2010 (2013)
  117. Wang Y et al. Nano Lett. 9 220 (2009)
  118. Sheka E F, Golubev E A Zh. Tekh. Fiz. 86 (7) 74 (2016); Sheka E F, Golubev E A Tech. Phys. 61 1032 (2016)
  119. Tada K et al. Phys. Rev. Lett. 107 217203 (2011)
  120. Ning G et al. Carbon 51 390 (2013)
  121. Magda G Z et al. Nature 514 608 (2014)
  122. Zvezdin A K i dr. Redkozemel’nye Iony v Magnitnouporyadochennykh Kristallakh (M.: Nauka, 1985)
  123. Van Vleck J H The Theory Of Electric And Magnetic Susceptibilities (Oxford: The Clarendon Press, 1932)
  124. Adamo C et al. J. Chem. Phys. 124 107101 (2006)
  125. Noodleman L J. Chem. Phys. 74 5737 (1981)
  126. Kahn O Molecular Magnetism (New York: VCH, 1993)
  127. Gao X et al. J. Phys. Chem. C 112 12677 (2008)
  128. Enoki T, Kobayashi Y J. Mater. Chem. 15 3999 (2005)
  129. Sheka E F, Zaets V A, Ginzburg I Ya Zh. Eksp. Teor. Fiz. 130 840 (2006); Sheka E F, Zaets V A, Ginzburg I Ya JETP 103 728 (2006)
  130. Nai C T et al. ACS Nano 10 1681 (2016)
  131. Hasan M Z, Kane C L Rev. Mod. Phys. 82 3045 (2010)
  132. Borovik E S, Eremenko V V, Mil’ner A S Lektsii Po Magnetizmu (M.: Fizmalit, 2005)
  133. Fu L, Kane C L Phys. Rev. Lett. 102 216403 (2009)
  134. Akhmerov A R, Nilsson J, Beenakker C W J Phys. Rev. Lett. 102 216404 (2009)
  135. Abanin D A, Pesin D A Phys. Rev. Lett. 106 136802 (2011)
  136. Dreiser J et al. ACS Nano 10 2887 (2016)
  137. Liu Q et al. Phys. Rev. Lett. 102 156603 (2009)
  138. Efimkin D K, Galitski V Phys. Rev. B 89 115431 (2014)
  139. Checkelsky J G et al. Nature Phys. 8 729 (2012)
  140. Katmis F et al. Nature 533 513 (2016)
  141. Cobas E D et al. ACS Nano 10 10357 (2016)
  142. Khoo K H et al. ACS Nano 10 11219 (2016)
  143. Valli A et al. Nano Lett. 18 2158 (2018)
  144. Zhang L et al. ACS Nano 10 3816 (2016)
  145. Zhang L et al. ACS Nano 11 6277 (2017)
  146. Song K et al. Nano Lett. 18 2033 (2018)
  147. Heersche H B et al. Nature 446 56 (2007)
  148. Tan Z B et al. Phys. Rev. Lett. 114 096602 (2015)
  149. Di Bernardo A et al. Nature Commun. 8 14024 (2017)
  150. Cao Y et al. Nature 555 151 (2018)
  151. Akinwande D et al. Extreme Mech. Lett. 13 42 (2017)
  152. Liu M et al. ACS Nano 7 10075 (2013)
  153. Tashiro K, Kobayashi M, Tadacoro H Polymer J. 24 899 (1992)
  154. Nair R R et al. Small 6 2877 (2010)
  155. Tobolsky A, Eyring H J. Chem. Phys. 11 125 (1943)
  156. Georgiou T et al. Appl. Phys. Lett. 99 093103 (2011)
  157. Ritter S K, Bryson R, Blair T K Chem. Eng. News 88 13 (2010)
  158. Kane C L, Mele E J Phys. Rev. Lett. 78 1932 (1997)
  159. Sasaki K, Saito R Prog. Theor. Phys. Suppl. 176 253 (2008)
  160. Levy N et al. Science 329 544 (2010)
  161. Georgi A et al. Nano Lett. 17 2240 (2017)
  162. Cervetti C et al. Nature Mater. 15 164 (2016)
  163. Osváth Z et al. Nanoscale 7 5503 (2015)
  164. Osváth Z et al. Nanoscale 6 6030 (2014)
  165. Gill S T et al. ACS Nano 9 5799 (2015)
  166. Vinogradov N A et al. J. Phys. Chem. C 115 9568 (2011)
  167. Li G et al. Appl. Phys. Lett. 100 013304 (2012)
  168. Sheka E F, Shaymardanova L Kh J. Mater. Chem. 21 17128 (2011)
  169. Sheka E F Topological Modelling Of Nanostructures And Extended Systems (Carbon Materials: Chemistry and Physics) Vol. 7 (Eds A R Ashrafi et al.) (Berlin: Springer, 2013) p. 137
  170. Zhang Y et al. Nano Lett. 18 2098 (2018)
  171. Wu Q et al. Chem. Commun. 49 677 (2013)
  172. Bissett M A et al. ACS Nano 7 10335 (2013)
  173. Rossi A et al. J. Phys. Chem. C 119 7900 (2015)
  174. Moritz W et al. Phys. Rev. Lett. 104 136102 (2010)
  175. Boukhvalov D W, Katsnelson M I J. Phys. Chem. C 113 14176 (2009)
  176. Goler S et al. J. Phys. Chem. C 117 11506 (2013)
  177. Castellanos-Gomez A et al. Nano Res. 58 550 (2012)
  178. Galiotis C et al. Annu Rev. Chem. Biomol. Eng. 6 121 (2015)
  179. Young R J et al. Composit. Sci. Technol. 72 1459 (2012)
  180. Suk J W et al. Phys. Status Sol. RRL 9 564 (2015)
  181. Shioya H et al. Nano Lett. 15 7943 (2016)
  182. Griep M et al. Nano Lett. 16 1657 (2016)
  183. Chen P-Y et al. Adv. Mater. 28 3564 (2016)
  184. Kudin K, Scuseria G E, Yakobson B I Phys. Rev. B 64 235406 (2001)
  185. Liu F, Ming P, Li J Phys. Rev. B 76 064120 (2007)
  186. Hemmasizadeh A et al. Thin Solid Films 516 7636 (2008)
  187. Wei X et al. Phys. Rev. B 80 205407 (2009)
  188. Shokrieh M M, Rafiee R Mater. Design 31 790 (2010)
  189. Li C, Chou T-W Int. J. Solids Struct. 40 2487 (2003)
  190. Sakhaee-Pour A Solid State Commun. 149 91 (2009)
  191. Hashemnia K, Farid M, Vatankhah R Comput. Mater. Sci. 47 79 (2009)
  192. Tsai J-L, Tu J-F Mater. Design 31 194 (2010)
  193. Bu H et al. Phys. Lett. A 373 3359 (2009)
  194. Van Lier G et al. Chem. Phys. Lett. 326 181 (2000)
  195. Gao Y, Hao P Physica E 41 1561 (2009)
  196. Topsakal M, Ciraci S Phys. Rev. B 81 024107 (2010)
  197. Sheka E F et al. Zh. Eksp. Teor. Fiz. 139 695 (2011); Sheka E F et al. JETP 112 602 (2011)
  198. Sheka E F et al. J. Mol. Model. 17 1121 (2011)
  199. Popova N A "Gidrirovanie i deformatsiya grafena v priblizhenii molekulyarnoi teorii" Diss. ... kand. fiz.-mat. nauk (M.: RUDN, 2011)
  200. Sheka E F, Popova V A, Popova N A Advances In Quantum Methods And Applications In Chemistry, Physics, And Biology (Progress in Theoretical Chemistry and Physics) Vol. 27 (Eds-in-Chief J Maruani, S Wilson) (Berlin: Springer, 2013) p. 285
  201. Maeda S et al. Int. J. Quantum Chem. 115 258 (2015)
  202. Dewar M J S Fortschr. Chem. Forsch. 23 1 (1971)
  203. Khavryutchenko V et al. Phys. Low-Dim. Struct. 6 65 (1995)
  204. Nikitina E A et al. J. Phys. Chem. A 103 11355 (1999)
  205. Lee C et al. Science 321 385 (2008)
  206. Jin C et al. Phys. Rev. Lett. 102 205501 (2009)
  207. Jhon Y I et al. Carbon 66 619 (2014)
  208. Zhou C et al. Nanoscale Res. Lett. 9 26 (2007)
  209. Sahin H et al. WIREs Comput. Mol. Sci. 5 255 (2015)
  210. Savchenko A Science 323 589 (2009)
  211. Munos E et al. Diam. Rel. Mat. 19 368 (2010)
  212. Topsakal V, Cahangirov S, Ciraci S Appl. Phys. Lett. 96 091912 (2010)
  213. Leenaerts O et al. Phys. Rev. B 82 195436 (2010)
  214. Cadelano E et al. Phys. Rev. B 82 235414 (2010)
  215. Scarpa F, Chowdhury R, Adhikari S Phys. Lett. 375 2071 (2011)
  216. Pei Q X, Zhang Y W, Shenoy V B Carbon 48 898 (2010)
  217. Popova N A, Sheka E F J. Phys. Chem. C 115 23745 (2011)
  218. Colombo L, Giordano S Rep. Prog. Phys. 74 116501 (2011)
  219. Ishigaki et al. Chem 4 795 (2018)
  220. Gribov L A, Dement’ev V A, Todorovskii A T Interpretirovannye Kolebatel’nye Spektry Alkanov, Alkenov i Proizvodnykh Benzola (M.: Nauka, 1986)
  221. Eliashberg M E Interpretirovannye Kolebatel’nye Spektry Uglevodorodov — Proizvodnykh Tsiklogeksana i Tsiklopentana (M.: Nauka, 1988)
  222. Mohr M et al. Phys. Rev. B 76 035439 (2007)
  223. Adamyan V, Zavalniuk V J. Phys. Condens. Matter. 23 015402 (2011)
  224. Peelaers H et al. Appl. Phys. Lett. 98 051914 (2011)
  225. Sun C Q et al. J. Phys. Chem. C 113 16464 (2009)
  226. Burmistrov I S et al. Phys. Rev. B 97 125402 (2018)
  227. Laughlin R B Phys. Rev. Lett. 50 1395 (1983)
  228. Arovas D, Schrieffer J R, Wilczek F Phys. Rev. Lett. 53 722 (1984)
  229. Ki D-K et al. Nano Lett. 14 2135 (2014)
  230. Diankov G et al. Nature Commun. 7 13908 (2016)
  231. Papić Z et al. Phys. Rev. X 8 011037 (2018)
  232. Burton H G A, Gross M, Thom A J W J. Chem. Theory Comput. 14 607 (2018)
  233. Lestrange P J et al. J. Chem. Theory Comput. 14 588 (2018)
  234. Krylov A I Reviews In Computational Chemistry Vol. 30 (Eds A L Parrill, K B Lipkowitz) (New York: John Wiley and Sons, 2017) p. 151
  235. Kaplan I Mol. Phys. 116 658 (2018)
  236. Orms N et al. J. Chem. Theory Comput. 14 638 (2018)
  237. Head-Gordon M Chem. Phys. Lett. 372 508 (2003)
  238. Boulanger N et al. Phys. Chem. Chem. Phys. 20 4422 (2018)
  239. Avvisati G et al. Nano Lett. 18 2268 (2018)
  240. Sadovnichii R V i dr. Tr. Karel’skogo Nauchnogo Tsentra RAN Geologiya dokembriya (2) 73 (2016)

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