On the Problem of He–He Bond in the Endohedral Fullerene He2@C60

  • G. A. Dolgonos Institute of Chemistry, University of Graz
  • E. S. Kryachko Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
  • T. Yu. Nikolaienko Taras Shevchenko National University of Kyiv, Faculty of Physics
Keywords: fullerene, endohedral fullerene, He@C60, He2@C60, bond, molecule, L¨owdin’s postulate

Abstract

For more than twenty years, the endohedral fullerene cavity is attracting a permanent attention of experimenters and theorists, computational chemists and physicists, who apply their efforts to simulate encapsulated atoms and molecules in the fullerene cavity on computers and analyze the arising phenomena of atomic bonding. In this work, recent developments concerning the endohedral fullerene He2@C60, in particular, its experimental observation and relevant computational works, are reviewed. On the one hand, the dihelium He2 embedded into the C60 cavity is observed experimentally. On the other hand, the computer simulation shows that each of the He atoms is characterized by an insignificant charge transfer to C60, so that the He dimer exists as a partially charged (He+b)2 entity. The key issue of the work concerns the existence of a bond between those two helium atoms. Since the bond is created between two particles, we assert that it suffices to define the bond on the basis of the molecular L¨owdin’s postulate and use it to study the He dimer in the C60 cavity in terms of the He–He potential energy well. It was analytically demonstrated that this well can contain at least one bound (ground) state. Therefore, according to L¨owdin’s postulate, which is naturally anticipated in quantum theory, the conclusion is drawn that the (He+b)2 entity is a diatomic molecule, in which two heliums are bound with each other. On the basis of those arguments, the concept of endohedral fullerene stability is proposed to be extended.

Author Biography

E. S. Kryachko, Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine

Григорій А. Довгонос, Institute of Chemistry, University of Graz, Heinrichstraße 28/IV, 8010 Graz, Austria: dolgonos@gmail.com

Тимофій Ю. Ніколаєнко, Фізичний факультет, Київський національний університет імені Тараса Шевченка, Україна 01601, місто Київ, вул. Володимирська, 64/13: tim_mail@ukr.net 

References


  1. V.V. Krasnogolovets, G.A. Puchkovska, A.A. Yakubov. Thermoinduced rearrangement of the hydrogen bond systems in liquid crystalline carboxylic acids. Mol. Cryst. Liq. Cryst. 265, 143 (1995).
    https://doi.org/10.1080/10587259508041686

  2. L.M. Babkov, E.S. Vedyaeva, S.I. Tatarinov, G.A. Puchkovska, A.A. Yakubov. Modeling of infrared spectra and structural aspects of polymorphism of mesogenes with hydrogen bonds. Mol. Cryst. Liq. Cryst. 482–483, 457 (1999).

  3. A. Barabash, T. Gavrilko, K. Eshimov, G. Puchkovska, A. Shanchuk. Vibrational spectra and lattice dynamics of hydrogen-bonded NH4IO3 crystal in the pretransition region. J. Mol. Struct. 511–512, 145 (1999).
    https://doi.org/10.1016/S0022-2860(99)00153-2

  4. T.S. Kuhn. The Structure of Scientific Revolutions (University of Chicago Press, 1970).

  5. P. Hobza, V. ? Spirko, Z. Havlas, K. Buchhold, B. Reimann, H.-D. Barth, B. Brutschy. Anti-hydrogen bond between chloroform and fluorobenzene. Chem. Phys. Lett. 299, 180 (1999).
    https://doi.org/10.1016/S0009-2614(98)01264-0

  6. B. Reimann, K. Buchhold, S. Vaupel, B. Brutschy, Z. Havlas, P. Hobza. Improper, blue-shifting hydrogen bond between fluorobenzene and fluoroform, J. Phys. Chem. A 105, 5560 (2001).
    https://doi.org/10.1021/jp003726q

  7. S.N. Delanoye, W.A. Herrebout, B.J. van der Veken. Blue shifting hydrogen bonding in the complexes of chlorofluoro haloforms with acetone-d6 and oxirane-d4, J. Am. Chem. Soc. 124, 11854 (2002).
    https://doi.org/10.1021/ja027610e

  8. H. Primas. Chemistry, Quantum Mechanics and Reductionism. Perspectives in Theoretical Chemistry (Springer, 1983).
    https://doi.org/10.1007/978-3-642-69365-6

  9. G.R. Desiraju. The book review "Essays in the philosophy of chemistry. Edited by E. Scerri and G. Fisher (Oxford University Press, 2016)". Curr. Sci. 112, 2488 (2017).

  10. T.S. Moore, T.F. Winmill. CLXXVII. – The state of amines in aqueous solution, J. Chem. Soc. 101, 1635 (1912).
    https://doi.org/10.1039/CT9120101635

  11. M. L. Huggins. Thesis in Advanced Inorganic Chemistry Course (University of California, 1919).

  12. M.L. Huggins. 50 years of hydrogen bond theory. Angew. Chem. Internat. Edit. 10, 147 (1971).
    https://doi.org/10.1002/anie.197101471

  13. W.M. Latimer, W.H. Rodebush. Polarity and ionization from the standpoint of the theory of valence, J. Am. Chem. Soc. 42, 1419 (1920).
    https://doi.org/10.1021/ja01452a015

  14. L. Pauling. The shared-electron chemical bond. Proc. Natl. Acad. Sci. USA 14, 359 (1928).
    https://doi.org/10.1073/pnas.14.4.359

  15. E.S. Kryachko. Neutral blue-shifting and blue-shifted hydrogen bonds. In Hydrogen Bonding – New Insights. Edited by S. Grabowski (Springer, 2006), p. 293.
    https://doi.org/10.1007/978-1-4020-4853-1_8

  16. G.N. Lewis. Valence and Structure of Atoms and Molecules (Chemical Catalog, 1923), Ch. 12.

  17. IUPAC, Compendium of Chemical Terminology, Gold Book, Version 2.3.3, 2014.

  18. E. Arunan, G.R. Desiraju, R.A. Klein, J. Sadlej, S. Scheiner, I. Alkorta, D.C. Clary, R.H. Crabtree, J.J. Dannenberg, P. Hobza, H.G. Kjaergaard, A.C. Legon, B. Mennucci, D.J. Nesbitt. Defining the hydrogen bond: An account (IUPAC Technical Report). Pure Appl. Chem. 83, 1619 (2011).
    https://doi.org/10.1351/PAC-REP-10-01-01

  19. G.C. Pimentel, A.L. McClellan. The Hydrogen Bond (Freeman, 1960), Section 6.1.

  20. The Hydrogen Bond. Recent Developments in Theory and Experiments. Vol. II. Structure and Spectroscopy. Edited by P. Schuster, G. Zundel, C. Sandorfy (North-Holland, 1976), Ch. 12.

  21. D. Deutsch. The Fabric of Reality: The Science of Parallel Universes and Its Implications (Viking Press, 1997).

  22. S.-G. Wang, Y.-X. Qiu, W.H.E. Schwarz. Bonding or nonbonding? Description or explanation? "Confinement bonding" of He@adamantane. Chem. Eur. J. 15, 6032 (2009).
    https://doi.org/10.1002/chem.200802596

  23. A.D. McNaught, A. Wilkinson. IUPAC Compendium of Chemical Terminology (Blackwell Scientific Publications, 1997) [on-line corrected version http://gold-book.iupac.org].

  24. H.W. Kroto, J.R. Heath, S.C. O'Brien, R.F. Curl, R.E. Smalley. C60 – buckminsterfullerene. Nature 318, 162 (1985).
    https://doi.org/10.1038/318162a0

  25. H.W. Kroto. C60 – buckminsterfullerene, the celestial sphere that fell to Earth. Angew. Chem. Int. Edit. 31, 111 (1992).
    https://doi.org/10.1002/anie.199201113

  26. H.W. Kroto, A.W. Allafand, S.P. Balm. C60: Buckmin-sterfullerene. Chem. Rev. 91, 1213 (1991).
    https://doi.org/10.1021/cr00006a005

  27. https://www.nobelprize.org/nobel_prizes/chemistry/laureates/1996/press.html.

  28. E. Osawa. Superaromaticity. Phil. Trans. Roy. Soc. London A 343, 1 (1993).
    https://doi.org/10.1098/rsta.1993.0035

  29. D.A. Bochvar, E.G. Galpern. On hypothetical systems: carbododecahedron, s-icosahedron, and carbo-s-icosahedron. Dokl. Akad. Nauk SSSR 209, 610 (1973) (in Russian).

  30. R.E. Curl. Dawn of the fullerenes: Experiment and conjecture. Rev. Mod. Phys. 69, 691 (1997).
    https://doi.org/10.1103/RevModPhys.69.691

  31. H.W. Kroto. Symmetry, space, stars, and C60. Rev. Mod. Phys. 69, 703 (1997).
    https://doi.org/10.1103/RevModPhys.69.703

  32. R. Smalley. Discovering the fullerenes. Rev. Mod. Phys. 69, 723 (1997).
    https://doi.org/10.1103/RevModPhys.69.723

  33. J.P. Hare, H.W. Kroto. A postbuckminsterfullerene view of carbon in the galaxy. Acc. Chem. Res. 25, 106 (1992).
    https://doi.org/10.1021/ar00015a002

  34. F. Diederich, R.L. Whetten. Beyond C60: the higher fullerenes. Acc. Chem. Res. 25, 119 (1992).
    https://doi.org/10.1021/ar00015a004

  35. P.J. Fagan, J.C. Calabrese, B. Malone. Metal complexes of buckminsterfullerene (C60). Acc. Chem. Res. 25, 134 (1992).
    https://doi.org/10.1021/ar00015a006

  36. R.C. Haddon. Electronic structure, conductivity, and superconductivity of alkali-metal doped C60. Acc. Chem. Res. 25, 127 (1992).
    https://doi.org/10.1021/ar00015a005

  37. J.M. Hawkins. Osmylation of C60: Proof and characterization of the soccer-ball framework. Acc. Chem. Res. 25, 150 (1992).
    https://doi.org/10.1021/ar00015a008

  38. R.D. Johnson, D.S. Bethune, C.S. Yannoni. Fullerene structure and dynamics: A magnetic-resonance potpourri. Acc. Chem. Res. 25, 169 (1992).
    https://doi.org/10.1021/ar00015a011

  39. S.W. McElvany, M.M. Ross, J.H. Callahan. Characterization of fullerenes by mass spectrometry. Acc. Chem. Res. 25, 162 (1992).
    https://doi.org/10.1021/ar00015a010

  40. R.E. Smalley. Self-assembly of the fullerenes. Acc. Chem. Res. 25, 98 (1992).
    https://doi.org/10.1021/ar00015a001

  41. J.H. Weaver. Fullerenes and fullerides: Photoemission and scanning tunneling microscopy studies. Acc. Chem. Res. 25, 143 (1992).
    https://doi.org/10.1021/ar00015a007

  42. F. Wudl. The chemical properties of buckminsterfullerene (C60) and the birth and infancy of fulleroids. Acc. Chem. Res. 25, 157 (1992).
    https://doi.org/10.1021/ar00015a009

  43. J. Cioslowski. Electronic Structure Calculations of Fullerenes and Their Derivatives (Oxford Univ. Press, 1995).

  44. A.V. Yeletskii, B.M. Smirnov. Fullerenes and carbon structures. Usp. Fiz. Nauk 165, 977 (1995) (in Russian).
    https://doi.org/10.1070/PU1995v038n09ABEH000103

  45. K. Hedberg, L. Hedberg, D.S. Bethune, C.A. Brown, H.C. Dorn, R.D. Johnson, M. Devries. Bond lengths in free molecules of buckminsterfullerene, C60, from gas-phase electron diffraction. Science 254, 410 (1991).
    https://doi.org/10.1126/science.254.5030.410

  46. M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. van der Zouw, A. Zeilinger. Wave-particle duality of C60 molecules. Nature 401, 680 (1999).
    https://doi.org/10.1038/44348

  47. A.I.M. Rae. Quantum physics – Waves, particles and fullerenes. Nature 401, 651 (1999).
    https://doi.org/10.1038/44294

  48. D.A. Garc??a-Hern?andez, A. Manchado, P. Garc??a-Lario, L. Stanghellini, E. Villaver, R.A. Shaw, R. Szczerba, J.V. Perea-Calder?on. Formation of fullerenes in H-containing planetary nebulae. Astrophys. J. Lett. 724, L39 (2010).

  49. R.C. Haddon, A.F. Hebard, M.J. Rosseinsky, D.W. Murphy, S.J. Duclos, K.B. Lyons, B. Miller,J.M. Rosamilia, R.M. Fleming, A.R. Kortan, S.H. Glarum, A.V. Makhija, A.J. Muller, R.H. Eick, S.M. Zahurak, R. Tycko, G. Dabbagh, F.A. Thiel. Conducting films of C60 and C70 by alkali-metal doping. Nature 350, 320 (1991).
    https://doi.org/10.1038/350320a0

  50. M. Kuhn et al. Atomically resolved phase transition of fullerene cations solvated in helium droplets. Nature Comm. 7, 13550 (2016).
    https://doi.org/10.1038/ncomms13550

  51. D. Xu, Y. Gao, W. Jiang. Unusual spin-polarized electron state in fullerene induced bycarbon adatom defect. Nanoscale 9, 7875 (2017).
    https://doi.org/10.1039/C7NR02335A

  52. E.K. Campbell, J.P. Maier. Perspective: C+60 and laboratory spectroscopy related to diffuse intrastellar bands. J. Chem. Phys. 146, 160901 (2017).
    https://doi.org/10.1063/1.4980119

  53. J. Cioslowski, E.D. Fleischmann. Endohedral complexes: atoms and ions inside the C60 cage. J. Chem. Phys. 94, 3730 (1991).
    https://doi.org/10.1063/1.459744

  54. "He atom trapped inside C60": https://www.youtube.com/watch?v=Cm6vXNPki-o.

  55. M. Saunders, H.A. Jim?enez-V?azquez, R.J. Cross, S. Mroczkowski, M.L. Gross, D.E. Giblin, R.J. Poreda. In-corporation of helium, neon, argon, krypton, and xenon into fullerenes using high-pressure. J. Am. Chem. Soc. 116, 2193 (1994).
    https://doi.org/10.1021/ja00084a089

  56. M. Saunders, H.A. Jim?enez-V?azquez, R.J. Cross, R.J. Poreda. Stable compounds of helium and neon: He@C60and Ne@C60. Science 259, 1428 (1993).
    https://doi.org/10.1126/science.259.5100.1428

  57. T. Weiske, H. Schwarz, D.E. Giblin, M.L. Gross. High-energy collisions of Kr@C+60 with helium. Evidence for the formation of HeKr@C+. Chem. Phys. Lett. 227, 87 (1994).
    https://doi.org/10.1016/0009-2614(94)00786-1

  58. M. B?uhl, W. Thiel. Ab initio helium NMR chemical shifts of endohedral fullerene compounds He@Cn (n = 32–180). Chem. Phys. Lett. 233, 585 (1995).
    https://doi.org/10.1016/0009-2614(94)01459-9

  59. R. Tonner, G. Frenking, M. Lein, P. Schwerdtfeger. Packed to the rafters: filling up C60 with raregas atoms. Chem. Phys. Chem. 12, 2081 (2011).
    https://doi.org/10.1002/cphc.201100360

  60. H.J. Cooper, C.L. Hendrickson, A.G. Marshall. Direct detection and quantitation of He@C60 by ultrahigh-resolution Fourier transform ion cyclotron resonance mass spectrometry. J. Am. Soc. Mass. Spectr. 13, 1349 (2002).
    https://doi.org/10.1016/S1044-0305(02)00650-5

  61. A.A. Popov, S.F. Yang, L. Dunsch. Endohedral fullerenes. Chem. Rev. 113, 5989 (2013).
    https://doi.org/10.1021/cr300297r

  62. R.J. Cross. Vibration-rotation spectroscopy of molecules trapped inside C60. J. Phys. Chem. A 112, 7152 (2008).
    https://doi.org/10.1021/jp802544p

  63. M.Z. Xu, M. Jim?enez-Ruiz, M.R. Johnson, S. Rols, S.F. Ye, M. Carravetta, M.S. Denning, X.G. Lei, Z. Ba-?ci?c, A.J. Horsewill. Confirming a predicted selection rule in inelastic neutron scattering spectroscopy: The quantum translator-rotator H2 entrapped inside C60. Phys. Rev. Lett. 113, 123001 (2014).
    https://doi.org/10.1103/PhysRevLett.113.123001

  64. T. Sternfeld, R.E. Hoffman, M. Saunders, R.J. Cross, M.S. Syamala, M. Rabinovitz. Two helium atomsinside fullerenes: Probing the internal magnetic field in C6?60 and C6?70 . J. Am. Chem. Soc. 124, 8786 (2002).
    https://doi.org/10.1021/ja025990y

  65. S. Osuna, M. Swart, M. Sol`a. The chemical reactivity of fullerenes and endohedral fullerenes: A theoretical perspective. In Carbon Bonding and Structures: Advances in Physics and Chemistry. Edited by M.V. Putz (Springer, 2011), p. 57.
    https://doi.org/10.1007/978-94-007-1733-6_4

  66. R.F. Peng, S.J. Chu, Y.M. Huang, H.J. Yu, T.S. Wang, B. Jin, Y.B. Fu, C.R. Wang. Preparation of He@C60 and He2@C60 byan explosive method. J. Mater. Chem. 19, 3602 (2009).
    https://doi.org/10.1039/b904234b

  67. M. B?uhl, S. Patchkovskii, W. Thiel. Interaction energies and NMR chemical shifts of noble gases in C60. Chem. Phys. Lett. 275, 14 (1997).
    https://doi.org/10.1016/S0009-2614(97)00733-1

  68. A. Khong, H.A. Jim?enez-V?azquez, M. Saunders, R.J. Cross, J. Laskin, T. Peres, C. Lifshitz, R. Strongin, A.B. Smith. An NMR study of He2 inside C70. J. Am. Chem. Soc. 120, 6380 (1998).
    https://doi.org/10.1021/ja980142h

  69. M.S. Syamala, R.J. Cross, M. Saunders. 129Xe NMR spectrum of xenon inside C60. J. Am. Chem. Soc. 124, 6216 (2002).
    https://doi.org/10.1021/ja012676f

  70. M. Saunders, R.J. Cross. Putting nonmetals into fullerenes. In Endofullerenes: A New Family of Carbon Clusters. Edited by T. Akasaka, Sh. Nagase (Kluwer, 2002), p. 1.
    https://doi.org/10.1007/978-94-015-9938-2_1

  71. N. Bartlett. Xenon hexafluoroplatinate(V) Xe+[Ptf6]?. Proc. Chem. Soc. 218 (1962).

  72. L. Graham, O. Graudejus, N.K. Jha, N. Bartlett. Con- cerning the nature of XePtF6. Coord. Chem. Rev. 197, 321 (2000).
    https://doi.org/10.1016/S0010-8545(99)00190-3

  73. J. Cioslowski, K. Raghavachari. Electrostatic potential, polarization, shielding, and charge transfer in endohedral complexes of the C60, C70, C76, C78, C82, and C84 clusters. J. Chem. Phys. 98, 8734 (1993).
    https://doi.org/10.1063/1.464481

  74. J. Cioslowski. Endohedral chemistry: Electronic structures of molecules trapped inside the C60 cage. J. Am. Chem. Soc. 113, 4139 (1991).
    https://doi.org/10.1021/ja00011a013

  75. Y. Wang, D. Tomanek, R.S. Ruoff. Stability of M@C60 endohedral complexes. Chem. Phys. Lett. 208, 79 (1993).
    https://doi.org/10.1016/0009-2614(93)80080-9

  76. S.C. Erwin. Electronic structure of the alkali- intercalated fullerides, endohedral fullerenes, and metal-adsorbed fullerenes. In Buckminsterfullerene. Edited by W.E. Billups, M.A. Ciofolini (VCH, 1993), P. 217.

  77. K. Jackson, E. Kaxiras, M.R. Pederson. Bonding of endohedral atoms in small carbon fullerenes. J. Phys. Chem. 98, 7805 (1994).
    https://doi.org/10.1021/j100083a010

  78. E.S. Kryachko, T.Y. Nikolaienko. He2@C60: Thoughts of the concept of a molecule and of the conceptof a bond in quantum chemistry. Int. J. Quantum Chem. 115, 859 (2015).
    https://doi.org/10.1002/qua.24916

  79. T.Y. Nikolaienko, E.S. Kryachko. Formation of dimers of light noble atoms under encapsulation within fullerene's voids. Nanoscale Res. Lett. 10, 185 (2015).
    https://doi.org/10.1186/s11671-015-0871-x

  80. M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G.A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H.P. Hratchian, A.F. Izmaylov, J. Bloino, G. Zheng, J.L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, Jr. J.A. Montgomery, J.E. Peralta, F. Ogliaro, M. Bearpark, J.J. Heyd, E. Brothers, K.N. Kudin, V.N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J.C. Burant, S.S. Iyengar, J. Tomasi, M. Cossi, N. Rega, N.J. Millam, M. Klene, J.E. Knox, JB. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, R.L. Martin, K. Morokuma, V.G. Zakrzewski, G.A. Voth, P. Salvador, J.J. Dannenberg, S. Dapprich, A.D. Daniels,? O. Farkas, J.B. Foresman, J.V. Ortiz, J. Cioslowski, D.J. Fox. Gaussian 09. Revision A.02. Gaussian Inc. (Wallingford CT, 2009).

  81. Y. Zhao, D.G. Truhlar. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: Two new functionals and systematic testing of our M06-class functionals and 12 other functionals. Theor. Chem. Acc. 120, 15 (2008).
    https://doi.org/10.1007/s00214-007-0310-x

  82. Y. Zhao, D.G. Truhlar. Density functionals with broad applicability in chemistry. Acc. Chem.Res. 41, 157 (2008).
    https://doi.org/10.1021/ar700111a

  83. H. Dodziuk, G. Dolgonos, O. Lukin. Molecular mechanics study of endohedral fullerene complexes with small molecules. Carbon 39, 1907 (2001).
    https://doi.org/10.1016/S0008-6223(00)00323-7

  84. H. Dodziuk. Modeling complexes of H2 molecules in fullerenes. Chem. Phys. Lett. 410, 39 (2005).
    https://doi.org/10.1016/j.cplett.2005.05.038

  85. G. Dolgonos. How many hydrogen molecules can be inserted into C60? Comments on the paper 'AM1 treatment of endohedrally hydrogen doped fullerene, nH2@C60' by L. T?urker and S. Erko?c [J. Mol. Struct. (Theochem) 638, 37 (2003)]. J. Mol. Struct. (Theochem) 732, 239 (2005).
    https://doi.org/10.1016/j.theochem.2005.02.017

  86. G. Dolgonos. A commentary on "Density functional calculation of hydrogen-filled C60 molecules" by C.-K. Yang [Carbon 45, 2451 (2007)]. Carbon 46, 704 (2008).
    https://doi.org/10.1016/j.carbon.2007.10.031

  87. S. Grimme, C. M?uck-Lichtenfeld, J. Antony. Noncovalent interactions between graphene sheets andin multishell (hyper)fullerenes. J. Phys. Chem. C 111, 11199 (2007).
    https://doi.org/10.1021/jp0720791

  88. H. Kruse, S. Grimme. Accurate quantum chemical description of non-covalent interactions in hydrogen filled endohedral fullerene complexes. J. Phys. Chem. C 113, 17006 (2009).
    https://doi.org/10.1021/jp904542k

  89. C. M?uck-Lichtenfeld, S. Grimme, L. Kobryn, A. Sygula. Inclusion complexes of buckycatcher with C60 and C70. Phys. Chem. Chem. Phys. 12, 7091 (2010).
    https://doi.org/10.1039/b925849c

  90. A. Krapp, G. Frenking. Is this a chemical bond? A theoretical study of Ng2@C60 (Ng = He, Ne, Ar,Kr, Xe). Chem. Eur. J. 13, 8256 (2007).
    https://doi.org/10.1002/chem.200700467

  91. J.F. Ogilvie. The nature of the chemical bond. J. Chem. Ed. 67, 280 (1990).
    https://doi.org/10.1021/ed067p280

  92. G.B. Bacskay, J.R. Reimers, S. Nordholm. The mechanism of covalent bonding. J. Chem. Ed. 74, 1494 (1997).
    https://doi.org/10.1021/ed074p1494

  93. J.N. Murrell, T.G. Wright, D. Bosanac. A search for bound levels of the Van der Waals molecules: H2(a3?+u), HeH(X2?+), LiH(a3?+) and LiHe(X2?+). J. Mol. Struct. (Theochem) 591, 1 (2002).
    https://doi.org/10.1016/S0166-1280(02)00205-1

  94. H. Olivares-Pil?on, A.V. Turbiner. H+2 and HeH: Approximating potential curves, rovibrational states. ArXiV: 1705.03608v1 (2017).

  95. J.C. Slater. The normal state of helium. Phys. Rev. 32, 349 (1928).
    https://doi.org/10.1103/PhysRev.32.349

  96. T.J. Giese, D.M. York. High-level ab initio methods for calculation of potential energy surfaces of van der Waals complexes. Int. J. Quantum. Chem. 98, 388 (2004).
    https://doi.org/10.1002/qua.20074

  97. I.G. Kaplan. Intermolecular Interactions: Physical Picture, Computational Methods and Model Potentials (Wiley, 2006).
    https://doi.org/10.1002/047086334X

  98. H.-J. Werner, P.J. Knowles, R. Lindh, F.R. Manby, M. Sch?utz, P. Celani, G. Knizia, T. Korona, R. Lindh, A. Mitrushenkov, G. Rauhut, T.B. Adler, R.D. Amos, A. Bernhardsson, A. Berning, D.L. Cooper, M.J.O. Deegan, A.J. Dobbyn, Eckert F, E. Goll, C. Hampel, A. Hesselmann, G. Hetzer, T. Hrenar, G. Jansen, C. K?oppl, Y. Liu, A.W. Lloyd, R.A. Mata, A.J. May, S.J. McNicholas, W. Meyer, M.E. Mura, A. Nicklass, P. Palmieri,

  99. H.J. Werner, P.J. Knowles, G. Knizia, F.R. Manby, M. Sch?utz. Molpro: A general – purpose quantum chemistryprogram package. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2, 242 (2012).
    https://doi.org/10.1002/wcms.82

  100. F. Luo, G.C. McBane, G. Kim, C.F. Giese, W.R. Gentry. The weakest bond: Experimental observationof helium dimer. J. Chem. Phys. 98, 3564 (1993).
    https://doi.org/10.1063/1.464079

  101. E.S. Meyer, J.C. Mester, I.F. Silvera. Comment on "The weakest bond: Experimental observation of helium dimer" [J. Chem. Phys. 98, 3564 (1993)]. J. Chem. Phys. 100, 4021 (1994).
    https://doi.org/10.1063/1.466338

  102. F. Luo, G.C. McBane, G. Kim, C.F. Giese, W.R. Gentry. Response to "Comment on 'The weakest bond: Experimental observation of heliumdimer' " [J. Chem. Phys. 100, 4021 (1994)] J. Chem. Phys. 100, 4023 (1994).
    https://doi.org/10.1063/1.466339

  103. R.J. Gdanitz. Accurately solving the electronic Schr?odinger equation of atoms and moleculesusing explicitly correlated (r?12)MR-CI. The helium dimer (He2) revisited. Mol. Phys. 99, 923 (2001).
    https://doi.org/10.1080/00268970010020609

  104. Y. Zhao, D.G. Truhlar. Comparative DFT study of van der Waals complexes: Rare-gas dimers, alkaline-earth dimers, zinc dimer, and zinc-rare-gas dimers. J. Phys. Chem. A 110, 5121 (2006).
    https://doi.org/10.1021/jp060231d

  105. W. Cencek, K. Szalewicz. Ultra-high accuracy calculations for hydrogen molecule and helium dimer. Int. J. Quantum Chem. 108, 2191(2008).
    https://doi.org/10.1002/qua.21740

  106. M. Przybytek,W. Cencek, B. Jeziorski, K. Szalewicz. Pair potential with submillikelvin uncertainties and nonadiabatic treatment of the halo state of helium dimer. Phys. Rev. Lett. 119, 123401 (2017).
    https://doi.org/10.1103/PhysRevLett.119.123401

  107. J.P. Toennies, Helium clusters and droplets: Microscopic superfluidity and other quantum effects. Mol. Phys. 111, 1879 (2013).
    https://doi.org/10.1080/00268976.2013.802039

  108. T. Havermeier, T. Jahnke, K. Kreidi, R. Wallauer, S. Voss, M. Schoffler, S. Schossler, L. Foucar, N. Neumann, J. Titze, H. Sann, M. Kuhnel, J. Voigtsberger, A. Malakzadeh, N. Sisourat,W. Schollkopf, H. Schmidt-Bocking, R.E. Grisenti,R. Dorner. Single photon double ionization of the helium dimer. Phys. Rev. Lett. 104, 153401 (2010).
    https://doi.org/10.1103/PhysRevLett.104.153401

  109. W. Sch?ollkopf, J.P. Toennies. Nondestructive mass selection of small van der Waals clusters. Science 266, 1345 (1994).
    https://doi.org/10.1126/science.266.5189.1345

  110. J. Laskin, T. Peres, C. Lifshitz, M. Saunders, R.J. Cross, A. Khong. An artificial molecule of Ne2 inside C70. Chem. Phys. Lett. 285, 7 (1998).
    https://doi.org/10.1016/S0009-2614(97)01473-5

  111. H. Dodziuk. Endohedral fullerene complexes and in-out isomerism in perhydrogenated fullerenes. In The Mathematics and Topology of Fullerenes. Edited by F. Cataldo, A. Graovac, O. Ori (Springer, 2011), p. 117.
    https://doi.org/10.1007/978-94-007-0221-9_7

  112. S. Iglesias-Groth, J. Breton, C. Girardet. Structure of the Van der Waals rare gas-C60 exohedral complexes [(C60)(RG)n; n = 1, 2]. Chem. Phys. 237, 285 (1998).
    https://doi.org/10.1016/S0301-0104(98)00296-1

  113. A. Hirsch. The Chemistry of the Fullerenes (Thieme, 1994).
    https://doi.org/10.1002/9783527619214

  114. M.J. Arce, A.L. Viado, Y.Z. An, S.I. Khan, Y. Rubin. Triple scission of a six-membered ring on the surface of C60 via consecutive pericyclic reactions and oxidative cobalt insertion. J. Am. Chem. Soc. 118, 3775 (1996).
    https://doi.org/10.1021/ja9601200

  115. L. Becker, R.J. Poreda, J.L. Bada. Extraterrestrial helium trapped in fullerenes in the sudbury impact structure. Science 272, 249 (1996).
    https://doi.org/10.1126/science.272.5259.249

  116. J.C. Hummelen, M. Prato, F. Wudl. There is a hole in my bucky. J. Am. Chem. Soc. 117,7003 (1995).
    https://doi.org/10.1021/ja00131a024

  117. R.L. Murry, G.E. Scuseria. Theoretical evidence for a C60 window mechanism. Science 263, 791(1994).
    https://doi.org/10.1126/science.263.5148.791

  118. C.M. Stanisky, J. Cross, R.J. Cross, M. Saunders, M. Murata, Y. Murata, K. Komatsu. Helium entry and escape through a chemically opened window in a fullerene. J. Am. Chem. Soc. 127, 299 (2005).
    https://doi.org/10.1021/ja045328x

  119. R. Murry, D.L. Strout, G.K. Odom, G.E. Scuseria. Role of sp3 carbon and 7-membered rings in fullerene annealing and fragmentation. Nature 366, 665 (1993).
    https://doi.org/10.1038/366665a0

  120. R. Shimshi, A.Khong, H.A. Jim?enez-V?azquez, R.J.Cross, M. Saunders. Release of noble gas atoms from inside fullerenes. Tetrahedron 52, 5143 (1996).
    https://doi.org/10.1016/0040-4020(96)00120-2

  121. R.B. Darzynkiewicz, G.E. Scuseria. Noble gas endohedral complexes of C60 buckminsterfullerene. J. Phys. Chem. A 101, 7141 (1997).
    https://doi.org/10.1021/jp971323t

  122. S. Patchkovskii, W. Thiel. How does helium get into buck-minsterfullerene? J. Am. Chem. Soc. 118, 7164(1996).
    https://doi.org/10.1021/ja9607695

  123. S. Maheshwari, D. Chakraborty, N. Sathyamurthy. Possibility of proton motion through buckminsterfullerene. Chem. Phys. Lett. 315, 181 (1999).
    https://doi.org/10.1016/S0009-2614(99)01229-4

  124. S. Osuna, M. Swart, M. Sol`a. Reactivity and regioselectivity of noble gas endohedral fullerenes Ng@C60 and Ng2@C60 (Ng = He–Xe). Chem. Eur. J. 15, 13111 (2009).
    https://doi.org/10.1002/chem.200901224

  125. C.N. Ramachandran, D. Roy, N. Sathyamurthy. Hostguest interaction in endohedral fullerenes. Chem. Phys. Lett. 461, 87 (2008).
    https://doi.org/10.1016/j.cplett.2008.06.073

  126. T. Weiske, D.K. B?ohme, J. Hru?s?ak, W. Kr?atschmer, H. Schwarz. Endohedral cluster compounds – inclusion of helium within C+60 and C+70 through collision experiments. Angew. Chem. Int. Edit. Engl. 30, 884 (1991).
    https://doi.org/10.1002/anie.199108841

  127. P.-O. L?owdin. In Molecules in Physics, Chemistry, and Biology. Vol II. Edited by J. Maruani (Kluwer, 1988), p. 3.

  128. P.-O. L?owdin. On nuclear motion and the definition of molecular structure. J. Mol. Struct. (Theochem) 76, 13 (1991).

  129. E.S. Kryachko. The force field picture of molecular shape response. Int. J. Quantum. Chem. 108, 1930 (2008).
    https://doi.org/10.1002/qua.21688

  130. E.S. Kryachko. Stability and protonation of multielectron systems: The concept of proton affinity. I. Vague limits. Int. J. Quantum Chem.111, 1792 (2011).
    https://doi.org/10.1002/qua.22811

  131. G. Leroy. Stability of chemical species. Int. J. Quantum Chem. 23, 271 (1983).
    https://doi.org/10.1002/qua.560230125

  132. B. Sutcliffe. Some observations on P.-O. L?owdin's definition of a molecule. Int. J. Quantum Chem. 90, 66 (2002).
    https://doi.org/10.1002/qua.1819

  133. R.G. Woolley, B.T. Sutcliffe. P.-O. L?owdin and the quantum mechanics of molecules. In Fundamental World of Quantum Chemistry. A Tribute to the Memory of Per-Olov L?owdin. Vol 1. Edited by E.J. Br?andas, E.S. Kryachko (Kluwer, 2003), p. 21.

  134. J. Miller. Efimov trimers imaged for the first time. Phys. Today 68, 10 (2015).
    https://doi.org/10.1063/PT.3.2834

  135. E. Cerpa, A. Krapp, R. Flores-Moreno, K.J. Donald, G. Merino. Influence of endohedral confinement on the electronic interaction between He atoms: A He2@C20H20 case study. Chem. Eur. J. 15, 1985 (2009).
    https://doi.org/10.1002/chem.200801399

  136. S.G. Wang, Y.X. Qiu, W.H.E. Schwarz. Antibond breaking – the formation and decomposition of He@adamantane: Descriptions, explanations, and meaning of concepts. Chem. Eur. J. 16, 9107 (2010).
    https://doi.org/10.1002/chem.201000789

  137. W.L. Zou, Y. Liu, W.J. Liu, T. Wang, J.E. Boggs. He@Mo6Cl8F6: A stable complex of helium. J. Phys. Chem. A 114, 646 (2010).
    https://doi.org/10.1021/jp908254r

  138. M. Khatua, S. Pan, P.K. Chattaraj. Movement of Ng2 molecules confined in a C60 cage: An ab initio molecular dynamics study. Chem. Phys. Lett. 610, 351 (2014).
    https://doi.org/10.1016/j.cplett.2014.06.052

  139. W.E. Curtis. A new band spectrum associated with helium. Proc. Roy. Soc. London Ser. A 89, 146 (1913).
    https://doi.org/10.1098/rspa.1913.0073

  140. N. Bonifaci, Z. Li, J. Eloranta, S.L. Fiedler. Interaction of helium Rydberg state molecules with dense helium. J. Phys. Chem. A 120, 9019 (2016).
    https://doi.org/10.1021/acs.jpca.6b08412

  141. . G.A. Olah, D.A. Klumpp. Superelectrophiles and Their Chemistry (Wiley, 2008).

  142. L. Pauling. The normal state of the helium molecule –ions He+2 and He2+2 . J. Chem. Phys. 1, 56 (1933).
    https://doi.org/10.1063/1.1749219

  143. J. Hern?andez-Rojas, J. Bret?on, J.M.G. Llorente. On polarization effects in endohedral fullerene complexes. Chem. Phys. Lett. 235, 160 (1995).
    https://doi.org/10.1016/0009-2614(95)00136-R

  144. L. Huang, L. Massa, J. Karle. Quantum kernels and quantum crystallography: Applications in biochemistry. In Quantum Biochemistry. Edited by C.F. Matta (Wiley-VCH, 2010), Vol. I, p. 1
    https://doi.org/10.1002/9783527629213.ch1

  145. F. Neese. The ORCA program system. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2, 73 (2012).
    https://doi.org/10.1002/wcms.81

  146. A. Sch?afer, H. Horn, R. Ahlrichs. Fully optimized contracted Gaussian-basis sets for atoms Li to Kr. J. Chem. Phys. 97, 2571 (1992).
    https://doi.org/10.1063/1.463096

  147. A. Sch?afer, C. Huber, R. Ahlrichs. Fully optimized contracted Gaussian-basis sets of triple zeta valence quality for atoms Li to Kr. J. Chem. Phys. 100, 5829 (1994).
    https://doi.org/10.1063/1.467146

  148. E.D. Glendening, C.R. Landis, F. Weinhold. Natural bond orbital methods. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2, 1 (2012).
    https://doi.org/10.1002/wcms.51

  149. A.E. Reed, L.A. Curtiss, F. Weinhold. Intermolecular interactions from a natural bond orbital,donor-acceptor viewpoint. Chem. Rev. 88, 899 (1988).
    https://doi.org/10.1021/cr00088a005

  150. F. Weinhold. Natural bond orbital methods. In Encyclopedia of Computational Chemistry, Vol. 3. Edited by P. von R. Schleyer, N.L. Allinger, T. Clark et al. (Wiley, 1998), p. 1792.

  151. F. Weinhold, C.R. Landis. Valency and Bonding: A Natural Bond Orbital Donor-Acceptor Perspective (Cambridge Univ. Press, 2005).
    https://doi.org/10.1017/CBO9780511614569

  152. A.E. Reed, R.B. Weinstock, F. Weinhold. Natural population analysis. J. Chem. Phys. 83, 735 (1985).
    https://doi.org/10.1063/1.449486

  153. T.Y. Nikolaienko, L.A. Bulavin, D.M. Hovorun. JANPA: An open source cross-platform implementation of the natural population analysis on the Java platform. Comput. Theor. Chem. 1050, 15 (2014).
    https://doi.org/10.1016/j.comptc.2014.10.002

  154. JANPA: A cross-platform open-source implementation of NPA with Java. Version: 1.03 [http://janpa.sourceforge.net ].

  155. T.Yu. Nikolaenko, E.S. Kryachko, G.A. Dolgonos. On the existence of He–He bond in the endohedral fullerene He2@C60. J. Comput. Chem. in press (2018).

  156. A. Herr?aez. Biomolecules in the computer: Jmol to the rescue. Biochem. Mol. Biol. Educ. 34, 255 (2006).
    https://doi.org/10.1002/bmb.2006.494034042644

  157. R.M. Hanson. Jmol – a paradigm shift in crystallographic visualization. J. Appl. Crystallogr. 43, 1250 (2010).
    https://doi.org/10.1107/S0021889810030256

  158. L.D. Landau, E.M. Lifshitz, Quantum Mechanics. Non-Relativistic Theory (Pergamon Press, 1981).

  159. V. Barone. Anharmonic vibrational properties by a fully automated second-order perturbative approach. J. Chem. Phys. 122, 014108 (2005).
    https://doi.org/10.1063/1.1824881

  160. T.Y. Nikolaienko, L.A. Bulavin, D.M. Hovorun. Analysis of 2-deoxy-D-ribofuranose molecule conformational capacity with the quantum-mechanical density functional method. Biopolym. Cell 27, 74 (2011).
    https://doi.org/10.7124/bc.000085

Published
2018-06-18
How to Cite
Dolgonos, G., Kryachko, E., & Nikolaienko, T. (2018). On the Problem of He–He Bond in the Endohedral Fullerene He2@C60. Ukrainian Journal of Physics, 63(4), 288. https://doi.org/10.15407/ujpe63.4.288
Section
Optics, atoms and molecules