Chemistry:Helium dimer

From HandWiki
helium dimer
Helium-dimer-2D-model.png
Names
Other names
dihelium
Identifiers
3D model (JSmol)
ChEBI
48
Properties
He2
Molar mass 8.0052 g/mol
Appearance colorless gas
Thermochemistry
1.1×10−5 kcal/mol
Related compounds
Related van der Waals molecules
 LiHe NeHe2 He3
Except where otherwise noted, data are given for materials in their standard state (at 25 °C [77 °F], 100 kPa).
☒N (what is ☑Y☒N ?)
Infobox references

The helium dimer is a van der Waals molecule with formula He2 consisting of two helium atoms.[2] This chemical is the largest diatomic molecule—a molecule consisting of two atoms bonded together. The bond that holds this dimer together is so weak that it will break if the molecule rotates, or vibrates too much. It can only exist at very low cryogenic temperatures.

Two excited helium atoms can also bond to each other in a form called an excimer. This was discovered from a spectrum of helium that contained bands first seen in 1912. Written as He2* with the * meaning an excited state, it is the first known Rydberg molecule.[3]

Several dihelium ions also exist, having net charges of negative one, positive one, and positive two. Two helium atoms can be confined together without bonding in the cage of a fullerene.

Molecule

Based on molecular orbital theory, He2 should not exist, and a chemical bond cannot form between the atoms. However, the van der Waals force exists between helium atoms as shown by the existence of liquid helium, and at a certain range of distances between atoms the attraction exceeds the repulsion. So a molecule composed of two helium atoms bound by the van der Waals force can exist.[4] The existence of this molecule was proposed as early as 1930.[5]

He2 is the largest known molecule of two atoms when in its ground state, due to its extremely long bond length.[4] The He2 molecule has a large separation distance between the atoms of about 5200 pm (= 52 ångström). This is the largest for a diatomic molecule without ro-vibronic excitation. The binding energy is only about 1.3 mK, 10−7eV[6][7] or 1.1×10−5 kcal/mol,[8] or 150 nanoelectron Volts.[9] The bond is 5000 times weaker than the covalent bond in the hydrogen molecule.[10]

Both helium atoms in the dimer can be ionized by a single photon with energy 63.86 eV. The proposed mechanism for this double ionization is that the photon ejects an electron from one atom, and then that electron hits the other helium atom and ionizes that as well.[11] The dimer then explodes as two helium cations ions repel each other with the same speed but opposite directions.[11]

A dihelium molecule bound by Van der Waals forces was first proposed by John Clarke Slater in 1928.[12]

Formation

The helium dimer can be formed in small amounts when helium gas expands and cools as it passes through a nozzle in a gas beam.[2] Only the isotope 4He can form molecules like this; 4He3He and 3He3He do not exist, as they do not have a stable bound state.[6] The amount of the dimer formed in the gas beam is of the order of one percent.[11]

Molecular ions

He2+ is a related ion bonded by a half covalent bond. It can be formed in a helium electrical discharge. It recombines with electrons to form an electronically excited He2(a3Σ+u) excimer molecule.[13] Both of these molecules are much smaller with more normally sized interatomic distances. He2+ reacts with N2, Ar, Xe, O2, and CO2 to form anions and neutral helium atoms.[14]

The helium dication dimer He22+ is extremely repulsive and would release much energy when it dissociated, around 835 kJ/mol.[15] Dynamical stability of the ion was predicted by Linus Pauling.[16] An energy barrier of 33.2 kcal/mol prevents immediate decay. This ion is isoelectronic with the hydrogen molecule.[17][18] He22+ is the smallest possible molecule with a double positive charge. It is detectable using mass spectroscopy.[15][19]

The negative helium dimer He2− is metastable and was discovered by Bae, Coggiola and Peterson in 1984 by passing He2+ through cesium vapor.[20] Subsequently, H. H. Michels theoretically confirmed its existence and concluded that the 4Πg state of He2− is bound relative to the a2Σ+u state of He2.[21] The calculated electron affinity is 0.233 eV compared to 0.077 eV for the He−[4P∘] ion. The He2− decays through the long-lived 5/2g component with τ∼350 μsec and the much shorter-lived 3/2g, 1/2g components with τ∼10 μsec. The 4Πg state has a 1σ2g1σu2σg2πu electronic configuration, its electron affinity E is 0.18±0.03 eV, and its lifetime is 135±15 μsec; only the v=0 vibrational state is responsible for this long-lived state.[22]

The molecular helium anion is also found in liquid helium that has been excited by electrons with an energy level higher than 22 eV. This takes place firstly by penetration of liquid He, taking 1.2 eV, followed by excitation of a He atom electron to the 3P level, which takes 19.8 eV. The electron can then combine with another helium atom and the excited helium atom to form He2−. He2− repels helium atoms, and so has a void around it. It will tend to migrate to the surface of liquid helium.[23]

Excimers

In a normal helium atom two electrons are found in the 1s orbital. However, if sufficient energy is added, one electron can be elevated to a higher energy level. This high energy electron can become a valence electron, and the electron that remains in the 1s orbital is a core electron. Two excited helium atoms can react with a covalent bond to form a molecule called dihelium that lasts for short times of the order of a microsecond up to second or so.[3] Excited helium atoms in the 23S state can last for up to an hour, and react like alkali metal atoms.[24]

The first clues that dihelium exists were noticed in 1900 when W. Heuse observed a band spectrum in a helium discharge. However, no information about the nature of the spectrum was published. Independently E. Goldstein from Germany and W. E. Curtis from London published details of the spectrum in 1913.[25][26] Curtis was called away to military service in World War I, and the study of the spectrum was continued by Alfred Fowler. Fowler recognised that the double headed bands fell into two sequences analogous to principal and diffuse series in line spectra.[27]

The emission band spectrum shows a number of bands that degrade towards the red, meaning that the lines thin out and the spectrum weakens towards the longer wavelengths. Only one band with a green band head at 5732 Å degrades towards the violet. Other strong band heads are at 6400 (red), 4649, 4626, 4546, 4157.8, 3777, 3677, 3665, 3356.5, and 3348.5 Å. There are also some headless bands and extra lines in the spectrum.[25] Weak bands are found with heads at 5133 and 5108.[27]

If the valence electron is in a 2s 3s, or 3d orbital, a 1Σu state results; if it is in 2p 3p or 4p, a 1Σg state results.[28] The ground state is X1Σg+.[29]

The three lowest triplet states of He2 have designations a3Σu, b3Πg and c3Σg.[30] The a3Σu state with no vibration (v=0) has a long metastable lifetime of 18 s, much longer than the lifetime for other states or inert gas excimers.[3] The explanation is that the a3Σu state has no electron orbital angular momentum, as all the electrons are in S orbitals for the helium state.[3]

The lower lying singlet states of He2 are A1Σu, B1Πg and C1Σg.[31] The excimer molecules are much smaller and more tightly bound than the van der Waals bonded helium dimer. For the A1Σu state the binding energy is around 2.5 eV, with a separation of the atoms of 103.9 pm. The C1Σg state has a binding energy 0.643 eV and the separation between atoms is 109.1 pm.[28] These two states have a repulsive range of distances with a maximum around 300 pm, where if the excited atoms approach, they have to overcome an energy barrier.[28] The singlet state A1Σ+u is very unstable with a lifetime only nanoseconds long.[32]

The spectrum of the He2 excimer contains bands due to a great number of lines due to transitions between different rotation rates and vibrational states, combined with different electronic transitions. The lines can be grouped into P, Q and R branches. But the even numbered rotational levels do not have Q branch lines, due to both nuclei being spin 0. Numerous electronic states of the molecule have been studied, including Rydberg states with the number of the shell up to 25.[33]

Helium discharge lamps produce vacuum ultraviolet radiation from helium molecules. When high energy protons hit helium gas it also produces UV emission at around 600 Å by the decay of excited highly vibrating molecules of He2 in the A1Σu state to the ground state.[34] The UV radiation from excited helium molecules is used in the pulsed discharge ionization detector (PDHID) which is capable of detecting the contents of mixed gases at levels below parts per billion.[35]

The Hopfield continuum is a band of ultraviolet light between 600 and 1000 Å in wavelength formed by photodissociation of helium molecules.[34]

One mechanism for formation of the helium molecules is firstly a helium atom becomes excited with one electron in the 21S orbital. This excited atom meets two other non excited helium atoms in a three body association and reacts to form a A1Σu state molecule with maximum vibration and a helium atom.[34]

Helium molecules in the quintet state 5Σ+g can be formed by the reaction of two spin polarised helium atoms in He(23S1) states. This molecule has a high energy level of 20 eV. The highest vibration level allowed is v=14.[36]

In liquid helium the excimer forms a solvation bubble. In a 3d state a He*2 molecule is surrounded by a bubble 12.7 Å in radius at atmospheric pressure. When pressure is increased to 24 atmospheres the bubble radius shrinks to 10.8 Å. This changing bubble size causes a shift in the fluorescence bands.[37]

state K electronic angular momentum Λ electronic spin S Hund's coupling case type energy dissociation energy eV length pm vibration levels
A1Σu 1,3,5,7 singlet 2.5 103.9
B1Πg singlet
C1Σg 0,2,4,6 singlet
a3Σu 1,3,5,7 triplet
b3Πg triplet
c3Σg 0,2,4,6 0 1 b triplet
5Σ+g quintet

Magnetic condensation

In very strong magnetic fields, (around 750,000 Tesla) and low enough temperatures, helium atoms attract, and can even form linear chains. This may happen in white dwarfs and neutron stars.[38] The bond length and dissociation energy both increase as the magnetic field increases.[39]

Use

The dihelium excimer is an important component in the helium discharge lamp.

A second use of dihelium ion is in ambient ionization techniques using low temperature plasma. In this helium atoms are excited, and then combine to yield the dihelium ion. The He2+ goes on to react with N2 in the air to make N2+. These ions react with a sample surface to make positive ions that are used in mass spectroscopy. The plasma containing the helium dimer can be as low as 30 °C in temperature, and this reduces heat damage to samples.[40]

Clusters

He2 has been shown to form van der Waals compounds with other atoms forming bigger clusters such as 24MgHe2 and 40CaHe2.[41]

The helium-4 trimer (4He3), a cluster of three helium atoms, is predicted to have an excited state which is an Efimov state.[42][43] This has been confirmed experimentally in 2015.[44]

Cage

Two helium atoms can fit inside larger fullerenes, including C70 and C84. These can be detected by the nuclear magnetic resonance of 3He having a small shift, and by mass spectrometry. C84 with enclosed helium can contain 20% He2@C84, whereas C78 has 10% and C76 has 8%. The larger cavities are more likely to hold more atoms.[45] Even when the two helium atoms are placed closely to each other in a small cage, there is no chemical bond between them.[10][46] The presence of two He atoms in a C60 fullerene cage is only predicted to have a small effect on the reactivity of the fullerene.[47] The effect is to have electrons withdrawn from the endohedral helium atoms, giving them a slight positive partial charge to produce He2δ+, which have a stronger bond than uncharged helium atoms.[48] However, by the Löwdin definition there is a bond present.[49]

The two helium atoms inside the C60 cage are separated by 1.979 Å and the distance from a helium atom to the carbon cage is 2.507 Å. The charge transfer gives 0.011 electron charge units to each helium atom. There should be at least 10 vibrational levels for the He-He pair.[49]

References

  1. ↑ "Substance Name: Dihelium". Toxnet. http://chem.sis.nlm.nih.gov/chemidplus/rn/12184-98-4. 
  2. ↑ 2.0 2.1 Schöllkopf, W; Toennies, JP (25 November 1994). "Nondestructive mass selection of small van der Waals clusters". Science 266 (5189): 1345–8. doi:10.1126/science.266.5189.1345. PMID 17772840. Bibcode: 1994Sci...266.1345S. 
  3. ↑ 3.0 3.1 3.2 3.3 Raunhardt, Matthias (2009). Generation and spectroscopy of atoms and molecules in metastable states (PDF) (Thesis). p. 84.
  4. ↑ 4.0 4.1 Kolganova, Elena; Motovilov, Alexander; Sandhas, Werner (November 2004). "Scattering length of the helium-atom–helium-dimer collision". Physical Review A 70 (5): 052711. doi:10.1103/PhysRevA.70.052711. Bibcode: 2004PhRvA..70e2711K. 
  5. ↑ Glockler, Geo. (1937). "Complex formation". Transactions of the Faraday Society 33: 224. doi:10.1039/TF9373300224.  (Subscription content?)
  6. ↑ 6.0 6.1 Al Taisan, Nada Ahmed (May 2013). Spectroscopic Detection of the Lithium Helium (LiHe) van der Waals Molecule (PDF) (Thesis). Archived from the original (PDF) on 4 March 2016. Retrieved 9 February 2015.
  7. ↑ Grisenti, R.; Schöllkopf, W.; Toennies, J.; Hegerfeldt, G.; Köhler, T.; Stoll, M. (September 2000). "Determination of the Bond Length and Binding Energy of the Helium Dimer by Diffraction from a Transmission Grating". Physical Review Letters 85 (11): 2284–2287. doi:10.1103/PhysRevLett.85.2284. PMID 10977992. Bibcode: 2000PhRvL..85.2284G. 
  8. ↑ Toennies, J. Peter. "Spectroscopy without Photons: Diffraction of Weakly Bound Complexes from Nano-Gratings". https://molspect.chemistry.ohio-state.edu/institute/toennies-abstract.htm. 
  9. ↑ Zeller, S.; Kunitski, M.; Voigtsberger, J.; Kalinin, A.; Schottelius, A.; Schober, C.; Waitz, M.; Sann, H. et al. (20 December 2016). "Imaging the He2 quantum halo state using a free electron laser". Proceedings of the National Academy of Sciences 113 (51): 14651–14655. doi:10.1073/pnas.1610688113. ISSN 0027-8424. PMID 27930299. Bibcode: 2016PNAS..11314651Z. 
  10. ↑ 10.0 10.1 Cerpa, Erick; Krapp, Andreas; Flores-Moreno, Roberto; Donald, Kelling J.; Merino, Gabriel (9 February 2009). "Influence of Endohedral Confinement on the Electronic Interaction between He atoms: A He2@C20H20 Case Study". Chemistry: A European Journal 15 (8): 1985–1990. doi:10.1002/chem.200801399. PMID 19021178. 
  11. ↑ 11.0 11.1 11.2 Havermeier, T.; Jahnke, T.; Kreidi, K.; Wallauer, R.; Voss, S.; Schöffler, M.; Schössler, S.; Foucar, L. et al. (April 2010). "Single Photon Double Ionization of the Helium Dimer". Physical Review Letters 104 (15): 153401. doi:10.1103/PhysRevLett.104.153401. PMID 20481987. Bibcode: 2010PhRvL.104o3401H. 
  12. ↑ Slater, J. (September 1928). "The Normal State of Helium". Physical Review 32 (3): 349–360. doi:10.1103/PhysRev.32.349. Bibcode: 1928PhRv...32..349S. 
  13. ↑ Callear, A. B.; Hedges, R. E. M. (16 September 1967). "Metastability of Rotationally Hot Dihelium at 77° K". Nature 215 (5107): 1267–1268. doi:10.1038/2151267a0. Bibcode: 1967Natur.215.1267C. 
  14. ↑ Jahani, H.R.; Gylys, V.T.; Collins, C.B.; Pouvesle, J.M.; Stevefelt, J. (March 1988). "The importance of three-body processes to reaction kinetics at atmospheric pressures. III. Reactions of He/sub 2//sup +/ with selected atomic and molecular reactants". IEEE Journal of Quantum Electronics 24 (3): 568–572. doi:10.1109/3.162. 
  15. ↑ 15.0 15.1 Guilhaus, Michael; Brenton, A. Gareth; Beynon, John H.; Rabrenović, Mila; von Ragué Schleyer, Paul (1985). "He22+, the experimental detection of a remarkable molecule". Journal of the Chemical Society, Chemical Communications (4): 210–211. doi:10.1039/C39850000210. 
  16. ↑ Pauling, Linus (1933). "The Normal State of the Helium Molecule-Ions He2+ and He2++". The Journal of Chemical Physics 1 (1): 56–59. doi:10.1063/1.1749219. Bibcode: 1933JChPh...1...56P. http://scarc.library.oregonstate.edu/coll/pauling/bond/notes/sci3.002.6.html. 
  17. ↑ Olah, George A.; Klumpp, Douglas A. (2008-01-03). Superelectrophiles and Their Chemistry. p. 12. ISBN 9780470185117. https://books.google.com/?id=hM3BqVkt-tAC&pg=PR12. Retrieved 19 February 2015. 
  18. ↑ Dunitz, J. D.; Ha, T. K. (1972). "Non-empirical SCF calculations on hydrogen-like molecules: the effect of nuclear charge on binding energy and bond length". Journal of the Chemical Society, Chemical Communications (9): 568. doi:10.1039/C39720000568. http://pubs.rsc.org/en/content/articlelanding/1972/c3/c39720000568. 
  19. ↑ Guilhaus, M.; Brenton, A. G.; Beynon, J. H.; Rabrenovic, M.; Schleyer, P. von Rague (14 September 1984). "First observation of He22+: charge stripping of He2+ using a double-focusing mass spectrometer". Journal of Physics B: Atomic and Molecular Physics 17 (17): L605–L610. doi:10.1088/0022-3700/17/17/010. Bibcode: 1984JPhB...17L.605G. 
  20. ↑ Bae, Y. K.; Coggiola, M. J.; Peterson, J. R. (1984-02-27). "Observation of the Molecular Helium Negative Ion He2−". Physical Review Letters 52 (9): 747–750. doi:10.1103/PhysRevLett.52.747. Bibcode: 1984PhRvL..52..747B. 
  21. ↑ Michels, H. H. (1984-04-16). "Electronic Structure of the Helium Molecular Anion He2−". Physical Review Letters 52 (16): 1413–1416. doi:10.1103/PhysRevLett.52.1413. Bibcode: 1984PhRvL..52.1413M. 
  22. ↑ Andersen, T. (1995). "Lifetimes of negative ions determined in a storage ring" (in en). Physica Scripta 1995 (T59): 230–235. doi:10.1088/0031-8949/1995/T59/031. ISSN 1402-4896. Bibcode: 1995PhST...59..230A. 
  23. ↑ Rodríguez-Cantano, Rocío; González-Lezana, Tomás; Villarreal, Pablo; Gianturco, Franco A. (14 March 2015). "A configurational study of helium clusters doped with He∗− and He2∗−". The Journal of Chemical Physics 142 (10): 104303. doi:10.1063/1.4913958. PMID 25770536. Bibcode: 2015JChPh.142j4303R. https://digital.csic.es/bitstream/10261/128098/1/A%20configurational.pdf. 
  24. ↑ Vrinceanu, D.; Sadeghpour, H. (June 2002). "He(1 ^{1}S)–He(2 ^{3}S) collision and radiative transition at low temperatures". Physical Review A 65 (6): 062712. doi:10.1103/PhysRevA.65.062712. Bibcode: 2002PhRvA..65f2712V. 
  25. ↑ 25.0 25.1 Curtis, W. E. (19 August 1913). "A New Band Spectrum Associated with Helium". Proceedings of the Royal Society of London. Series A 89 (608): 146–149. doi:10.1098/rspa.1913.0073. Bibcode: 1913RSPSA..89..146C. 
  26. ↑ Goldstein, E. (1913). "Über ein noch nicht beschriebenes, anscheinend dem Helium angehörendes Spektrum". Verhandlungen der Physikalischen Gessellschaft 15 (10): 402–412. 
  27. ↑ 27.0 27.1 Fowler, Alfred (1 March 1915). "A New Type of Series in the Band Spectrum Associated with Helium". Proceedings of the Royal Society of London. Series A 91 (627): 208–216. doi:10.1098/rspa.1915.0011. Bibcode: 1915RSPSA..91..208F. 
  28. ↑ 28.0 28.1 28.2 Guberman, S.L.; Goddard, W.A. (15 June 1972). "On the origin of energy barriers in the excited states of He2". Chemical Physics Letters 14 (4): 460–465. doi:10.1016/0009-2614(72)80240-9. Bibcode: 1972CPL....14..460G. 
  29. ↑ Kristensen, Martin; Keiding, Søren R.; van der Zande, Wim J. (December 1989). "Lifetime determination of the long-lived B 1Πg state in He2* by photofragment spectroscopy". Chemical Physics Letters 164 (6): 600–604. doi:10.1016/0009-2614(89)85266-2. Bibcode: 1989CPL...164..600K. 
  30. ↑ Hazell, I.; Norregaard, A.; Bjerre, N. (July 1995). "Highly Excited Rotational and Vibrational Levels of the Lowest Triplet States of He2: Level Positions and Fine Structure". Journal of Molecular Spectroscopy 172 (1): 135–152. doi:10.1006/jmsp.1995.1162. Bibcode: 1995JMoSp.172..135H. 
  31. ↑ Focsa, C.; Bernath, P.F.; Colin, R. (September 1998). "The Low-Lying States of He2". Journal of Molecular Spectroscopy 191 (1): 209–214. doi:10.1006/jmsp.1998.7637. Bibcode: 1998JMoSp.191..209F. 
  32. ↑ Carter, F.W.; Hertel, S.A.; Rooks, M.J.; McClintock, P.V.E.; McKinsey, D.N.; Prober, D.E. (4 May 2016). "Calorimetric observation of single He∗ 2 excimers in a 100 mK He bath". arXiv:1605.00694v1 [cond-mat.other].
  33. ↑ Panock, R.; Freeman, R.R.; Storz, R.H.; Miller, Terry A. (September 1980). "Observation of laser driven transitions to high rydberg states of He2". Chemical Physics Letters 74 (2): 203–206. doi:10.1016/0009-2614(80)85142-6. Bibcode: 1980CPL....74..203P. 
  34. ↑ 34.0 34.1 34.2 Hill, Peter (November 1989). "Ultraviolet continua of helium molecules". Physical Review A 40 (9): 5006–5016. doi:10.1103/PhysRevA.40.5006. Bibcode: 1989PhRvA..40.5006H. 
  35. ↑ Cai, Huamin; Stearns, Stanley D. (April 2013). "Pulsed discharge helium ionization detector with multiple combined bias/collecting electrodes for gas chromatography". Journal of Chromatography A 1284: 163–173. doi:10.1016/j.chroma.2013.01.100. PMID 23484651. 
  36. ↑ Beams, Timothy J.; Peach, Gillian; Whittingham, Ian B. (18 July 2006). "Spin-dipole-induced lifetime of the least-bound 5Σ+g state of He(23S1)+He(23S1)". Physical Review A 74 (1): 014702. doi:10.1103/PhysRevA.74.014702. Bibcode: 2006PhRvA..74a4702B. 
  37. ↑ Bonifaci, Nelly; Li, Zhiling; Eloranta, Jussi; Fiedler, Steven L. (4 November 2016). "Interaction of Helium Rydberg State Molecules with Dense Helium". The Journal of Physical Chemistry A 120 (45): 9019–9027. doi:10.1021/acs.jpca.6b08412. Bibcode: 2016JPCA..120.9019B. 
  38. ↑ Lai, Dong (29 August 2001). "Matter in strong magnetic fields". Reviews of Modern Physics 73 (3): 629–662. doi:10.1103/RevModPhys.73.629. 
  39. ↑ Lange, K. K.; Tellgren, E. I.; Hoffmann, M. R.; Helgaker, T. (19 July 2012). "A Paramagnetic Bonding Mechanism for Diatomics in Strong Magnetic Fields". Science 337 (6092): 327–331. doi:10.1126/science.1219703. PMID 22822146. Bibcode: 2012Sci...337..327L. 
  40. ↑ Seró, R.; Núñez, Ó.; Moyano, E. (2016). Ambient Ionisation–High-Resolution Mass Spectrometry. Comprehensive Analytical Chemistry. 71. pp. 51–88. doi:10.1016/bs.coac.2016.01.003. ISBN 9780444635723. 
  41. ↑ Liu, Min-min; Han, Hui-li; Li, Cheng-bin; Gu, Si-hong (October 2013). "Binding energies and geometry of the 24Mg–He2 and 40Ca–He2 triatomic systems". Physical Review A 88 (4): 042503. doi:10.1103/PhysRevA.88.042503. Bibcode: 2013PhRvA..88d2503L. 
  42. ↑ Kolganova, Elena A. (26 Nov 2010). "Helium Trimer in the Framework of Faddeev Approach". Physics of Particles and Nuclei 41 (7): 1108–1110. doi:10.1134/S1063779610070282. Bibcode: 2010PPN....41.1108K. https://sts-karelia09.jinr.ru/publish/Pepan/2010-v41/v-41-7/27-kol.pdf. Retrieved 28 February 2015. 
  43. ↑ Kolganova, E. A.; Motovilov, A. K.; Sandhas, W. (4 May 2011). "The 4He Trimer as an Efimov System". Few-Body Systems 51 (2–4): 249–257. doi:10.1007/s00601-011-0233-x. Bibcode: 2011FBS....51..249K. 
  44. ↑ Kunitski, Maksim; Zeller, Stefan; Voigtsberger, Jörg; Kalinin, Anton; Schmidt, Lothar Ph. H.; Schöffler, Markus; Czasch, Achim; Schöllkopf, Wieland et al. (May 2015). "Observation of the Efimov state of the helium trimer". Science 348 (6234): 551–555. doi:10.1126/science.aaa5601. PMID 25931554. Bibcode: 2015Sci...348..551K. 
  45. ↑ Wang, Guan-Wu; Saunders, Martin; Khong, Anthony; Cross, R. James (April 2000). "A New Method for Separating the Isomeric C84 Fullerenes". Journal of the American Chemical Society 122 (13): 3216–3217. doi:10.1021/ja994270x. 
  46. ↑ Krapp, Andreas; Frenking, Gernot (5 October 2007). "Is This a Chemical Bond? A Theoretical Study of Ng2@C60 (Ng=He, Ne, Ar, Kr, Xe)". Chemistry: A European Journal 13 (29): 8256–8270. doi:10.1002/chem.200700467. PMID 17639524. 
  47. ↑ Osuna, Sílvia; Swart, Marcel; Solà, Miquel (7 December 2009). "Reactivity and Regioselectivity of Noble Gas Endohedral Fullerenes Ng@C60 and Ng2@C60(Ng=He-Xe)". Chemistry: A European Journal 15 (47): 13111–13123. doi:10.1002/chem.200901224. PMID 19859923. http://iqc.udg.es/articles/pdf/iqc677.pdf. 
  48. ↑ Kryachko, Eugene S.; Nikolaienko, Tymofii Yu. (15 July 2015). "He2@C60: Thoughts of the concept of a molecule and of the concept of a bond in quantum chemistry". International Journal of Quantum Chemistry 115 (14): 859–867. doi:10.1002/qua.24916. 
  49. ↑ 49.0 49.1 Dolgonos, G. A.; Kryachko, E. S.; Nikolaienko, T. Yu (18 June 2018). "До питання Не–Не зв'язку у ендоедральному фулерені Не2@C60 (On the Problem of He–He Bond in the Endohedral Fullerene He2@C60)" (in en). Ukrainian Journal of Physics 63 (4): 288. doi:10.15407/ujpe63.4.288. ISSN 2071-0194. open access

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