The Electron Bubble and the \(He_{60}\) Fullerene: A First-Principles Approach

  • R. SantamariaEmail author
  • J. Soullard
  • R. G. Barrera


Helium has a light atomic mass and, as a closed shell element, shows minimal interaction with other particles of the environment. Such properties favor the capture of an electron by liquid helium, leading to the formation of an electron bubble. The helium bubbles are of theoretical importance since different levels of quantum mechanical models can be tested for the correct prediction of a single quantum particle trapped in a cage. In this work, we propose a first-principles model of the electron bubble that takes, for the first time, the electronic structure of the cage into consideration. The model consists of a fullerene-type cage made of He atoms with an additional electron. The solution of the many-body Schroedinger equation is then performed using density functional theory, with a small and an extra-large atomic basis set. Several major improvements over the model of a particle in a rigid or soft spherical potential are assessed in this way, such as the localization and delocalization of the electron in the helium bubble, the transition of the electron to the continuum, the polarization of the He atoms building the wall, the ionic state of the electron bubble, besides the determination of relations of the volume-pressure type.


Electron bubble Confinement of an electron Electronic properties Localized–delocalized states Density functional theory 



The authors express gratitude to DGTIC-UNAM for the supercomputing facilities, and the computing staff of the Institute of Physics, UNAM, for their valuable support. RS acknowledges financial support from IF-UNAM, under project PIIF-03, and project IN-111-918 from PAPIIT-DGAPA to perform this research.


  1. 1.
    J. Poitrenaud, F.I.B. Williams, Precise measurement of effective mass of positive and negative charge carriers in liquid helium II. Phys. Rev. Lett. 29, 1230–1232 (1972). Erratum Phys. Rev. Lett. 32, 1213 (1974)ADSCrossRefGoogle Scholar
  2. 2.
    T. Ellis, P.V.E. McClintock, Effective mass of the normal negative-charge carrier in bulk \(He\) II. Phys. Rev. Lett. 48, 1834–1837 (1982)ADSCrossRefGoogle Scholar
  3. 3.
    T. Ellis, P.V.E. McClintock, R.M. Bowley, Pressure dependence of the negative ion effective mass in \(He\) II. J. Phys. C Solid State Phys. 16, L485–L489 (1983)ADSCrossRefGoogle Scholar
  4. 4.
    Y. Huang, H.J. Maris, Effective mass of an electron bubble in superfluid helium-4. J. Low. Temp. Phys. 186, 208–216 (2017)ADSCrossRefGoogle Scholar
  5. 5.
    W.T. Sommer, Liquid helium as a barrier to electrons. Phys. Rev. Lett. 12, 271–273 (1964)ADSCrossRefGoogle Scholar
  6. 6.
    L. Meyer, F. Reif, Mobilities of \(He\) ions in liquid helium. Phys. Rev. 110, 279–280 (1958)ADSCrossRefGoogle Scholar
  7. 7.
    L. Meyer, F. Reif, Scattering of thermal energy ions in superfluid liquid \(He\) by phonons and \(He^3\) atoms. Phys. Rev. Lett. 5, 1–3 (1960)ADSCrossRefGoogle Scholar
  8. 8.
    F. Reif, L. Meyer, Study of superfluidity in liquid \(He\) by ion motion. Phys. Rev. 119, 1164–1173 (1960)ADSCrossRefGoogle Scholar
  9. 9.
    G. Baym, R.G. Barrera, C.J. Pethick, Mobility of the electron bubble in superfluid helium. Phys. Rev. Lett. 22, 20–23 (1969)ADSCrossRefGoogle Scholar
  10. 10.
    R. Barrera, G. Baym, Roton-limited mobility of ions is superfluid \(He^4\). Phys. Rev. A6, 1558–1566 (1972)ADSCrossRefGoogle Scholar
  11. 11.
    K.W. Schwarz, Charge-carrier mobilities in liquid helium at the vapor pressure. Phys. Rev. A 6, 837–843 (1972)ADSCrossRefGoogle Scholar
  12. 12.
    V. Grau, M. Barranco, R. Mayol, M. Pi, Electron bubbles in liquid helium: density functional calculations of infrared absorption spectra. Phys. Rev. B 73, 064502 (2006)ADSCrossRefzbMATHGoogle Scholar
  13. 13.
    J. Elorantaa, V.A. Apkarian, A time dependent density functional treatment of superfluid dynamics: equilibration of the electron bubble in superfluid 4 \(He\). J. Phys. Chem. 117, 10139–10150 (2002)CrossRefGoogle Scholar
  14. 14.
    C. Grimes, G. Adams, Infrared spectrum of the electron bubble in liquid helium. C. Phys. Rev. B 41, 6366–6371 (1990)ADSCrossRefGoogle Scholar
  15. 15.
    C.C. Grimes, G. Adams, Infrared-absorption spectrum of the electron bubble in liquid helium. Phys. Rev. B 45, 2305–2310 (1992)ADSCrossRefGoogle Scholar
  16. 16.
    A.Y. Parshin, S.V. Pereverzev, Direct observation of optical absorption by excess electrons in liquid helium. JETP Lett. 52, 282–284 (1990)ADSGoogle Scholar
  17. 17.
    A.Y. Parshin, S.V. Pereverzev, Spectroscopic study of excess electrons in liquid helium. Sov. Phys. JETP 74, 68–76 (1992)Google Scholar
  18. 18.
    S.V. Pereverzev, A.Y. Parshin, Spectroscopic study of excess electrons in liquid helium. Physica B Phys. Condens. Matter. 197, 347–359 (1994)ADSCrossRefGoogle Scholar
  19. 19.
    G.W. Rayfield, F. Reif, Quantized vortex rings in superliquid helium. Phys. Rev. A 136, 1194–1208 (1964). Erratum Phys. Rev. 137, AB4 (1965)ADSCrossRefGoogle Scholar
  20. 20.
    H.J. Maris, On the fission of elementary particles and the evidence for fractional electrons in liquid helium. J. Low. Temp. Phys. 120, 173–204 (2000)ADSCrossRefGoogle Scholar
  21. 21.
    W. Wei, Z. Xie, L.N. Cooper, G.M. Seidel, H.J. Maris, Study of exotic ions in superfluid helium and the possible fission of the electron wave function. J. Low. Temp. Phys. 178, 78–117 (2015)ADSCrossRefGoogle Scholar
  22. 22.
    Y.H. Huang, R.E. Lanou, H.J. Maris, G.M. Seidel, B. Sethumadhavan, W. Yao, Potential for precision measurement of solar neutrino luminosity by HERON. Astropart. Phys. 30, 1–11 (2008)ADSCrossRefGoogle Scholar
  23. 23.
    F. Ancilotto, F. Toigo, Properties of an electron bubble approaching the surface of liquid helium. Phys. Rev. B 50, 12820–12830 (1994)ADSCrossRefGoogle Scholar
  24. 24.
    D. Elwell, H. Meyer, Molar volume, coefficient of thermal expansion, and related properties of liquid \(He^4\) under pressure. Phys. Rev. 164, 245–255 (1967)ADSCrossRefGoogle Scholar
  25. 25.
    D.G. Hurst, D.G. Henshaw, Atomic distribution in liquid helium by neutron diffraction. Phys. Rev. 100, 994–1001 (1955)ADSCrossRefGoogle Scholar
  26. 26.
    R.G. Parr, Y. Weitao, Density-Functional theory of atoms and molecules, Chapter 7 & 8 (Clarendon Press, Oxford, 1989). ISBN-13: 978-0195092769Google Scholar
  27. 27.
    A.D. Becke, Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A 38, 3098–3100 (1988)ADSCrossRefGoogle Scholar
  28. 28.
    Chengteh Lee, Weitao Yang, Robert G. Parr, Development of the Colle–Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 37, 785–789 (1988)ADSCrossRefGoogle Scholar
  29. 29.
    J. Soullard, R. Santamaria, S.A. Cruz, Endohedral confinement of molecular hydrogen. Chem. Phys. Lett. 391, 187–190 (2004)ADSCrossRefGoogle Scholar
  30. 30.
    J. Soullard, R. Santamaria, J. Jellinek, Pressure and size effects in endohedrally confined hydrogen clusters. J. Chem. Phys. 128, 064316 (2008)ADSCrossRefGoogle Scholar
  31. 31.
    R. Santamaria, A. Alvarez de la Paz, L. Roskop, L. Adamowicz, Statistical contact model for the confinement of atoms. J. Stat. Phys. 164, 1000–1025 (2016)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    M.G. Medvedev, I.S. Bushmarinov, Ji Sun, J.P. Perdew, K.A. Lyssenko, Density functional theory is straying from the path toward the exact functional. Science 355, 49–52 (2017)ADSCrossRefGoogle Scholar
  33. 33.
    M. Valiev, E.J. Bylaska, N. Govind, K. Kowalski, T.P. Straatsma, H.J.J. Van Dam, D. Wang, J. Nieplocha, E. Apra, T.L. Windus, W.A. de Jong, NWChem: a comprehensive and scalable open-source solution for large scale molecular simulations. Comput. Phys. Commun. 181, 1477–1489 (2010)ADSCrossRefzbMATHGoogle Scholar
  34. 34.
    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, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, T. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. 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 E.01, Gaussian, Inc., Wallingford (2013)Google Scholar
  35. 35.
    T. Kinoshita, Ground state of the helium atom. Phys. Rev. II 115, 366–374 (1959)ADSCrossRefzbMATHGoogle Scholar
  36. 36.
    T. Koga, S. Morishita, Optimal Kinoshita wave functions for helium-like atoms. Z. Phys. D Atoms Mol. Clust. 34, 71–74 (1995)CrossRefGoogle Scholar
  37. 37.
    R. Santamaria, J. Soullard, The atomization process of endohedrally confined hydrogen molecules. Chem. Phys. Lett. 414, 483–488 (2005)ADSCrossRefGoogle Scholar
  38. 38.
    A. Austin, G. Petersson, M.J. Frisch, F.J. Dobek, G. Scalmani, K. Throssell, A density functional with spherical atom dispersion terms. J. Chem. Theory Comput. 8, 4989–5007 (2012)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Instituto de Física, UNAMCd. MexicoMexico

Personalised recommendations