Skip to main content
SpringerLink
Log in

Many-electron atom confinement by a penetrable prolate spheroidal cavity

  • Regular Article - Atomic Physics
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

Confinement effects on the ground-state energy of many-electron atoms located inside a penetrable prolate spheroidal cavity are studied within a variational treatment of the Thomas–Fermi–Dirac–Weizsäcker density functional scheme. Given a confining cavity size and shape as well as barrier height, isotropic and anisotropic confinement effects on the energy evolution, ionization potentials and pressure are discussed as well as their different conditions for electron escape. Comparison of the spheroidal box results for the energy evolution with corresponding ab initio calculations for endohedral confinement of Ne within the supermolecule approach \(\hbox {Ne@}\hbox {Ne}_{\mathrm {10}}\) (\(\hbox {He}_{\mathrm {10}})\) suggests that reasonable agreement between both types of calculation is achieved provided the atom-in-a-box model incorporates the mean size of surrounding atoms with nuclei positioned at the spheroidal baseline of the cavity and a realistic choice of the mean confining barrier height.

Graphic abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All data generated in this work have been incorporated in this published paper.]

References

  1. E. Degoli, S. Ossicini, Advances in Quantum Chemistry 58, 203 (2009)

    Article  Google Scholar 

  2. T. Sako, G.H.F. Diercksen, J. Phys. B 36, 1681 (2003)

    Article  ADS  Google Scholar 

  3. R.J. Hemley, Ann. Rev. Phys. Chem. 51, 763 (2000)

    Article  ADS  Google Scholar 

  4. M. Bayer, O. Stern, P. Hawrylak, S. Fafard, A. Forchel, Nature 405, 923 (2000)

    Article  ADS  Google Scholar 

  5. R. Cammi, J. Comput. Chem. 36, 2246 (2015)

    Article  Google Scholar 

  6. D.K. Spaulding, G. Weck, P. Loubeyre, F. Datchi, P. Dumas, M. Hanfland, Nature Communications |5:5739| https://doi.org/10.1038/ncomms6739|www.nature.com/naturecommunications

  7. J.P. Connerade, AIP Conference Proceedings 1197, 1 (2009)

    ADS  Google Scholar 

  8. J. Kozowska, R. Zaleny, W. Bartkowiak, Chem. Phys. 428, 19 (2014)

    Article  Google Scholar 

  9. U. Sarkar, S. Giri, P.K. Chattaraj, J. Phys. Chem. A 113(40), 10759 (2000)

    Article  Google Scholar 

  10. V.K. Dolmatov, S.T. Manson, Phys. Rev. A 82, 023422 (2010)

    Article  ADS  Google Scholar 

  11. A. Borgoo, D.J. Tozer, P. Geerlings, F. De Proft, Phys. Chem. Chem. Phys. 11, 2862 (2009)

    Article  Google Scholar 

  12. Z.K. Tang, Y. Nozue, T. Goto, J. Phys. Soc. Japan 61, 2943 (1992)

    Article  ADS  Google Scholar 

  13. O.A. Yeshchenko, I.M. Dmitruk, S.V. Koryakov, I.P. Pundyk, Y.A. Barkanov, Solid State Comm. 133, 109 (2005)

    Article  ADS  Google Scholar 

  14. M. Rahm, R. Cammi, N.W. Ashcroft, R. Hoffmann, J. Am. Chem. Soc. 141, 10253 (2019)

    Article  Google Scholar 

  15. P.O. Fröman, S. Yngve, N. Fröman, J. Math. Phys. 28, 1813 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  16. W. Jaskolski, Physics Reports 1, 271 (1996)

    Google Scholar 

  17. J.P. Connerade, Journal of Physics: Conference Series 438, 012001 (2013)

    Google Scholar 

  18. J.R. Sabin, E. Brandas, S.A. Cruz (eds.), Advances in Quantum Chemistry, vol. 57 (Academic Press, New York, 2009)

  19. J.R. Sabin, E. Brandas, S.A. Cruz (eds.), Advances in Quantum Chemistry, vol. 58 (Academic Press, New York, 2009)

  20. K.D. Sen (ed.), Electronic Structure of Quantum Confined Atoms and Molecules (Springer, Cham, Switzerland, 2014)

  21. E. Ley-Koo, Revista Mexicana de Física 64, 326 (2018)

    Article  MathSciNet  Google Scholar 

  22. S.A. Cruz, C. Díaz-García, G. Covarrubias, Int. J. Quantum Chem. 102, 897 (2005)

    Article  ADS  Google Scholar 

  23. J. Garza, R. Vargas, N. Aquino, K.D. Sen, J. Chem. Sci. 117, 379 (2005)

    Article  Google Scholar 

  24. M. van Faassen, J. Chem. Phys. 131, 104108 (2009)

    Article  ADS  Google Scholar 

  25. J.A. Ludlow, T.G. Lee, Phys. Rev. A 91, 032507 (2015)

    Article  ADS  Google Scholar 

  26. A. Sarsa, E. Buendia, F.J. Gálvez, J. Phys. B: At. Mol. Opt. Phys. 47, 185002 (2014)

    Article  ADS  Google Scholar 

  27. S.A. Cruz, Adv. Quantum Chem. 57, 255 (2009)

    Article  ADS  Google Scholar 

  28. C. Díaz-García, S.A. Cruz, Int. J. Quantum Chem. 108, 1572 (2008)

    Article  ADS  Google Scholar 

  29. M. Rodríguez-Bautista, C. Díaz-García, A.M. Navarrete-López, R. Vargas, J. Garza, J. Chem. Phys. 143, 034103 (2015)

    Article  ADS  Google Scholar 

  30. Shuai Kang, Qiang Liu, Hui-Yan Meng, Ting-Yun Shi, Physics Letters A 360, 608 (2007)

    Article  ADS  Google Scholar 

  31. S.H. Patil, J. Phys. B: At. Mol. Opt. Phys. 34, 1049 (2001)

    Article  ADS  Google Scholar 

  32. J.P. Connerade, A.G. Lyalin, R. Semaoune, S.K. Semenov, A.V. Solovyov, J. Phys. B: At. Mol. Opt. Phys. 34, 2505 (2001)

    Article  ADS  Google Scholar 

  33. P.V. Yurenev, A.V. Scherbinin, V.I. Pupyshev, Int. J. Quantum Chem. 108, 2666 (2008)

    Article  ADS  Google Scholar 

  34. S.A. Ndengué, O. Motapon, R.L.Melingui Melono, A.J. Etindele, J. Phys. B: At. Mol. Opt. Phys. 47, 015002 (2014)

    Article  ADS  Google Scholar 

  35. R. Cabrera-Trujillo, R. Méndez-Fragoso, S.A. Cruz, J. Phys. B: At. Mol. Opt. Phys. 49, 015005 (2016)

    Article  ADS  Google Scholar 

  36. V.I. Pupyshev, Int. J. Quantum Chem. 111, 2510 (2011)

    Article  Google Scholar 

  37. G.Micca Longo, S. Longo, D. Giordano, Phys. Scr. 90, 085402 (2015)

    Article  ADS  Google Scholar 

  38. A. Corella-Madueño, R.A. Rosas, J.L. Marin, R. Riera, Int. J. Quantum Chem. 77, 509 (2000)

    Article  Google Scholar 

  39. S.A. Cruz, C. Díaz-García, H. Olivares-Pilón, R. Cabrera-Trujillo, Rad. Eff. and Defects in Solids 171, 123–134 (2016)

    Article  ADS  Google Scholar 

  40. E. Clementi, C. Roetti, Atomic Data and Nuclear Data Tables 14, 177 (1974)

    Article  ADS  Google Scholar 

  41. F.G. Allen, G.W. Gobeli, Phys. Rev. 127, 150 (1962)

    Article  ADS  Google Scholar 

  42. F. Freund, Journal of Asian Earth Sciences 41, 383 (2011). and references therein

    Article  ADS  Google Scholar 

  43. Frisch, M.J., Trucks, G.W., Schlegel, H.B., Scuseria, G.E., Robb, M.A., Cheeseman, J.R., Scalmani, G., Barone, V., Mennucci, B., Petersson, G.A., Nakatsuji, H., Caricato, M., Li, X., Hratchian, H.P.,Izmaylov, A.F., Bloino, J., Zheng, G., Sonnenberg, J.L., Hada, M., Ehara, M., Toyota, K., Fukuda, R., Hasegawa, J., Ishida, M., Nakajima, T., Honda, Y., Kitao, O., Nakai, H., Vreven, T., Montgomery, Jr., J.A., Peralta, J.E., Ogliaro, F., Bearpark, M., Heyd, J.J., Brothers, E., Kudin, K.N., Staroverov, V.N., Keith, T., Kobayashi, R., Normand, J., Raghavachari, K., Rendell, A., Burant, J.C., Iyengar, S.S., Tomasi, J., Cossi, M., Rega, N., Millam, J.M., Klene, M., Knox, J.E., Cross, J.B., Bakken, V., Adamo, C., Jaramillo, J., Gomperts, R., Stratmann, R.E., Yazyev, O., Austin, A.J., Cammi, R., Pomelli, C., Ochterski, J.W., Martin, R.L., Morokuma, K., Zakrzewski, V.G., Voth, G.A., Salvador, P., Dannenberg, J.J., Dapprich, S., Daniels, A.D., Farkas, O., Foresman, J.B., Ortiz, J.V., Cioslowski, J., Fox, D.J., Gaussian 09, Revision B.01, Gaussian Inc.: Wallingford, CT, (2010)

  44. R.L. DeKock, J.R. Strikwerda, E.X. Yu, Chemical Physics Letters 547, 120 (2012)

    Article  ADS  Google Scholar 

  45. E. Ley-Koo, S. Rubinstein, J. Chem. Phys. 71, 351 (1979)

    Article  ADS  Google Scholar 

  46. S. Mateos-Cortes, E. Ley-Koo, S.A. Cruz, Int. J. Quantum Chem. 86, 376 (2002)

    Article  Google Scholar 

  47. J.P. Connerade, V.K. Dolmatov, P.A. Lakshmi, S.T. Manson, J. Phys. B: At. Mol. Opt. Phys. 32, L239 (1999)

    Article  ADS  Google Scholar 

  48. E.M. Nascimento, F.V. Prudente, N.M. Guimaraes, A.M. Maniero, J. Phys. B: At. Mol. Opt. Phys. 44, 015003 (2011)

    Article  ADS  Google Scholar 

  49. J.P. Connerade, V.K. Dolmatov, S.T. Manson, J. Phys. B: At. Mol. Opt. Phys. 33, L275 (2000)

    Article  ADS  Google Scholar 

  50. V.K. Dolamtov, J.L. King, J. Phys. B: At. Mol. Opt. Phys. 45, 225003 (2012)

    Article  ADS  Google Scholar 

  51. V.K. Dolmatov, J. Phys. B: At. Mol. Opt. Phys. 46, 095005 (2013)

    Article  ADS  Google Scholar 

  52. F. Arias de Saavedra, E. Buendía, F.J. Gálvez, Chem. Phys. Lett. 763, 138197 (2021)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, Apartado Postal 55-534, 09340, Mexico, D.F., Mexico

    S. A. Cruz, C. Díaz-García, D. Garrido-Aguirre & R. Reyes-García

Authors
  1. S. A. Cruz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Díaz-García
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. Garrido-Aguirre
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. R. Reyes-García
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. A. Cruz.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cruz, S.A., Díaz-García, C., Garrido-Aguirre, D. et al. Many-electron atom confinement by a penetrable prolate spheroidal cavity. Eur. Phys. J. D 75, 143 (2021). https://doi.org/10.1140/epjd/s10053-021-00150-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/s10053-021-00150-3

Search

Navigation