Skip to main content
SpringerLink
Log in

Asymptotic neutrality of diatomic molecules

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

We use the no-binding theorem of Thomas-Fermi theory to prove that a large diatomic molecule is “almost” neutral. That is to say, that if the total nuclear charge isZ then the numberN of electrons required for the diatomic molecule to be stable satisfies\(\mathop {\lim }\limits_{Z \to \infty } N/Z = 1\). In contrast to the atomic case the emphasis here is on the lower bound onN. Our analysis will imply a new bound on the size of the molecule. These results are proved in the Born-Oppenheimer approximation. We also give bounds onN which hold for allZ by a very elementary method, not assuming the Born-Oppenheimer approximation.

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

Similar content being viewed by others

References

  1. Benguria, R.: Dependence of the Thomas-Fermi energy on the nuclear coordinates. Commun. Math. Phys.81, 419–428 (1981)

    Google Scholar 

  2. Benguria, R., Lieb, E.H.: Proof of stability of highly negative ions in the absence of the Pauli principle. Phys. Rev. Lett.50, 1771–1774 (1983)

    Google Scholar 

  3. Brezis, H., Lieb, E.H.: Long range potentials in Thomas-Fermi theory. Commun. Math. Phys.65, 231–246 (1979)

    Google Scholar 

  4. Cycon, H.L., Froese, R. G., Kirsch, W., Simon, B.: Schrödinger Operators. Berlin, Heidelberg, New York: Springer 1987

    Google Scholar 

  5. Fefferman, C.L. Seco, L.A.: Asymptotic neutrality of large ions. Commun. Math. Phys. 1989 (in press)

  6. Lieb, E.H.: Thomas-Fermi and related theories of atoms and molecules. Rev. Mod. Phys.53, 603–641 (1981)

    Google Scholar 

  7. Lieb, E.H.: Bound on the maximum negative ionization of atoms and molecules. Phys. Rev. A29, 3018–3028 (1984)

    Google Scholar 

  8. Lieb, E.H., Sigal, I.M., Simon, B., Thirring, W.: Asymptotic neutrality of large-Z ions. Commun. Math. Phys.116, 635–644 (1988)

    Google Scholar 

  9. Lieb, E.H., Thirring, W.E.: Universal nature of the van der Waals forces for Coulomb systems. Phys. Rev. A34, 40–46 (1986)

    Google Scholar 

  10. Ruskai, M.B.: Limit on the excess negative charge of a dynamic diatomic molecule. Preprint, 1989

  11. Ruskai, M.B.: Limits on stability of positive molecular ions. Lett. Math. Phys.18, 121–132 (1989)

    Google Scholar 

  12. Seco, L.A., Sigal, I.M., Solovej, J.P.: Bound on the ionization energy of large atoms. Commun. Math. Phys. (to appear)

  13. Thirring, W.E.: A course in mathematical physics, vol. III. Berlin, Heidelberg, New York: Springer 1981

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Princeton University, 08544, Princeton, NJ, USA

    Jan Philip Solovej

Authors
  1. Jan Philip Solovej
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by B. Simon

Work supported by a Danish Research Academy fellowship and U.S. National Science Foundation grant PHY-85-15288-A03

Adress from September 1989: Department of Mathematics, The University of Michigan, Ann Arbor, Michigan 48109 USA

Rights and permissions

Reprints and permissions

About this article

Cite this article

Solovej, J.P. Asymptotic neutrality of diatomic molecules. Commun.Math. Phys. 130, 185–204 (1990). https://doi.org/10.1007/BF02099881

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02099881

Keywords

Search

Navigation