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Explicit large nuclear charge limit of electronic ground states for Li, Be, B, C, N, O, F, Ne and basic aspects of the periodic table

By Gero Friesecke and B. (Benjamin) Goddard


This paper is concerned with the Schrödinger equation for atoms and ions with $N=1$ to 10 electrons. In the asymptotic limit of large nuclear charge $Z$, we determine explicitly the low-lying energy levels and eigenstates. The asymptotic energies and wavefunctions are in good quantitative agreement with experimental data for positive ions, and in excellent qualitative agreement even for neutral atoms ($Z=N$). In particular, the predicted ground state spin and angular momentum quantum numbers ($^1S$ for He, Be, Ne, $^2S$ for H and Li, $^4S$ for N, $^2P$ for B and F, and $^3P$ for C and O) agree with experiment in every case. The asymptotic Schrödinger ground states agree, up to small corrections, with the semiempirical hydrogen orbital configurations developed by Bohr, Hund, and Slater to explain the periodic table. In rare cases where our results deviate from this picture, such as the ordering of the lowest $^1D^o$ and $^3S^o$ states of the carbon isoelectronic sequence, experiment confirms our predictions and not Hund's

Topics: QC
Publisher: Society for Industrial and Applied Mathematics
Year: 2009
OAI identifier: oai:wrap.warwick.ac.uk:2209

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  2. (2001). Atkins’ Physical Chemistry, 7th ed.,
  3. (1986). Atomic energies from the large-dimension limit, doi
  4. (1930). Atomic shielding constants, doi
  5. (1980). Atomic Structure, doi
  6. (1986). Benchmark full configuration-interaction calculations on H2O, doi
  7. (1984). Bound on the maximum negative ionization of atoms and molecules,P h y s . doi
  8. (1986). Dimensional interpolation for two-electron atoms,J .C h e m .P h y s . doi
  9. (1960). Discussion of the spectrum of Schr¨ odinger operators for systems of many particles,
  10. (1951). Fundamental properties of Hamiltonian operators of Schr¨ odinger type,T r a n s . doi
  11. (1967). Ground state energy of lithium and three-electron ions by perturbation theory, doi
  12. (1972). Handbook of Mathematical Functions with Formulas, Graphs, doi
  13. (1962). Hartree-Fock and correlation energies for 1s2s 3S and 1S states of helium-like ions, doi
  14. (1993). Inorganic Chemistry: Principles of Structure and Reactivity,H a r p e r Collins, doi
  15. (1995). Introduction to Quantum Mechanics, Prentice-Hall,
  16. (1984). Many-body perturbation theory using a bare-nucleus reference function: A model study, doi
  17. Mathematical Models in Quantum Chemistry, monograph in preparation.
  18. (1996). Modern Quantum Chemistry,
  19. (1994). Numerical Hartree-Fock energies of low-lying excited states of neutral atoms doi
  20. (1959). On a screening theory of atomic spectra, doi
  21. (1971). Perturbation calculation of the helium ground state energy, doi
  22. (1995). Perturbation Theory of Linear Operators, doi
  23. (1929). Quantum mechanics of many-electron systems, doi
  24. (1957). Quantum Mechanics of One- doi
  25. (2001). Quantum Mechanics, doi
  26. (1980). Quarks, atoms, and the 1/N expansion, doi
  27. (2007). R e a d e r
  28. (2002). Riemannian Geometry and Geometric Analysis, doi
  29. (1970). Selected Tables of Atomic Spectra
  30. (1957). The Calculation of Atomic Structures, doi
  31. (1977). The Hartree-Fock Method for Atoms. A Numerical Approach, doi
  32. (2003). The multiconfiguration equations for atoms and molecules, doi
  33. (1922). The Theory of Atomic Spectra and Atomic Constitution, doi
  34. (1935). The Theory of Atomic Spectra, doi
  35. (2000). The theory of two-electron atoms: Between ground state and complete fragmentation, doi
  36. (1928). The wave mechanics of an atom with a non-Coulomb central field. Part I—Theory and methods, doi
  37. (1930). Uber der Grundterm der Zweielecktronenprobleme von doi
  38. (1925). Zur Deutung verwickelter Spektren, insbesondere der Elemente Scandium bis doi

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