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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
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Friesecke, Gero and Goddard, B. (Benjamin). (2009) 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. SIAM Journal on Mathematical Analysis, Vol.41 (No.2). pp. 631664. ISSN 00361410

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Official URL: http://dx.doi.org/10.1137/080729050
Abstract
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 lowlying 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.
Item Type:  Journal Article  

Alternative Title:  Explicit large nuclear charge limit of electronic ground states for Lithium, Beryllium, Boron, Carbon, Nitrogen, Oxygen, Fluorine, Neon and basic aspects of the periodic table  
Subjects:  Q Science > QC Physics  
Divisions:  Faculty of Science > Mathematics  
Library of Congress Subject Headings (LCSH):  Quantum chemistry  Research, Electronic structure  Research, Periodic law  Research, Schrödinger equation, Particles (Nuclear physics)  Research  
Journal or Publication Title:  SIAM Journal on Mathematical Analysis  
Publisher:  Society for Industrial and Applied Mathematics  
ISSN:  00361410  
Official Date:  21 May 2009  
Dates: 


Volume:  Vol.41  
Number:  No.2  
Page Range:  pp. 631664  
Identifier:  10.1137/080729050  
Status:  Peer Reviewed  
Access rights to Published version:  Open Access  
References:  [AS72] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, 

URI:  http://wrap.warwick.ac.uk/id/eprint/2209 
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