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. 631-664. ISSN 0036-1410

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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 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.

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:	0036-1410
Date:	21 May 2009
Volume:	Vol.41
Number:	No.2
Page Range:	pp. 631-664
Identification Number:	10.1137/080729050
Status:	Peer Reviewed
Access rights to Published version:	Open Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/2209

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