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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

Provided by:
Warwick Research Archives Portal Repository

- (2009). Asymptotics-based CI models for atoms: Properties, exact solution of a minimal model for Li to Ne, and application to atomic spectra, Multiscale Model. Simul., to appear
- (2001). Atkins’ Physical Chemistry, 7th ed.,
- (1986). Atomic energies from the large-dimension limit,
- (1930). Atomic shielding constants,
- (1980). Atomic Structure,
- (1986). Benchmark full conﬁguration-interaction calculations on H2O,
- (1984). Bound on the maximum negative ionization of atoms and molecules,P h y s .
- (1986). Dimensional interpolation for two-electron atoms,J .C h e m .P h y s .
- (1960). Discussion of the spectrum of Schr¨ odinger operators for systems of many particles,
- (1951). Fundamental properties of Hamiltonian operators of Schr¨ odinger type,T r a n s .
- (1967). Ground state energy of lithium and three-electron ions by perturbation theory,
- (1972). Handbook of Mathematical Functions with Formulas, Graphs,
- (1962). Hartree-Fock and correlation energies for 1s2s 3S and 1S states of helium-like ions,
- (1993). Inorganic Chemistry: Principles of Structure and Reactivity,H a r p e r Collins,
- (1995). Introduction to Quantum Mechanics, Prentice-Hall,
- (1984). Many-body perturbation theory using a bare-nucleus reference function: A model study,
- Mathematical Models in Quantum Chemistry, monograph in preparation.
- (1996). Modern Quantum Chemistry,
- (1994). Numerical Hartree-Fock energies of low-lying excited states of neutral atoms
- (1959). On a screening theory of atomic spectra,
- (1971). Perturbation calculation of the helium ground state energy,
- (1995). Perturbation Theory of Linear Operators,
- (1929). Quantum mechanics of many-electron systems,
- (1957). Quantum Mechanics of One-
- (2001). Quantum Mechanics,
- (1980). Quarks, atoms, and the 1/N expansion,
- (2007). R e a d e r
- (2002). Riemannian Geometry and Geometric Analysis,
- (1970). Selected Tables of Atomic Spectra
- (1957). The Calculation of Atomic Structures,
- (1977). The Hartree-Fock Method for Atoms. A Numerical Approach,
- (2003). The multiconﬁguration equations for atoms and molecules,
- (1922). The Theory of Atomic Spectra and Atomic Constitution,
- (1935). The Theory of Atomic Spectra,
- (2000). The theory of two-electron atoms: Between ground state and complete fragmentation,
- (1928). The wave mechanics of an atom with a non-Coulomb central ﬁeld. Part I—Theory and methods,
- (1930). Uber der Grundterm der Zweielecktronenprobleme von
- (1925). Zur Deutung verwickelter Spektren, insbesondere der Elemente Scandium bis

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