TY - JOUR
T1 - 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
AU - Friesecke, G.
AU - Goddard, B.D.
PY - 2009/1/1
Y1 - 2009/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?partnerID=yv4JPVwI&eid=2-s2.0-70450247361&md5=61b18580fceafe05c3a81d0a68830d58
U2 - 10.1137/080729050
DO - 10.1137/080729050
M3 - Article
AN - SCOPUS:70450247361
VL - 41
SP - 631
EP - 664
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
SN - 0036-1410
IS - 2
ER -