Multielectron Atoms

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Multielectron Atoms

• Eisberg Resnick, Ch 10

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Exchange Symmetry
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SO AS FAR AS SPATIAL DISTANCES ARE CONCERNED
Indistinguishable SYM spatial wavefns
are
closer together in space
Indistinguishable ASYM spatial wavefns
are
farther apart in space
than for Distinguishable particles
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Helium Summary
exchange-related Repulsion (spin)
1P1
l-related repulsion
spin-singlet
3P0,1,2
spin-triplet
1s2p
n-related repulsion
spin-singlet
1S0
H-basis functions
spin-triplet
3S1
1s2s
1s2
1s2 s,p
1S0
spin-singlet
x
1s1s
1s1s
1s1s
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Hartree-Fock Methods
Choose initial shape For Coulomb Potl V(r)
Solve Schro Eqn for En Yn
Insert fine structure corrections
Build atom according to This set of orbital
energies En
Loop until V(r) doesnt change much
Use the collection of YnYn to Get new electron
charge distrib
Use Gauss Law to get new V(r) shape
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Note This shows how the orbitals shift as
viewed from the perspective of an s-orbital.
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Hartree-FockEffective Charge Effects
r2 n2 ao / Zeff
En (Zeff2/n2) ( -13.6 eV )
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Hierarchy of Interactions

• Hartree-Fock Central Coulomb
• Residual Coulomb
• Stot ordering
• Ltot ordering
• Spin-Orbit

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Impact upon a 3d4p basis config
( sample )
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Zeeman
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Weak Field Zeeman

• Hartree-Fock Coulomb
• Residual Coulomb
• stot effects
• ltot effects
• Fine Structure
• spin-orbit ( jtot becomes important )
• relativistic
• Zeeman

HZeeman - mtot Bext
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Weak Field Zeeman
mtot
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Weak Field Zeeman
Jtot
mtot
project average mtot onto Jtot
g
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Weak Field Zeeman
Jtot
monto J
projection of mtot onto J onto B
Bext
HZeeman - mtot Bext
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stot0
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Strong Field Zeeman

• Hartree-Fock Coulomb
• Residual Coulomb
• stot effects
• ltot effects
• Zeeman
• Fine Structure
• spin-orbit
• relativistic

HZeeman - mtot Bext
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Strong Field Zeeman
Ltot
Stot
Bext
HZeeman - mtot Bext
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