Getting info from R(r)

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Getting info from R(r)

• Identify the general form of the radial functions
• R (constant)(eqn in s)(sx)(e-s/y)
• What do the plots show you about nodes? (Define
  node)
• /- sign of ?
• How do you determine the number of planar nodes
  in an orbital?
• How do you determine the number of spherical
  nodes in an orbital?
• Planar nodes ?Radial n- ? -1
• R (constant)(eqn in s) (s?) (e-s/n)
  ( radial) ( planar)
  (radial diffuseness)
• 6p R K(840-840s252s2-28s3s4)ses/2
• 5d R K42-14ss2s2e-s/2

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Orbital Pictures

• Many ways to represent electron densityFigure
  2.8 (p. 32) - Constant Electron Density
  SurfacesValues are fraction of maximum electron
  density
• Terms used in describing orbitals gerade (d
  orbitals), ungerade (p orbitals)
• Figure 2.6 - Boundary surfaces (calculated
  probability surfaces, 90)
• Dot pictures - Photograph of electron location
  over time

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Orbital Phases
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Electrons in Orbitals

• Recall ms, spin quantum number (1/2)
• Aufbau principle building up electrons in
  atoms, continuous increase in quantum numbers
• Pauli exclusion principle each electron has a
  unique set of quantum numbers

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Electrons in Orbitals

• Hunds rule of maximum multiplicity
  (multiplicity n 1 number of possible
  energy levels that depend on the orientation of
  the net magnetic moment in a magnetic field)
• Why maximize multiplicity?Repulsion energy (?c -
  coulombic, increases energy)Exchange energy (? e
  - negative, lowers energy)
• 2 electrons in p orbitals
• Degenerate orbitals favor maximum
  multiplicity

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Orbital Energy and Shielding

• Hydrogen atom (single electron) vs.Multi-elect
  ron atoms
• Why does this happen?Why does 1s fill before
  2s?Why does 2s fill before 2p?
• Radial functions, superimpose 1s, 2s, 2p

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Orbital Energy and Shielding

• Hydrogen atom (single electron) vs.Multi-elect
  ron atoms
• Why does this happen?Why does 1s fill before
  2s?Why does 2s fill before 2p?
• Radial functions, superimpose 1s, 2s, 2p
• Shielding, Slaters Rules (page 39)
• Do calculation for Li-Kr, main group elements
  only
• Transition metals - Cr, Fe, Ni (4s vs. 3d)
• Shielding and atomic size, IE, EA, orbital
  energies

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Slaters Rules of Shielding

• Z Z- S Z atomic S Shielding
• Write electron configuration in order of
  increasing quantum
• numbers n and l, grouping as follows
• (1s)(2s, 2p)(3s, 3p)(3d)(4s,4p)(4d)(4f)(5s, 5p),
  etc.
• 2. Electrons in groups to the right in this list
  do not shield electrons to their left.
• 3. The shielding constant S for electrons in
  these groups are determined as
• follows
• a. Each electron in the same group
  contributes 0.35 to S.
• (exception 1s electron
  contributes 0.30 to another 1s electron)
• b. Each electron in n-1 groups contribute
  0.85 to S.
• c. Each electron in n-2 or lower groups
  contribute 1.00 to S.
• 4. For nd or nf valence electrons
• a. Each electron in the same group
  contributes 0.35 to S (same as for s and p)
• b. All electrons in groups to the left
  contribute 1.00 to S.

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Examples
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Electron configurations

• Transition, lanthanide, and actinide elements

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Covalent radii

• Difficult to obtain consistent data - covalent,
  atomic, van der Waals radii all frequently used

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Atomic radii
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Ionization energy and Electron affinity

• Define
• Explain the trends and the exceptions