Getting info from R(r)
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Identify the general form of the radial functions
R = (constant)(eqn in σ)(σx)(e-σ/y)
What do the plots show you about nodes? (Define node)
+/- sign of Ψ
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 σ) (σ)
(e-σ/n)
(# radial)
(# planar)
(radial diffuseness)
• 6p: R = K[(840-840σ+252σ2-28σ3+σ4)σe–σ/2
• 5d: R = K[42-14σ+σ2]σ2e-σ/2
Orbital Pictures
• Many ways to represent electron density
Figure 2.8 (p. 32) - Constant Electron Density Surfaces
Values 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
Orbital Phases
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
Electrons in Orbitals
• Hund’s 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
Orbital Energy and Shielding
• Hydrogen atom (single electron)
vs.
Multi-electron atoms
• Why does this happen?
Why does 1s fill before 2s?
Why does 2s fill before 2p?
• Radial functions, superimpose 1s, 2s, 2p
Orbital Energy and Shielding
• Hydrogen atom (single electron)
vs.
Multi-electron atoms
• Why does this happen?
Why does 1s fill before 2s?
Why does 2s fill before 2p?
• Radial functions, superimpose 1s, 2s, 2p
• Shielding, Slater’s 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
Slater’s Rules of Shielding
Z* = Z- S
Z = atomic #; S = Shielding
1. 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.
Examples:
Electron configurations
• Transition, lanthanide, and actinide elements
Covalent radii
• Difficult to obtain consistent data - covalent, atomic,
van der Waals radii all frequently used
Atomic
radii
Ionization energy and Electron
affinity
• Define
• Explain the trends and the exceptions