Getting info from R(r) 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 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