Getting info from R(r)

1. 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

2. 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

6. Orbital Phases

8. 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

10. 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

11. 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

14. 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

16. 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.

17. Examples:

18. Electron configurations • Transition, lanthanide, and actinide elements

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

20. Atomic radii

21. Ionization energy and Electron affinity • Define • Explain the trends and the exceptions