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 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

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