Find all the terms for the d3 electron configuration. Predict the energy order for the terms.
For a more quantitative consideration of multielectron systems requires better wavefunctions or the introduction of fudge factors. We convert multielectron systems to hydrogen-like systems by introducing the effective nuclear charge, Z*:
Z* = Z - S
Z* = effective nuclear charge
Z = true nuclear charge
S = screening or shielding constant
We can find S a number of ways: Clementi and Raimondi used accurate numerical calculations to fit S to experiment.
An easier, less quantitatively accurate method is Slaters: he used the radial (n) and nodal (l) characteristics of hydrogenic wavefunctions to establish shielding constants:
1. Write electron configurations according to principal quantum number, grouping s and p orbitals: (1s)(2s2p)(3s3p)(3d)(4s4p)(4d)(4f)...
2. Any electron to the right of the selected electron is ignored (contributes 0 to S)
3. If the electron under consideration is in an (nsnp) group:
a) all other electrons in the same group contribute 0.35/e to S (except 1s, 0.30)
b) all electrons in the n-1 shell contribute 0.85/e to S
c) all electrons in n-2 and lower shells contribute 1.00/e to S
4. If the electron under consideration is in an (nd) or (nf) group:
a) all other electrons in the same group contribute 0.35/e to S
b) all electrons to the left of the selected group contribute 1.00/e to S
Periodic Trends in Z* : Z* increases to the right on the Periodic Table, increases as go down the Periodic Table.
Ionization Potential (IP)
A(g) A+(g) + e
IP is thermodynamically positive (not favored) generally follows Z*
Electron configurations can account for some of the fine structure, but not all.
Electron Affinity (EA)
A(g) + e A(g)
Usually thermodynamically negative but reported with the wrong sign (i.e., reported as a positive number for most elements)
Related Atomic Properties:
(Hardness is a measure of how easily an electron moves around in space about an atom.)
Pauling: "the tendency of an atom in a bond to attract electrons to itself"
Paulings thermodynamic quantitation:
= DAB -(DAA + DBB)/2
D are bond energies between A and A, B and B, or A and B
This requires that all bonds be of the same type (single, double, triple, etc); these can be hard to find for some atoms; requires an arbitrary standard (H = 2.2) - this gives F as 4.0. Pauling was able to assign electronegativities to most of the Periodic Table: generally increases to the right and decreases down the Table
Allred and Rochow suggested that electronegativities are due to an electrostatic force:
Z* is the effective nuclear charge calculated using Slaters rules
rcov is the covalent radius (1/2 the homonuclear bond distance)
This better accounts for some of the subtleties of the Periodic Table but generally is pretty close to Paulings values.