CHM 501 Lecture



Example

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:

Slaters rules:

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.




Periodic Properties

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:

Absolute Electronegativity 

Absolute Hardness 

(Hardness is a measure of how easily an electron moves around in space about an atom.)



Electronegativity

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.