Concise Physical Chemistry

c17 JWBS043-Rogers September 13, 2010 11:28 Printer Name: Yet to Come

THE SCF ENERGIES OF FIRST-ROW ATOMS AND IONS 281

nature” of an element is defined by its tendency to lose an electron. The next six

elements—B, C, N, O, F, and Ne—correspond to the filling of the 2px,2py, and 2pz

orbitals with two electrons each. The 3sand 3porbitals are filled in a similar way

presenting elements that are roughly similar to their first row counterparts.

Atomic energy levels are not energetically very far apart, and one should not

expect complete regularity in the table. Small energetic perturbations cause them to

shift around a bit. Sometimes the order of orbital filling,s,p,d,...is disrupted by

external fields brought in by orbital interactions, ligands, solvents, or intentionally

imposed magnetic fields.

17.9 THE SCF ENERGIES OF FIRST-ROW ATOMS AND IONS

Starting from any reasonable value ofa, one can calculate a value forb(Section

17.4.1), substitute it as a parameter at the top of aMathcad©Cprogram, and repeat

the calculation to self-consistency for other small atoms. (Ignore negligibly small

imaginary roots.) Usually only three or four iterations are necessary.

The same calculation can be carried out for the single positive ions. The energy

difference between the atom and its single+ion is the energy necessary to drive

off one electron, that is, the first ionization potential IP 1. A collection of IP 1 values

calculated in this way is depicted in Fig. 17.1. Notice the sharp drop at Li(Z= 3 ),

B(Z= 5 ), and O(Z= 8 ). The drop at Li results from the greater distance of the

probability antinode for 2srelative to 1s. The drop at B results from shielding of the

2 pxorbital by the 1s^2 electrons, and the drop at O results from the increased shielding

of the 2p^2 x 2 py 2 pzconfiguration relative to the 2px 2 py 2 pzof N(Z= 7 ).

Atomic Number

0 2 4 6 8 10 12

IP, hartrees

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

FIGURE 17.1 Calculated IP 1 for elements 1–10. Experimental results follow this pattern,

but they are not identical. A more complete graph of this kind is presented in most general

chemistry texts.