Orbital energy penetration

In the hydrogen atom the energy is the same for the 2s and the three 2p states. In an atom with more electrons the energy is still the same for the three 2p states, but then the 2s state has a lower energy (penetrating orbits, p. 13). 

Shielding and penetration -> Qualitative understanding of orbital energies in atoms... 

Figure 8.2 Penetration and orbital energy. Radial probability distributions show that a 2s electron spends most of its time slightly farther from the nucleus than does a 2p electron but penetrates near the nucleus for a small part of the time. Penetration by the 2s electron increases its overall attraction to the nucleus thus, the 2s orbital is more stable (lower in energy) than the 2p.

What is penetration How is it related to shielding Use the penetration effect to explain the difference in relative orbital energies of a 3p and a 3d electron in the same atom. 

This will have further consequence in adjusting of corresponding sub-orbital energies in various atomic structures, depending on the degree of these orbital penetrations, providing the successive eneigetic series of... 

Fig. R.2. The hydrogen molecule in the simplest basis set of two Is Slater type orbitals (STO). (a) The overlap integral S as a function of the intemuclear distance R. (b) The penetration energy represents the difference between the eleetron- roton interaction calculated assuming the eleetronie eharge distribution and the same energy ealculated with the point charges (the eleetron is loeated on nucleus a), (c) The energies + and E- of the bonding (lower curve and of the antibonding (upper curve) orbitals. Energies and distances in a.u.

The elements of periods 5 and 6 may also form such complexes with less electronegative ligands, for example, SnCl , SnBr ", TeCl ", TeBr ". This situation is caused by a greater decrease in valence orbital energies of Ad, 5d, or 6d as compared to 3d, because the former orbitals more strongly penetrate the inner electron shells. 

It is obvious from the above that the orbital energies, or more precisely the order by which orbitals are filled, depends on the shielding effect, the effect of electron penetration, and the filling level of the neighboring orbitals. 

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