Penetrating orbitals

It might be thought that these values of y are not correct because of the fact that the electron shells actually do not consist of hydrogen-like electrons, but rather themselves of penetrating electrons. However, as Z increases the penetrating orbits become more and more hydrogen-like and these... 

The use of these expressions describing the penetrating orbit in predicting the physical properties of many-electron atoms will be exemplified in the following sections. 

The energy of removal of an outer electron in a penetrating orbit is found with our treatment to be... 

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). 

Penetrating orbitals of higher shells may be lower in energy than less penetrating orbitals of lower shells. 

Kinematical relativistic effects are caused by the fact that in the vicinity of the nucleus the electrons acquire high velocities, at a substantial fraction of the velocity of light. The direct influence of the relativistic kinematics (the so-called direct relativistic effect) is thus largest in the vicinity of the nucleus. However, as far as their impact on chemistry is concerned, relativistic effects are most important in the valence shells, which despite the small velocities of outer electrons are still strongly affected by relativistic kinematics (Schwarz et al. 1989). In particular, valence s and p orbitals possess inner tails they are core-penetrating orbitals, which means that there is a nonvanishing probability of finding their electrons close to the nucleus and thus... 

The next point to note is the existence of so-called penetrating orbits,8 i.e. the occurrence of wavefunctions of the type shown in fig. 2.5. These are wavefunctions whose innermost loop penetrates the core, but which are otherwise quite hydrogenic, as expected in the outer reaches of the atom. For large enough n, such wavefunctions recapitulate as indeed do the radial wavefunctions of H this means that, apart from a normalisation factor, the inner part changes very slowly with increasing n beyond the first few values, as can be seen in fig. 2.5, and that the radial positions of all except the outermost nodes are stable. 

The Rydberg-Ritz formula can be established empirically not only for the terms of the outer orbits, but also for orbits which penetrate the core and which we shall call penetrating orbits. It may in fact be derived theoretically for very general cases. 

The Rydberg correction for penetrating orbits is not very different2 from the radial action integral of the largest orbit, completely contained in the core, divided by h. 

Quantum defects for non-penetrating orbits (Pasadena meeting of the American Physical Society, 8 Dec. 1928). Phys. Rev. (Bull. Am. Phys. Soc.) 33 (1929) 270. Photocopy. 

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