Orbitals core-penetrating

In the first two chapters we have seen that the Na atom, for example, differs from the H atom because the valence electron orbits about a finite sized Na+ core, not the point charge of the proton. As a result of the finite size of the Na+ core the Rydberg electron can both penetrate and polarize it. The most obvious manifestation of these two phenomena occurs in the lowest states, which are substantially depressed in energy below the hydrogenic levels by core penetration. Core penetration is a short range phenomenon which is well described by quantum defect theory, as outlined in Chapter 2. 

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 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 electron density i/ (0)p at the nucleus primarily originates from the ability of s-electrons to penetrate the nucleus. The core-shell Is and 2s electrons make by far the major contributions. Valence orbitals of p-, d-, or/-character, in contrast, have nodes at r = 0 and cannot contribute to iA(0)p except for minor relativistic contributions of p-electrons. Nevertheless, the isomer shift is found to depend on various chemical parameters, of which the oxidation state as given by the number of valence electrons in p-, or d-, or /-orbitals of the Mossbauer atom is most important. In general, the effect is explained by the contraction of inner 5-orbitals due to shielding of the nuclear potential by the electron charge in the valence shell. In addition to this indirect effect, a direct contribution to the isomer shift arises from valence 5-orbitals due to their participation in the formation of molecular orbitals (MOs). It will be shown in Chap. 5 that the latter issue plays a decisive role. In the following section, an overview of experimental observations will be presented. 

Fig. 2.1 Rydberg atoms of (a) H and (b) Na. In H the electron orbits around the point charge of the proton. In Na it orbits around the +11 nuclear charge and ten inner shell electrons. In high states Na behaves identically to H, but in low states the Na electron penetrates and polarizes the inner shell electrons of the Na+ core.

The 4f orbitals penetrate the xenon core appreciably. Because of this, they cannot overlap with ligand orbitals and therefore do not participate significantly in bonding. As a result of... 

As the series La-Lu is traversed, there is a decrease in both the atomic radii and in the radii of theLn + ions, more markedly at the start of the series. The 4f electrons are inside the 5s and 5p electrons and are core-like in their behaviour, being shielded from the ligands, thus taking no part in bonding, and having spectroscopic and magnetic properties largely independent of environment. The 5s and 5p orbitals penetrate the 4f subshell and are not shielded from... 

The radial distribution of electron probability density for the sodium atom. The shaded area represents the 10 core electrons. The radial distributions of the 3s, Ip, and 3d orbitals are also shown. Note the difference in the penetration effects of an electron in these thiee orbitals. 

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