Orbital penetration

Pauli exclusion principle See exclusion principle. p-clcctron An electron in a p-orbital. penetration The possibility that an s-electron may be found inside the inner shells of an atom and hence close to the nucleus. 

The treatment of atoms with more than one electron (polyelectronic atoms) requires consideration of the effects of interelectronic repulsion, orbital penetration towards the nucleus, nuclear shielding, and an extra quantum number (the spin quantum number) which specifies the intrinsic energy of the electron in any orbital. The restriction on numbers of atomic orbitals and the number of electrons that they can contain leads to a discussion of the Pauli exclusion principle, Hund s rules and the aufbau principle. All these considerations are necessary to allow the construction of the modern form of the periodic classification of the elements. 

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 penetration effect also helps to explain why the 4s orbital fills before the 3d orbital. Recall that potassium has the electron configuration ls22s22p63s23p64s1 rather than the expected ls22s22p63s23p63d1. We can explain this result by observing that an electron in a 4s orbital penetrates much... 

The dependence of the energy on in addition to n can be explained by comparing the extent of shielding in different subshells. Figures 5.4 through 5.10 show that only the s orbitals penetrate to the nucleus both p and d orbitals have nodes at the nucleus. Consequently, the shielding will be smallest, and the electron most tightly bound, in s orbitals. Calculations show that... 

The Orbital Penetration Term in Aromatic Substitutuent Effects. 

The quantum defect is about 1.0 for user orbitals of molecules composed of atoms between Li and N, since these orbitals penetrate into the molecular core (cf. Mulliken, 1964) and consequently are strongly modified by the presence of inner electrons of the same sa symmetry. The quantum defect is of the order 0.7 for npa and npn orbitals, which are less modified by the core, and nearly zero for ndcr, ndir, and ndS orbitals, which have no precursors in the core. For a given molecule this quantum defect is roughly independent of the ion state to which the Rydberg series converges (see, for example, for O2, Table 1 of Wu, 1987). 

In the case of Na a noticeable irregularity is present in the course of the S-values between the d- and p-terms this suggests that the d-orbits arc situated entirely outside the core and that the s- and p-orbits penetrate into the core. 

In the case of the very light elements, the p-orbits are still external the smallness of the Rydberg corrections, and small core radii, suggest that this may also be the case for Cu, Ag, and Au, but the magnitude of the doublet separations and the variation of the value of the correction for different atoms of the same atomic structure (Cu, Zn+, Ga++, Ge+++, etc.1) seem to show conclusively that the p-orbits penetrate., The apparently small Rydberg corrections for... 

The binding energy of an electron to its nucleus is proportional to its mass, so the electrons of the lanthanides are bound more strongly and thus the ionic size is reduced more strongly than would be expected from the increase in nuclear charge and orbital penetration" (Platt 2012). 

Orbital penetration is a term that illustrates the proximity of electrons in an orbital to the nucleus. If the penetration for an electron is greater, it experiences less shielding, and therefore a larger effective nuclear charge. 

The penetration effect also helps to explain why the 4s orbital fills before the 3d orbital. Recall that potassium has the electron confignration ls 2s 2p 3s 3p 4s rather than the expected ls 2s 2p 3s 3p 3r/. We can explain this result by observing that an electron in a 4s orbital penetrates mnch more than an electron in a 3d orbital, as shown graphically in Fig. 12.34. Note that although the most probable distance from the nnclens for a 3d electron is less than that for a 4s electron, the 4s electron has a significant probability of penetrating close to the nucleus. This explains why the potassinm atom in its lowest-energy state has its last electron in the 4s orbital rather than in the 3d orbital. 

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... 

By the requirement of orthogonality, which affects mainly valence orbitals with low angular momentum quantum number (in a classical picture the corresponding orbits penetrate into the core region). 

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