Electron shell, contraction

A contraction resulting from the filling of the 4f electron shell is of course not exceptional. Similar contractions occur in each row of the periodic table and, in the d block for instance, the ionic radii decrease by 20.5 pm from Sc to Cu , and by 15 pm from Y to Ag . The importance of the lanthanide contraction arises from its consequences ... 

Figure 4.4 Valence relativistic s-shell contraction (/ )r/(/ )nr (4s for Cu, 5s forAg, SsforAu and 7s for Fr). Here the ns-shell remains singly occupied and the x-axis gives the total number of electrons N with additional electrons filled in successively from the inner shells. For example N = 3 for Au describes the occupation ls 6s and N — 11 the occupation ls 2s 2p 6s ...

Filling of the inner 4f electron shell across the lanthanide series results in decreases of ionic radii by as much as 15% from lanthanum to lutetimn, referred to as the lanthanide contraction (28). While atomic radius contraction is not rmique across a series (i.e., the actinides and the first two rows of the d-block), the fact that all lanthanides primarily adopt the tripositive oxidation state means that this particular row of elements exhibits a traceable change in properties in a way that is not observed elsewhere in the periodic table. Lanthanides behave similarly in reactions as long as the mnnber of 4f electrons is conserved (29). Thus, lanthanide substitution can be used as a tool to tune the ionic radius in a lanthanide complex to better elucidate physical properties. 

The elements with atomic numbers from 57 (l thanum) to 71 (lutetium) are referred to as the lanthanide elements. These elements and two others, scandium and yttrium, exhibit chemical and physical properties very similar to lanthanum. They are known as the rare earth elements or rare earths (RE). Such similarity of the RE elements is due to the configuration of their outer electron shells. It is well known that the chemical and physical properties of an element depend primarily on the structure of its outermost electron shells. For RE elements with increasing atomic number, the first electron orbit beyond the closed [Xe] shell (65 remains essentially in place while electrons are added to the inner 4f orbital. Such disposition of electrons about the nucleus of the rare earth atoms is responsible for the small effect an atomic number increase from 57 to 71 has on the physical and chemical properties of the rare earths. Their assignment to the 4f orbital leads to slow contraction of rare earth size with increasing atomic number. The 4f orbitals of both europium and gadolinium are half occupied [Xe] (4F6s and [Xe] (4F5d 6s, so that there... 

This lanthanide contraction is associated with the filling of the 4f shell across the lanthanide series. The effect is mainly due to an incomplete shielding of the nuclear charge by the 4f electrons and yields a contraction of the radii of outer electron shells. 

The superheavy elements are beyond the quenching regime, however, and the spin-orbit effect is so large that it is not quenched. In HUus, for example, the lp /2 shell contracts significantly and forms an inert pair, leaving an unpaired 7p3/2 electron to form an s-p j bond, which is weaker than a regular a bond and contains a significant lone-pair component (Saue et al. 1996). 

The ionic radius is a useful parameter with which to correlate numerous physical and thermodynamic properties of the actinide elemoits. Its usefulness for this purpose is not usually dependent on how it is d ned or on the absolute values that are used when comparing members of the series. Nevertheless, the tom radii implies spherical ions, and the modes of deriving such radii from crystallographic data usually assume that these spheres are in contact with spherical anions. When this assumption is not true, as in most real crystals, the derived radii depend on the method of calculation and are somewhat arbitrary. Consequently, there have been published for the actinide elements several tables of radii which differ both in absolute values and in the slope of the curve obtained when they are plotted against atomic number. All of these sets of radii have in common, however, two qualitative features a contraction of the radius with increasing atomic number and a cusp at the half-filled 5f-electron shell. Additional perturbations of the curve at the one-fourth- and three-fourths-fiUed shells have not been established for the actinides, although slight effects were shown to exist for the lanthanides... 

More promising is to describe the deformation electron density by a series of spherical harmonic density functions (multipoles), which can be included into least-squares refinement. The inner (core) electron shells of an atom are presumed and the k parameter, which describes the isotropic expansion (ic <1) or contraction (/c > 1) of the valence shell as a whole. Multipole parameters of higher orders describe deviations of the electron density from spherical symmetry. They can be related to the products of atomic... 

The opposite extreme to a shared interaction occurs when two closed-shell systems interact, as found in ionic, hydrogen-bonded, van der Waals, and repulsive interactions. In such closed-shell interactions, the requirement of the Pauli exclusion principle leads to the removal of electron density from the region of contact, the interatomic surface. All of the curvatures of Pb are relatively small in magnitude but the positive curvature of Pb along the bond path is dominant and V pb > 0. Since the electron density contracts away from the surface, the interaction is characterized by a relatively low value of pb and the electron density is concentrated. separately in each of... 

The trend in radius, shown for the M(III) ion in Table 15.2, is the result of the increasing number of protons in the nucleus causing the electron shells to contract in the lanthanide contraction-, the/electrons added are deep-lying and inefficient at screening the nuclear charge. In most of chemistry, when we move from one element to the next, the changes in atomic size and preferred valency are abrupt. Here, in contrast, the radius varies smoothly and the M(III) valence state remains preferred, so we have nice control over the M-L bond length. As this... 

In general, atomic radii increase while going down the group. Therefore, the atomic radii of the elements of second transition series have hi er values than those of the elements of first transition series. This is due to increase in the number of electron shells. The atomic radii of the elements of third transition series except lanthanum have almost the same atomic radii as the elements of second transition series. This is due to lanthanide contraction. The fourteen lanthanides are present between lanthanum and hafiiium (syLa - 72HiD and there is a continuous decrease in atomic size from cerium (sgCe) to luteciiun (yiLu) so that the atomic size of hafnium becomes almost equal to the size of zirconium. 

In nature, hafnium is found together with zirconium and as a consequence of the contraction in ionic radii that occurs due to the -electron shell, the ionic radius... 

SBKJC VDZ Available for Li(4.v4/>) through Hg(7.v7/ 5d), this is a relativistic basis set created by Stevens and coworkers to replace all but the outermost electrons. The double-zeta valence contraction is designed to have an accuracy comparable to that of the 3—21G all-electron basis set. Hay-Wadt MB Available for K(5.v5/>) through Au(5.v6/ 5r/), this basis set contains the valence region with the outermost electrons and the previous shell of electrons. Elements beyond Kr are relativistic core potentials. This basis set uses a minimal valence contraction scheme. These sets are also given names starting with LA for Los Alamos, where they were developed. 

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