Periodic table contractions

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 ... 

This would not be expected simply on the basis of a crystal-field model, for the d orbitals will contract with increasing positive charge and hence interact less well with the ligand point charges . The modest decreases in bond length as one traverses the series (Eq. 6.9) are unlikely to compensate for, let alone override, the effects of such orbital contraction. Finally, to add to the confusion, we also note from Eq. (6.7) that zio -t values increase as we go down the periodic table (Eq. 6.10). 

The 1-solar-mass star is not capable of producing the heavier nuclei and the majority of the elements in the Periodic Table. With sufficient initial mass of H the He core produces 12C, the point at which the star starts to die. The formation of an almost pure He core results in the end of the star s main-sequence lifetime. The core of the star begins to contract, raising the temperature to 108 K until the nuclear reactions involving He start. 

Quantum chemists have developed considerable experience over the years in inventing new molecules by quantum chemical methods, which in some cases have been subsequently characterized by experimentalists (see, for example, Refs. 3 and 4). The general philosophy is to explore the Periodic Table and to attempt to understand the analogies between the behavior of different elements. It is known that for first row atoms chemical bonding usually follows the octet rule. In transition metals, this rule is replaced by the 18-electron rule. Upon going to lanthanides and actinides, the valence f shells are expected to play a role. In lanthanide chemistry, the 4f shell is contracted and usually does not directly participate in the chemical bonding. In actinide chemistry, on the other hand, the 5f shell is more diffuse and participates actively in the bonding. 

It is not possible to use normal AO basis sets in relativistic calculations The relativistic contraction of the inner shells makes it necessary to design new basis sets to account for this effect. Specially designed basis sets have therefore been constructed using the DKH Flamiltonian. These basis sets are of the atomic natural orbital (ANO) type and are constructed such that semi-core electrons can also be correlated. They have been given the name ANO-RCC (relativistic with core correlation) and cover all atoms of the Periodic Table.36-38 They have been used in most applications presented in this review. ANO-RCC are all-electron basis sets. Deep core orbitals are described by a minimal basis set and are kept frozen in the wave function calculations. The extra cost compared with using effective core potentials (ECPs) is therefore limited. ECPs, however, have been used in some studies, and more details will be given in connection with the specific application. The ANO-RCC basis sets can be downloaded from the home page of the MOLCAS quantum chemistry software (http //www.teokem.lu.se/molcas). 

Finally, a word of caution should be offered against making a straightforward comparison of the M-Si bonds in complexes of different metals, since this parameter is strongly affected by the size of the metal. The latter tends to decrease from left to right in a given row of the Periodic Table due to the d-contraction, but increases down the Group (particularly between the first and second transition series). 

As we go from left to right across the transition metals in the periodic table, the metal atoms become smaller, much as in the lanthanide contraction (Section 2.6). Furthermore, the atoms of elements of the first transition series are smaller than those of corresponding members of the second and third. Consequently, interstitial carbides are particularly important for metals toward the lower left of the series, as with TiC, ZrC, TaC, and the extremely hard tungsten carbide WC, which is used industrially as an abrasive or cutting material of almost diamond like hardness. The parallel with trends in chemisorption (Section 6.1) will be apparent. 

It was discovered that the optimum combination of speed and accuracy (when comparing to calculations using STOs) was achieved for M = 3. Figure 6.2 compares a Is function using die STO-3G formalism to the corresponding STO and shows also the 3 primitives from which the contracted basis function is constructed. STO-3G basis functions have been defined for most of die atoms in the periodic table. 

While the contraction resulting from the poor shielding of 4/ electrons ceases at hafnium, the relativistic effect continues across the sixth row of the periodic table. It is largely responsible for the stabilization of the 6. orbital and the inert s pair effect shown by the elements Hg-Bi. It also stabilizes one40 of the 6p orbitals of bismuth allowing the unusual i-l oxidation state in addition to +3 and + 5.4 ... 

LANTHANIDE CONTRACTION. The decreasing sequence of crystal radii of the triposiiivc rare-earth ions with increasing atomic number in the group of elements 157) lanthanum through (71) lutetiunt of the Lanthanide Series in the periodic table. 

RARE-EARTH ELEMENTS AND METALS. Sometimes referred to as the fraternal fifteen," because of similarities in physical and chemical properties, the rare-earth elements actually are not so rare. This is attested by Fig. 1, which shows a dry lake bed in California that alone contains well in excess of one million pounds of two of die elements, neodymium and praseodymium. The world s largest rare earth body and mine near Baotou, Inner Mongolia, China is shown in Fig. 2. It contains 25 million tons of rare earth oxides (about one quarter of the world s human reserves. The term rare arises from the fact that these elements were discovered in scarce materials. The term earth stems from die tact that the elements were first isolated from their ores in the chemical form of oxides and that the old chemical terminology for oxide is earth. The rare-earth elements, also termed Lanthanides, are similar in that they share a valence of 3 and are treated as a separate side branch of the periodic table, much like die Actinides. See also Actinide Contraction Chemical Elements Lanthanide Series and Periodic Table of the Elements. 

Deviations from this rule may occur for elements to the right of the lanthanides in the periodic table. Here the nuclear charge has increased much more than in the previous row of the periodic table, because of the additional lanthanide elements, and the ionization potentials of many of these elements are in fact higher than the potentials of their family members in preceding rows of the periodic table (compare this to the lanthanide contraction, p. 52). 

One property of a transition metal ion that is particularly sensitive to crystal field interactions is the ionic radius and its influence on interatomic distances in a crystal structure. Within a row of elements in the periodic table in which cations possess completely filled or efficiently screened inner orbitals, there should be a decrease of interatomic distances with increasing atomic number for cations possessing the same valence. The ionic radii of trivalent cations of the lanthanide series for example, plotted in fig. 6.1, show a relatively smooth contraction from lanthanum to lutecium. Such a trend is determined by the... 

The alkaline earth metals (group 2A of the periodic table) include Mg and Ca, which play both structural and physiological roles. Aside from its structural importance in bones and teeth, calcium is critical in processes ranging from vascular tone, nerve impulse transmission, muscle contraction, blood clot formation, the secretion of hormones such as insulin, and cell signaling. Calcium levels in cells, blood, and extracellular fluid are very tightly controlled. If calcium intake is insufficient, calcium is liberated from bones in order to support these physiological functions. 

In 1926, Goldschmidt demonstrated the analogies between the elements Th, Pa, U and the lanthanides on the basis of the observation that the volumes of Th and U showed the same contractions as the ions of the lanthanide series. Striking early examples of periodic tables in which actinium, thorium, protactinium, and uranium are considered as homologues of the rare earths lanthanum, cerium, praseodymium, and neodymium are the circular system and left-step table of Charles Janet (Janet, 1929). 

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