Isoelectronic series of ions

This is an isoelectronic series of ions with the krypton electron configuration. Since these ions all have the same number of electrons, their sizes will depend on nuclear charge. The Z values are 34 for Se2, 35 for Br, 37 for Rb+, and 38 for Sr2+. Since the nuclear charge is greatest for Sr2+, it is the smallest of these ions. The Se2 ion is largest ... 

These are chosen to span the space required to describe the occupied states. The choice can be optimised to lower the total energy E, but this is a laborious process requiring a complete Hartree—Fock calculation for each variation. An extensive investigation of this has resulted in the tables of Clementi and Roetti (1974) for the low-lying states of neutral atoms, positive ions and isoelectronic series of ions up to Z=54. These eigenvectors have been very sensitively verified by the (e,2e) reaction (chapter 11) and form an excellent start for structure calculations. 

A is correct. This is an isoelectronic series, which means that the number of electrons on each ion is the same. In an isoelectronic series of ions, the nuclear charge increases with increasing atomic number and draws the electrons inward with greater force. The ion with fewest protons produces the weakest attractive force on the electrons and thus has the largest size. 

The effect of varying nuclear charge on ionic radii is seen in the variation in radius in an isoelectronic series of ions. The term isoekctronic means that flie ions possess the same number of electrons. For example, each ion in the series 0, F , Na, Mg, and Al has 10 electrons. The nuclear chaige in this series increases steadily in the order listed. (Recall that the charge on the nucleus of an atom or monatomic ion is given by the atomic number of the element.) Because the number of electrons remains constant, the radius of the ion decreases with... 

Solution This is an isoelectronic series of ions, with all ions having 18 electrons. In such a series, size decreases as the nuclear charge (atomic number) of the ion increases. The atomic numbers of the ions are S (16), Cl (17), K (19), and Ca (20). Thus, the ions decrease in size in the order > d > K" " > Ca +... 

We can observe an interesting trend in ionic size by examining the radii of an isoelectronic series of ions— ions with the same number of electrons. Consider the following ions and their radii ... 

Table 1 po for the first few isoelectronic series of atoms and ions, calculated in the crudest approximation. E = -pI/2. 

Having constructed the matrices and T", we are in a position to calculate the spectra of an isoelectronic series of atoms and ions for all values of the nuclear charge Z, and for all values of the external electric field. We first choose a value of Z. Then, for many values of 17 we solve the secular equation (46). Finally, making use of the relationship 17 = /pl, we are able to plot atomic spectra, induced dipole moments, induced transition dipole... 

Some evidence of periodicity within the series is apparent in the oxidation state, magnetic properties and thermod5mamic stability. All these data reflect preferences for the 4/ , 4/ and 4/i electronic configurations. With regard to the oxidation state, the normal valence of the rare-earth ions is known to be 3+. However, as a result of the distinct 4/ , 4P and 4/i stability, there are known in solid-state chemistry isoelectronic or closely isoelectronic groups of ions which also possess ions with charges other them 3 - - La +, Ce +(4/ ), Pr + 4/i) Sm2+ (4/6), Eu2+, Gd3+, Tb4+(4/7) Yb2+, Lu +(4/i4). 

Cations are smaller than their parent atoms anions are larger than their parent atoms. For ions of the same charge, size increases going down a column of the periodic table. An Isoelectronic series is a series of ions that has the same number of electrons. For such a series, size decreases with increasing nuclear charge as the electrons are attracted more strongly to the nucleus. 

In sharp contrast to the stable [H2S. .SH2] radical cation, the isoelectron-ic neutral radicals [H2S.. SH] and [H2S. .C1] are very weakly-bound van der Waals complexes [125]. Furthermore, the unsymmetrical [H2S.. C1H] radical cation is less strongly bound than the symmetrical [H2S.. SH2] ion. The strength of these three-electron bonds was explained in terms of the overlap between the donor HOMO and radical SOMO. In a systematic study of a series of three-electron bonded radical cations [126], Clark has shown that the three-electron bond energy of [X.. Y] decreases exponentially with AIP, the difference between the ionisation potentials (IP) of X and Y. As a consequence, many of the known three-electron bonds are homonuclear, or at least involve two atoms of similar IP. 

Calculations on the isoelectronic series Me(Ph)B , Me(Ph)C , and [Me(Ph)N ]+ show that the singlet-state geometries are different, reflecting differences in the orbital interactions between the hypovalent atom and the 7r-system. The high calculated barrier (21.5 kcal moP ) for [1,2]-H shift in the nitrenium ion is the result of migration using the orbital which is conjugated with the tt-system. 

Free-ion polarizabilities, arranged in isoelectronic series, are listed in table 1.7. A semilogarithmic plot of the listed values (figure 1.6) reveals a functional dependence on atomic number. This dependence, quite marked, allows us to estimate the free-ion polarizability for ions for which there are no precise experimental data (values in parentheses in table 1.7 estimates according to Viellard, 1982). 

Figure 1,6 Free-ion polarizability as a function of atomic number. Curves are drawn for isoelectronic series. Reprinted from Viellard (1982), Sciences Geologiques, Memoir n°69, Universite Louis Pasteur, with kind permission of the Director of Publication.

Table 1.7 Free-Ion polarizability (o ) arranged in isoelectronic series. Data in A. N = number of electrons (adapted from Viellard, 1982).

Results Obtained with the Iterative 4-MCSE Method for the Ground State of Some Ions of the BeryUium Isoelectronic Series... 

In a series of papers some thieno fused boron compounds have been subjected to structure determination by X-ray methods. Thus the bis(dithienoborepinyl) ether (26 R = C10H6BS2O) has dimensions close to those of the isoelectronic dithienotropylium ion (74ACS(B)998>. The borepin ring is almost planar, and the B—C bond length was found to be 1.533 A. 

The radius of an ion decreases with increasing positive charge. Compare, for example, the following isoelectronic series (all radii in pm) ... 

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