Beryllium-like ions

Table 8 Second-order many-body perturbation theory corrections to beryllium-like ions using non-relativistic (E ), Dirac-Coulomb (E ) and Dirac-Coulomb-Breit (E ) hamiltonians, obtained using the atomic precursor to BERTHA, known as SWIRLES. Basis sets are even-tempered S-spinors of dimension N= 17, with exponent sets, Xi generated by Xi = abi-i, with a = 0.413, and p = 1.376. Angular momenta in the range 0 < / < 6 have been included in the partial wave expansion of each second-order energy, and the total relativistic correction toE has been collected as Ef. All energies in hartree.

The use of a systematic sequence of basis sets can, of course, be usefully combined with the use of a universal basis set(52). In Figure 8, we display the results of Hartree-Fock calculations on the radial beryllium-like ions Li", B+, C2+, N +, Ol++, F5+, Ne6+, using the basis set given by Schmidt and Ruedenberg(56) specifi-ically for the beryllium atom. It can be seen that for the positive ions the basis sets give a uniform convergence rate. In... 

Figure 8. Plot of ln(E[n"s] — E[n s]j against basis set size for beryllium-like ions.

Figure 9. Energy difference AE = E(2s2p J = 0) - E 2s J = 0) (in atomic units) from numerical Dirac-Fock-Coulomb calculations for beryllium-like ions with 100 < Z < 120, and point-like nucleus , right axis) or finite nucleus 0 or o, left axis).

Table 8 Second-order many-body perturbation theory corrections to beryllium-like ions using non-relativistic (E ), Dirac-Coulomb (E ) andDirac-Coulomb-Breit hamiltonians, obtained using the...

Predictions of [13] also include 2s 2p levels of some ions isoelectronic with O, N, C, B, Be, and Li. The elements Os, Ir, and Pt are not considered, but relevant data can be derived by interpolation. Isoelectronic trends in the n=2 —n=2 transition probabilities are sketched in [14] for boron-like ions by the relativistic parametric potential method and in [15] for beryllium-like ions by a 1/Z perturbation method. In a survey of the lithium-like sequence, Steiger reports spontaneous emission rates and energies for three forbidden transitions of lr + [16]. A relativistic model potential method was used by Gogava etal. for deriving the lowest 15 energy levels of all lithium-like ions [17]. 

The element with Z = 4 is beryllium (Be), with four electrons. The first three electrons form the configuration ls22s1, like lithium. The fourth electron pairs with the 2s-electron, giving the configuration ls22s2, or more simply [He 2s2 (41. A beryllium atom therefore has a heliumlike core surrounded by a valence shell of two paired electrons. Like lithium—and for the same reason—a Be atom can lose only its valence electrons in chemical reactions. Thus, it loses both 2s-electrons to form a Be2+ ion. 

Beryllium, at the head of Group 2, resembles its diagonal neighbor aluminum in its chemical properties. It is the least metallic element of the group, and many of its compounds have properties commonly attributed to covalent bonding. Beryllium is amphoteric and reacts with both acids and alkalis. Like aluminum, beryllium reacts with water in the presence of sodium hydroxide the products are the beryl-late ion, Be(OH)42, and hydrogen ... 

Another view, equally consistent with the source abundances and better suited to account for the abundance of light elements like beryllium in stars of the Galactic halo (see below), is that dust particles in the supernova ejecta are the source of ions that are preferentially accelerated within the hot, tenuous gas of superbubbles surrounding regions of star formation (Lingenfelter, Ramaty Kozlovsky 1998). 

What type of ion is beryllium most likely to form ... 

The study of coordination compounds of the lanthanides dates in any practical sense from around 1950, the period when ion-exchange methods were successfully applied to the problem of the separation of the individual lanthanides,131-133 a problem which had existed since 1794 when J. Gadolin prepared mixed rare earths from gadolinite, a lanthanide iron beryllium silicate. Until 1950, separation of the pure lanthanides had depended on tedious and inefficient multiple crystallizations or precipitations, which effectively prevented research on the chemical properties of the individual elements through lack of availability. However, well before 1950, many principal features of lanthanide chemistry were clearly recognized, such as the predominant trivalent state with some examples of divalency and tetravalency, ready formation of hydrated ions and their oxy salts, formation of complex halides,134 and the line-like nature of lanthanide spectra.135... 

Like a strong acid, a strong base dissociates completely into ions in water. All oxides and hydroxides of the alkali metals—Group 1 (IA)—are strong bases. The oxides and hydroxides of the alkaline earth metals—Group 2 (IIA)—below beryllium are also strong bases. 

Most of the Group IA and IIA metals react with hydrogen to form metal hydrides. For all of the metals in these two groups except Be and Mg, the hydrides are considered to be ionic or salt-like hydrides containing H ions (see Chapter 6). The hydrides of beryllium and magnesium have considerable covalent character. The molten ionic compounds conduct electricity, as do molten mixtures of the hydrides in alkali halides, and during electrolysis of the hydrides, hydrogen is liberated at the anode as a result of the oxidation of H ... 

VII.l INTRODUCTION In the previous chapters the discussions were restricted to those cations and anions which occur most often in ordinary samples. Having studied the reactions, separation, and identification of those ions, the student should now concentrate on the so-called rarer elements. Many of these, like tungsten, molybdenum, titanium, vanadium, and beryllium, have important industrial applications. 

Some pertinent data for the elements are given in Table 4-1. Beryllium has unique chemical behavior with a predominantly covalent chemistry, although it forms an aqua ion [Be(H20)4]2+. Magnesium has a chemistry intermediate between that of Be and the heavier elements, but it does not stand in as close relationship with the predominantly ionic heavier members as might have been expected from the similarity of Na, K, Rb, and Cs. It has considerable tendency to covalent bond formation, consistent with the high charge/radius ratio. For instance, like beryllium, its hydroxide can be precipitated from aqueous solutions, whereas hydroxides of the other elements are all moderately soluble, and it readily forms bonds to carbon. 

The most comprehensive information about ion-solvent complex formation follows from potentiometric titrations and some NMR measurements. This applies to NMR studies with solutions of ions like aluminum(III), gallium(III), beryllium(II) or magnesium(II) which interact so strongly with the molecules of several dipolar solvents that the lifetime of the molecules in the solvation shell is very long. Then the solvent exchange kinetics is slow enough to observe in the NMR spectrum of the solvent separate lines for coordinated solvent molecules and for free solvent. 

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