Three-electron ions

Hurst, R. P., Gray, J. D., Brigman, G. H., and Matsen, F. A., Mol. Phys. 1, 189, "Open shell calculations for two- and three-electron ions." The improvement over closed shell calculations becomes less with increasing atomic number. 

Bond Strength and Atomic Connectivity Studies of the Unsymmetrical Two-Center Three-Electron Ion, [Et2S. SMe2]+. 

I have mentioned here only a small selection of theoretical papers on Ingvar s publication list, which contains about 150 titles in total. A few weeks ago 1 received a preprint of his invited talk at the 1996 ICAP conference where Ingvar and coworkers review QED effects in heavy, highly charged ions, in particular the Lamb shift for one-, two-, and three-electron ions [Proc. 15th Int. Conf. on Atomic Physics, World Scientific 1996], and he has published at least four more papers this year. 

P. Indelicato, J. P. Desclaux. Multiconfiguration Dirac-Fock calculations of transition energies with QED corrections in three-electron ions. Phys. Rev. A, 42 (1990) 5139-5149. 

Obviously sufficient energy is available to break the A1—Cl covalent bonds and to remove three electrons from the aluminium atom. Most of this energy comes from the very high hydration enthalpy of the AP (g) ion (p. 78). Indeed it is the very high hydration energy of the highly charged cation which is responsible for the reaction of other essentially covalent chlorides with water (for example. SnCl ). 

The physical techniques used in IC analysis all employ some type of primary analytical beam to irradiate a substrate and interact with the substrate s physical or chemical properties, producing a secondary effect that is measured and interpreted. The three most commonly used analytical beams are electron, ion, and photon x-ray beams. Each combination of primary irradiation and secondary effect defines a specific analytical technique. The IC substrate properties that are most frequendy analyzed include size, elemental and compositional identification, topology, morphology, lateral and depth resolution of surface features or implantation profiles, and film thickness and conformance. A summary of commonly used analytical techniques for VLSI technology can be found in Table 3. 

Consider electrons of mass m and velocity v, and atoms of mass M and velocity V we have mjM 1. The distribution function for the electrons will be denoted by /(v,<) (we assume no space dependence) that for the atoms, F( V), assumed Maxwellian as usual, in the collision integral, unprimed quantities refer to values before collision, while primed quantities are the values after collision. In general, we would have three Boltzmann equations (one each for the electrons, ions, and neutrals), each containing three collision terms (one for self-collisions, and one each for collisions with the other two species). We are interested only in the equation for the electron distribution function by the assumption of slight ionization, we neglect the electron-electron... 

The presence of polymer, solvent, and ionic components in conducting polymers reminds one of the composition of the materials chosen by nature to produce muscles, neurons, and skin in living creatures. We will describe here some devices ready for commercial applications, such as artificial muscles, smart windows, or smart membranes other industrial products such as polymeric batteries or smart mirrors and processes and devices under development, such as biocompatible nervous system interfaces, smart membranes, and electron-ion transducers, all of them based on the electrochemical behavior of electrodes that are three dimensional at the molecular level. During the discussion we will emphasize the analogies between these electrochemical systems and analogous biological systems. Our aim is to introduce an electrochemistry for conducting polymers, and by extension, for any electrodic process where the structure of the electrode is taken into account. 

Figure C.6 shows another pattern in the charges of monatomic cations. For elements in Croups 1 and 2, for instance, the charge of the ion is equal to the group number. Thus, cesium in Group 1 forms Cs+ ions barium in Group 2 forms Ba2+ ions. Figure C.6 also shows that atoms of the d-hlock elements and some of the heavier metals of Groups 13/111 and 14/IV can form cations with different charges. An iron atom, for instance, can lose two electrons to become Fe + or three electrons to become Fe 1. Copper can lose either one electron to form Cu or two electrons to become Cu2+.

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. 

In the d block, the energies of the (n — l )d-orbitals lie below those of the ns-orbitals. Therefore, the ws-electrons are lost first, followed by a variable number of (n — 1 )d-electrons. For example, to obtain the configuration of the Fe3+ ion, we start from the configuration of the Fe atom, which is [Ar]3d 64s2, and remove three electrons from it. The first two electrons removed are 4s-electrons. The third electron comes from the Id-subshell, giving [Ar 3d5. 

The Helium Molecule and Molecule-ion.—The simplest example of a molecule containing a three-electron bond is the helium molecule-ion, in which a Is eigenfunction for each of two identical atoms is involved. The two unperturbed states of equal energy are He He+ and He-+ He. The formation of this molecule might be represented by the equation He Is2 >5 + He+ Is 5 —>- He (Is + ls) 2 Three dots in a horizontal line placed between the two atomic symbols may be used to designate a three-electron bond He He+. 

I believe that the explanation of these facts is provided by the three-8 W. Weizel, Z. Physik, 59,320 (1929). Weizel and F. Hund [ibid., 63, 719 (1930) ] have discussed the possible electronic states of the helium molecule. Neither one, however, explains why He Is2 + He+ Is form a stable molecule-ion, nor gives the necessary condition for the formation of a three-electron bond. In earlier papers they assumed that both atoms had to be excited in order to form a stable molecule [W. Weizel, ibid., 51,328 (1928) F. Hund, ibid., 51, 759 (1928)]. 

In Sections 42 and 43 we shall describe the accurate and reliable wave-mechanical treatments which have been given the hydrogen molecule-ion and hydrogen molecule. These treatments are necessarily rather complicated. In order to throw further light on the interactions involved in the formation of these molecules, we shall preface the accurate treatments by a discussion of various less exact treatments. The helium molecule-ion, He , will be treated in Section 44, followed in Section 45 by a general discussion of the properties of the one-electron bond, the electron-pair bond, and the three-electron bond. 

The properties of a compound depend on two main factors, the nature of the bonds between the atoms, and the nature of the atomic arrangement. It is convenient to consider that actual bonds approach more or less closely one or another of certain postulated extreme bond types (ionic, electron-pair, ion-dipole, one-electron, three-electron, metallic, etc.), or... 

Some substituents have a pair of electrons (usually unshared) that may be contributed toward the ring. The three arenium ions would then look like this... 

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. 

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