Electronic Structures of Free Atoms and Ions

We intend in this chapter to consider the manner in which the symmetry of the chemical surroundings of an ion determines the effect of this environment on the energy levels of the ion. In the crystal field and ligand field theories we often wish to regard the effect of the environment as a small perturbation on the states of the free ion. For the benefit of readers not acquainted with certain general features of the electronic structures of free atoms and ions, a brief resume of the subject is given in this section. 

Wave Functions and Quantum Numbers for a Single Electron 

The wave function F for a single electron, in a hydrogen atom for example, may be written as a product of four factors. These are the radial function R(r), which is dependent only on the radial distance rfrom the nucleus two angular functions 0(0) and ( ), which depend only on the angles 0 and (j  

This overall wave function and each of its factors separately have a parametric dependence on certain quantities called quantum numbers, of which there are four /i, /, ra, s. 

The principal quantum number n takes all integral values from 1 to infinity. It determines the nature of the radial part R(r) of the wave function only. 

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We here consider yrms (the root-mean-square Electron-Cloud Radius of the outermost electrons) obtained by equation 1 from the outer diamagnetism. This quantity will be compared with X-ray evidence on ionic Electron-Cloud radii (cp. a pioneer paper by Bider (17)), with Structural Radii for different types of bond, and Avith theoretical calculations for the free atoms and ions. 

The application of refractions to the study of structures is based on comparing the experimental values with those calculated on various structural assumptions, of which the most important is additivity (Landolt, 1862) in the first approximation (within ca 10 %), the refraction of a compound is the sum of constant increments of different atoms, ions and bonds. Refractions of some isolated atoms can be measured by the deviation of an atomic beam in an inhomogeneous electric field or by spectroscopic methods. In other cases electronic polarizabilities of free atoms were calculated by ab initio methods. All available experimental and the best of the computed refractions of free atoms are presented in Table 11.5. These values can be used to calculate the energy of van der Waals interactions, magnetic susceptibility, or to establish correlations with atomic and molecular-physical properties. The formation of covalent bonds changes the refractions of isolated atoms and their values transform into the covalent refractions, which are different for isolated molecules and for crystals. Direct measurements of RI of A2 molecules or elemental solids give the most accurate information on the covalent refractions, in other cases the latter have to be calculated from molecular refractions by the additive method. 

SPECTRA AND ELECTRONIC STRUCTURE OF FREE ACTINIDE ATOMS AND IONS... 

We begin with a presentation of the ideas of the electronic structure of metals. A liquid or solid metal of course consists of positively charged nuclei and electrons. However, since most of the electrons are tightly bound to individual nuclei, one can treat a system of positive ions or ion cores (nuclei plus core electrons) and free electrons, bound to the metal as a whole. In a simple metal, the electrons of the latter type, which are treated explicitly, are the conduction electrons, whose parentage is the valence electrons of the metal atoms all others are considered as part of the cores. In some metals, such as the transition elements, the distinction between core and conduction electrons is not as sharp. 

These three structures are the predominant structures of metals, the exceptions being found mainly in such heavy metals as plutonium. Table 6.1 shows the structure in a sequence of the Periodic Groups, and gives a value of the distance of closest approach of two atoms in the metal. This latter may be viewed as representing the atomic size if the atoms are treated as hard spheres. Alternatively it may be treated as an inter-nuclear distance which is determined by the electronic structure of the metal atoms. In the free-electron model of metals, the structure is described as an ordered array of metallic ions immersed in a continuum of free or unbound electrons. A comparison of the ionic radius with the inter-nuclear distance shows that some metals, such as the alkali metals are empty i.e. the ions are small compared with the hard sphere model, while some such as copper are full with the ionic radius being close to the inter-nuclear distance in the metal. A consideration of ionic radii will be made later in the ionic structures of oxides. 

Multiplet structures are ignored completely and electronic configurations are defined only in terms of the occupation numbers of the various orbitals. Accordingly, the radial HFS wave equations for a free atom or ion are written in the form... 

This class of ion-radicals is characterized by the localization of an unpaired electron at the atom bearing a free (valence) electron pair. Although their applicability in organic synthesis remains an open question, the preparative methods and electron structure of carbene ion-radicals attract some attention of the researchers. Probably, it is an initial step to a new chapter in organic ion-radical chemistry. 

The electron spin resonance (ESR) spectra of the radical ions of 230 indicate there are no large deviations from the free-electron g value that would have been expected had the 3d orbitals of the sulfur atom played an important part in influencing the spin density of the molecule. Consequently, structure 230 may not be the main contributor to the electronic structure of the compound. Such stability in this compound could be attributed to the inertness of the NSN group and the presence of the aromatic naphthalene ring. However, the H-NMR chemical shifts (8 = 4.45 ppm) suggest the compound is antiaromatic. The compound is therefore referred to as an ambiguous aromatic compound (78JA1235). 

Mineral grinding leads to distorsion of chemical and ionic bonds between atoms and ions. In the fracture areas binding and coordination states get asymmetric, and new electron and electric valences occur. Spontaneous reactions in the crystalline structure and with contact phases are the consequence of the distorsion. Surface distorsion of the crystalline structure may be diminished or completely abolished. At the same time, the free surface energy decreases due to polarization of surface ions. These ions are redistributed in the inner or outer layer of the crystalline surface and/or due to chemisorption of molecules and ions1. All these changes occur side by side, but one of them can suppress the effect of the others in a decisive manner. 

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