Atom hardness

Figure Bl.21.1. Atomic hard-ball models of low-Miller-index bulk-temiinated surfaces of simple metals with face-centred close-packed (fee), hexagonal close-packed (licp) and body-centred cubic (bcc) lattices (a) fee (lll)-(l X 1) (b)fcc(lO -(l X l) (c)fcc(110)-(l X 1) (d)hcp(0001)-(l x 1) (e) hcp(l0-10)-(l X 1), usually written as hcp(l010)-(l x 1) (f) bcc(l 10)-(1 x ]) (g) bcc(100)-(l x 1) and (li) bcc(l 11)-(1 x 1). The atomic spheres are drawn with radii that are smaller than touching-sphere radii, in order to give better depth views. The arrows are unit cell vectors. These figures were produced by the software program BALSAC [35]-...

Figure Bl.21.2. Atomic hard-ball models of stepped and kinked high-Miller-index bulk-temiinated surfaces of simple metals with fee lattices, compared with anfcc(l 11) surface fcc(755) is stepped, while fee...

Although the subject of stability of complexes will be discussed in greater detail in Chapter 19 it is appropriate to note here some of the general characteristics of the metal-ligand bond. One of the most relevant principles in this consideration is the hard-soft interaction principle. Metal-ligand bonds are acid-base interactions in the Lewis sense, so the principles discussed in Sections 9.6 and 9.8 apply to these interactions. Soft electron donors in which the donor atom is sulfur or phosphorus form more stable complexes with soft metal ions such as Pt2+ or Ag+, or with metal atoms. Hard electron donors such as H20, NH3( or F generally form stable complexes with hard metal ions like Cr3+ or Co3+. 

This chapter aims to present the fundamental formal and exact relations between polarizabilities and other DFT descriptors and is organized as follows. For pedagogical reasons, we present first the polarizability responses for simple models in Section 24.2. In particular, we introduce a new concept the dipole atomic hardnesses (Equation 24.20). The relationship between polarizability and chemical reactivity is described in Section 24.3. In this section, we clarify the relationship between the different Fukui functions and the polarizabilities, we introduce new concepts as, for instance, the polarization Fukui function, and the interacting Fukui function and their corresponding hardnesses. The formulation of the local softness for a fragment in a molecule and its relation to polarization is also reviewed in detail. Generalization of the polarizability and chemical responses to an arbitrary perturbation order is summarized in Section 24.4. 

The importance of solvent effects has been outlined in Section 2.2.1. An illustration with some of the fluoroionophores described in this section is given in Table 2.2. For alkali and alkaline-earth metal ions, the stability constants are higher in acetonitrile than in methanol these cations are indeed hard and have a stronger affinity for oxygen atoms (hard) than for nitrogen atoms (soft). In contrast, the soft silver atom has a strong affinity for nitrogen atoms and no complexation is observed in acetonitrile, whereas complexes in methanol, ether, and 1,2-dichloromethane are formed. 

Temperature changes do not appreciably affect ultraviolet optical properties of both metals and insulators, although at low temperatures absorption bands associated with excitons and electron band transitions are usually sharper, and frequencies of peak absorption may shift slightly. In the soft x-ray region, transitions of core electrons buried in the interior of atoms hardly notice temperature changes. 

Neutral extracting agents possessing oxygen-donor atoms (hard bases) in their structure easily coordinate trivalent lanthanide and actinide cations, but do not discriminate between the two families of elements, because the ion-dipole (or ion-induced dipole type) interactions mostly rely on the charge densities of the electron donor and acceptor atoms. As a result, the similar cation radii of some An(III) and Ln(III) and the constriction of the cation radius along the two series of /elements make An(III)/Ln(III) separation essentially impossible from nitric acid media. They can be separated, however, if soft-donor anions, such as thiocyanates, SCN-, are introduced in the feed (34, 35, 39, 77). 

There are various types of organic proton exchangers (34, 35, 38). Diesters of phosphoric acid, (RO)2P = 0(0H), phosphonic acids, R(RO)P = 0(0H), and phos-phinic acids, R2P = 0(0H), where R represents linear or branched alkyl or phenyl substituents, are the most common cation exchangers developed in liquid-liquid extraction for the extraction of trivalent 4/and 5/elements. They were initially developed for the American TALSPEAK and the Japanese DIDPA processes and have recently been introduced in the French DIAMEX-SANEX process. As for previously described NOPCs, these organophosphorus acids present oxygen-donor atoms (hard bases) in their structures and therefore will easily coordinate trivalent lanthanide and actinide cations, but they will not allow complete discrimination of the two families of elements. However, contrary to previously described neutral organophosphorus... 

On their basis were isolated (4.39) the complexes with participation of a cyclopenta-dienyl fragment (soft donor center 866a), or the N atom (hard donor center 866b), or some other with different donor places of localization of the coordination bond. 

Atomic hardness of an atom with the most negative charge... 

In the present contribution, the calculational and conceptual aspects of DFT will be illustrated together with some recent applications situated around a central theme atomic hardnesses and softnesses and the Hard and Soft Acids... 

Figure 4.3 Atomic hardness [eV] plotted against the atomic number Z. Shells and sub-shells...

In the case X = SCI, A 15N depends only a little on R, which means that the geometry of the nitrogen atom hardly depends on the substituent. 

Figure Bl.21.1. Atomic hard-ball models of low-Miller-index bulk-terminated surfaces of simple metals with face-centred close-packed (fee), hexagonal close-packed (hep) and body-centred cubic (bcc) lattices (a) fee... 

The complexing abilities of thiacrown ethers and related macrocycles depend on several factors that have not been fully investigated. These factors include ligand cavity size, spatial distribution of binding sites within the ring, types of donor atoms, hard and soft acid-base rule , cation diameter, solvent, macrocycle conformation, and other factors . 

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