Structural trends within molecules

The Jensen symbols are very important in helping to unravel the relationship between the different structure types in neighbouring domains. For example, it is not fortuitous that the NaCl and NiAs domains adjoin each other. Their Jensen symbols 6/6 and 8IV/6 tell us immediately that in NaCl the Na and Cl sites are octahedrally coordinated, whereas in NiAs the Ni site is octahedrally coordinated (but with two extra capping atoms), and the As site is trigonally coordinated. It is also not surprising that at the boundary between cF8 (NaCl) 6/6 and hP4(NiAs) IV/6 we find the two much smaller domains of hP8(TiAs) 7/6, 6 and tI8(NbAs) 6 /6. Nor is it unexpected to find the two islands of oP8(MnP) 10 78 stability in the hP4(NiAs) 8rv/6 domain. A distorted NiAs structure type, MnP leads to the bicapping of the trigonal prismatic coordination about the As site, that is 6 - 8W (cf Fig. 1.9). Further, we see that the cP8(FeSi) 13713 domain adjoins a cP2(CsCl) 14/14 domain they are related structure types as mentioned earlier. 

We would like theory to be able to explain at least the relative structural trends that are observed amongst the ten most frequently occurring structure types which we have discussed above. 

The concepts required for understanding the bonding and structure of the elements and binary compounds are most easily introduced by considering first the nature of the chemical bond in small molecules. We will use theory 

What determines the structural trends amongst the homovalent sp valent molecules with up to six atoms that are displayed in Fig. 1.14 In particular, why amongst the many possible structural variants does Na3 take a bent configuration, Na4 a rhombus, Na5 a two-dimensional 

Before addressing these questions we need to remind ourselves of some of the pertinent concepts of quantum mechanics. 

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The concepts which we need for understanding the structural trends within covalently bonded solids are most easily introduced by first considering the much simpler system of diatomic molecules. They are well described within the molecular orbital (MO) framework that is based on the overlapping of atomic wave functions. This picture, therefore, makes direct contact with the properties of the individual free atoms which we discussed in the previous chapter, in particular the atomic energy levels and angular character of the valence orbitals. We will see that ubiquitous quantum mechanical concepts such as the covalent bond, overlap repulsion, hybrid orbitals, and the relative degree of covalency versus ionicity all arise naturally from solutions of the one-electron Schrodinger equation for diatomic molecules such as H2, N2, and LiH. 

In this chapter we will show that the tight binding ( ) description of the covalent bond is able to provide a simple and unifying explanation for the above structural trends and behaviour. We will see that the ideas already introduced in chapter 4 on the structures of small molecules may be taken over to these infinite bulk systems. In particular, we will find that the trends in structural stability across the periodic table or within the structure maps can be linked directly to the topology of the local atomic environment through the moments theorem of Ducastelle and Cyrot-Lackmann (1971). 

Association and mobilities are related in a complex way to the bulk properties of the solvent and solute. These properties include the charge density and distribution on the ions and the Lewis base properties, the strength and nature of the solvent molecule dipole, the hydrogen-bonding capability, and the intermolecular structure of the solvent. Some correlations can be made on the basis of mobility and association trends in series such as the halides and alkali metals within a single solvent others can be drawn between solvents for a given ion. It appears that conductance measurements provide a clear measure of the sum of ion-solvent interactions, but that other techniques must be used in conjunction with conductance if assessments of individual contributions from specific factors are to be made. 

Abstract. We present a quantum-classieal determination of stable isomers of Na Arii clusters with an electronically excited sodium atom in 3p P states. The excited states of Na perturbed by the argon atoms are obtained as the eigenfunctions of a single-electron operator describing the electron in the field of a Na Arn core, the Na and Ar atoms being substituted by pseudo-potentials. These pseudo-potentials include core-polarization operators to account for polarization and correlation of the inert part with the excited electron . The geometry optimization of the excited states is carried out via the basin-hopping method of Wales et al. The present study confirms the trend for small Na Arn clusters in 3p states to form planar structures, as proposed earlier by Tutein and Mayne within the framework of a first order perturbation theory on a "Diatomics in Molecules" type model. 

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