Local atomic covalence

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). 

In the early 1990s, Brenner and coworkers [163] developed interaction potentials for model explosives that include realistic chemical reaction steps (i.e., endothermic bond rupture and exothermic product formation) and many-body effects. This potential, called the Reactive Empirical Bond Order (REBO) potential, has been used in molecular dynamics simulations by numerous groups to explore atomic-level details of self-sustained reaction waves propagating through a crystal [163-171], The potential is based on ideas first proposed by Abell [172] and implemented for covalent solids by Tersoff [173]. It introduces many-body effects through modification of the pair-additive attractive term by an empirical bond-order function whose value is dependent on the local atomic environment. The form that has been used in the detonation simulations assumes that the total energy of a system of N atoms is ... 

Covalent solids (or network solids ) can be considered giant molecules that consist of covalently bonded atoms in an extended, rigid crystalline network. Diamond (one crystalline form of carbon) and quartz are examples of covalent solids (Figure 13-32). Because of their rigid, strongly bonded structures, mst covalent solids are very hard and melt at high temperatures. Because electrons are localized in covalent bonds, they are not freely... 

From the extended adjacency matrix defined above two spectral indices, called extended adjacency matrix indices, were proposed as molecular descriptors. Moreover, the extended adjacency ID numberwas derived from an extended adjacency matrix defined in terms of atomic covalent radii and local vertex invariants computed from layer matrices. 

Although the title has an almost magical sound to it, the nature of the chemical bond was truly the domain Pauling began to explore. He formulated the concept of hybridization to explain how localized atomic orbitals best overlap to form two-electron bonds. The Kossel-Lewis-Langmuir picture explained ionic and covalent bonding in terms of the octet rule. An interesting question was... 

In the second part (applications) we discuss some recent applications of LCAO methods to calculations of various crystalline properties. We consider, as is traditional for such books the results of some recent band-structure calculations and also the ways of local properties of electronic- structure description with the use of LCAO or Wannier-type orbitals. This approach allows chemical bonds in periodic systems to be analyzed, using the well-known concepts developed for molecules (atomic charge, bond order, atomic covalency and total valency). The analysis of models used in LCAO calculations for crystals with point defects and surfaces and illustrations of their applications for actual systems demonstrate the eflSciency of LCAO approach in the solid-state theory. A brief discussion about the existing LCAO computer codes is given in Appendix C. 

The Wiberg indices (4.137) and atomic covalence (4.140) are called the local properties of the electronic structure of periodic systems. These properties also include AO populations, atomic charges (electrovalencies) and total atomic valences [97]. The analysis of the local properties of the electronic structure in molecular quantum chemistry is very popular as it gives useful information about the chemical bonding. The local properties of the electronic structure of crystals are considered in more detail in Chap. 9. The above consideration holds for the density matrix of the basic domain of the crystal that is, it is assumed that the number N of primitive cells in this domain is so large that the introduction of cyclic boundary conditions virtnaUy does not affect the density matrix of the infinite crystal. 

However, a material merely composed of atoms covalently linked together in all directions will not only be very strong, like diamond, but also be extremely brittle since it does not have a mechanism that prevents crack propagation by eliminating local stress concentrations. These... 

When using localized orbitals covalent interactions can be analyzed by orbital occupation number fluetuations and the local spin, calculated with respect to one or more orbitals local-ized on a specific atom [77,78]. The orbital occupation number fluctuations are defined as... 

Ollis and Ramsden state that A compound may be appropriately called mesoionic if it is a five-membered heterocycle which cannot be represented satisfactorily by any one covalent or polar structure and possesses a sextet of electrons in association with the five atoms comprising the ring . From the point of view of systematic nomenclature, compounds of this type are difficult to deal with, since most available nomenclature systems are designed so as to name one particular bond- and charge-localized canonical form. 

A comparative study on ylide stability as a function of the heteroatom type was carried out by Doering et al. [3,4]. They concluded that the phosphorus and sulfur ylides are the most stable ones. The participation of three-dimensional orbitals in the covalency determines the resonance stabilization of the phosphorus and sulfur ylides [5-8]. The nitrogen ylides are less stable from this point of view. The only stabilization factor involves electrostatic interactions between the two charges localized on adjacent nitrogen and carbon atoms [9]. 

In the perfect lattice the dominant feature of the electron distribution is the formation of the covalent, directional bond between Ti atoms produced by the electrons associated with d-orbitals. The concentration of charge between adjacent A1 atoms corresponds to p and py electrons, but these electrons are spatially more dispersed than the d-electrons between titanium atoms. Significantly, there is no indication of a localized charge build-up between adjacent Ti and A1 atoms (Fu and Yoo 1990 Woodward, et al. 1991 Song, et al. 1994). The charge densities in (110) planes are shown in Fig. 7a and b for the structures relaxed using the Finnis-Sinclair type potentials and the full-potential LMTO method, respectively. 

This type of argument leads us to picture a metal as an array of positive ions located at the crystal lattice sites, immersed in a sea of mobile electrons. The idea of a more or less uniform electron sea emphasizes an important difference between metallic bonding and ordinary covalent bonding. In molecular covalent bonds the electrons are localized in a way that fixes the positions of the atoms quite rigidly. We say that the bonds have directional character— the electrons tend to remain concentrated in certain regions of space. In contrast, the valence electrons in a metal are spread almost uniformly throughout the crystal, so the metallic bond does not exert the directional influence of the ordinary covalent bond. 

---