Core-and-valence-shell picture

This leads to an interesting extension of the core-and-valence-shell picture. Where the valence of a bond was previously defined as the flux linking the cation core to the electrons it contributes to the bond, in the ionic model it is defined by the same flux which now links the cation to the anion. If the positions of the atoms in the array are known from experiment, this flux can be directly calculated. The calculation involves extensive computation, but Preiser et al. [17] have shown that in stmctures in equilibrium, the correlation between the bond flux and bond length is the same as the correlation that had previously been observed between the bond valence and bond length, showing that the electrostatic flux and bond valence are indeed the same. 

The network equations (14a) and (14b) can only be used if the graph of the bond network is bipartite, that is, if every bond has a cation at one end and an anion at the other. In inorganic compounds, and particularly in organic compounds, this condition is not always satisfied. Although this restricts the application of the bond valence theory, the core-and-valence-shell picture of the atom is still valid, as is the description of the chemical bonds this picture gives. 

As shown in Sect. 5 of [1] the ionic model is by no means restricted to structures containing only ionic bonds it apphes to the majority of structures with localized bonds including many organic compounds. It is Umited only by its inability to describe the bonds formed between two cations or between two anions. If such bonds are present, a more sophisticated model is needed, one in which there is no distinction between the anion and the cation. The core-and-valence-shell picture of the atom is described in Sect. 2 of [1]. 

This chapter starts with a description of the core-and-valence-shell picture of the atom, followed by a derivation of the principal theorems of bond valence theory. The later sections of the chapter illustrate the ways in which these theorems are applied over a range of chemical bonds and structures. 

Fig. 2 The core-and-valence-shell picture of an atom. The core is shown as dark gray, the valence shell in light gray, and the nucleus is shown in black. The number of lines of field (electrostatic fiux) is proportional to the negative charge on the valence shell as well as the positive charge on the core...

NBOs were conceived as a chemist s basis set since they correspond closely to the picture of localized bonds and lone pairs as basic units of molecular structure. The procedure for obtaining them starts from the one-particle density matrix, from which a set of orthonormal NBOs is obtained. The transformation from canonical orbitals to NBOs includes several steps that are not described here, but it is important to stress that the main contribution to the total density matrix comes from a set of one- and two-centred occupied orbitals, w, the former being identified either as core orbitals or lone pairs and the latter as <7 or tt bonds. The transformation also yields unoccupied orbitals, ijj, that are identified as cr or tt antibonds (<7 or tt ) or extra-valence-shell... 

The picture provided by the ELF function displays silicon cores and oxygen cores surrounded by a valence shell [52]. The oxygen valence shell as shown on figure 2 contains 3,5 and 4 basins for the 2, 3 and 4 oxygen coordinations respectively. The pictures for quartz and CaCl2 structures have not been reported because they are almost identical to those of cristobalite and stishovite. There is no additional valence domain on the silicon side, this latter atom only gives rise to a spherical L-shell core domain enclosing the A-shell one. 

Within the atomic orbital picture discussed earlier for solids with 5 and p electrons, we can construct a simple argument to rationalize hydrogen bonding in the case of ice. The O atom has six valence electrons in its 5 and p shells and therefore needs two more electrons to complete its electronic structure. The two H atoms that are attached to it to form the water molecule provide these two extra electrons, at the cost of an anisotropic bonding arrangement (a completed electronic shell should be isotropic, as in the case of Ne which has two more electrons than O). The cores of the H atoms (the protons), having lost their electrons to O, experience a Coulomb repulsion. The most favorable structure for the molecule which optimizes this repulsion would be to place the two H atoms in diametrically opposite positions relative to the O atom, but this would involve only one p orbital of the O atom to which both H atoms would bond. This is an unfavorable situation as far as formation of covalent bonds is concerned, because it is not possible to... 

This model explicitly does not give a picture of the tme electron density since the physical location of the electrons is not relevant to the model and, indeed, cannot be derived from the model. Superimposing the valence shell and core does not yield a true physical picture of the atom because the purpose of the model is not to reproduce the true electron density, but rather to keep track of the roles played by the valence shell and core electrons. The model s validity does not depend on its ability to predict the electron density, which it is neither intended, nor is it able to do, but on its ability to predict the bonding structures in crystals and molecules. In this respect it performs at least as well as any other model and in many respects better. 

This qualitative picture is taken into account in the unrestricted Hartree-Fock (UHF) approach, but it is found that UHF calculations normally overestimate Ajgo drastically. To obtain reliable results, the interactions between the electrons must be described much more accurately. Furthermore, in difference to most other electronic properties, such as dipole moments etc., a proper treatment of the hfcc s also requires special consideration of the inner valence and the Is core regions, since these electrons possess a large probability density at the position of the nucleus. Because the contributions from various shells are similar in magnitude but differ in sign, a balanced description of the electron correlation effects for all occupied shells is essential. All this explains the strong dependence of A on the atomic orbital basis and on the quality of the wavefunction used for the calculation. 

Speaking at a higher theoretical level, the closed-shell electronic ground-state phenol molecule is described by the 25 occupied molecular orbitals whose 3D patterns are partly pictured in Figure 5. These 25 occupied MOs are partitioned into two classes, the first comprising the seven core orbitals (Is atomic orbitals on the carbon and oxygen atoms) and the second including 18 valence orbitals. The latter represent six a C—C bonds (all... 

---