Valence bond spin structures

It is useful to represent the polyelectronic wave function of a compound by a valence bond (VB) structure that represents the bonding between the atoms. Frequently, a single VB structure suffices, sometimes it is necessary to use several. We assume for simplicity that a single VB stiucture provides a faithful representation. A common way to write down a VB structure is by the spin-paired determinant, that ensures the compliance with Pauli s principle (It is assumed that there are 2n paired electrons in the system)... 

Figure 1. Schematic valence bond orbital (a) and valence bond spin (b) structures of CH4.

In compounds of the type F2C=CXY, a linear correlation between F-F geminal coupling constants and fluorine chemical shift has been found. It has been ascribed to a change in the density of the nuclear spin information carrying electrons to the intervening carbon atom due to valence bond resonance structures such as F2C -CF=CF-0 . 

Although the simple valence-bond approach to the bonding in coordination compounds has many deficiencies, it is still useful as a first attempt to explain the structure of many complexes. The reasons why certain ligands force electron pairing will be explored in Chapter 17, but it is clear that high- and low-spin complexes have different magnetic character, and the interpretation of the results of this technique will now be explored. 

Modem valence bond (VB) theories such as Spin-Coupled theory, together with DFT and Molller-Plesset MO methods, and ab initio molecular dynamics, were employed to study structure/dynamics in representative carbonium ions. 

We focus in this Section on particular aspects relating to the direct interpretation of valence bond wavefunctions. Important features of a description in terms of modern valence bond concepts include the orbital shapes (including their overlap integrals) and estimates of the relative importance of the different structures (and modes of spin coupling) in the VB wavefunction. We address here the particular question of defining nonorthogonal weights, as well as certain aspects of spin correlation analysis. 

The formation of a Si crystal is shown in Fig. 1.10. Aside from the core, each Si atom has four valence electrons two 3s electrons and two 3p electrons. To form a Si crystal, one of the 3s electrons is excited to the 3p orbital. The four valence electrons form four sp hybrid orbitals, each points to a vertex of a tetrahedron, as shown in Fig. 1.10. Thpse four sp orbitals are unpaired, that is, each orbital is occupied by one electron. Since the electron has spin, each orbital can be occupied by two electrons with opposite spins. To satisfy this, each of the directional sp orbitals is bonded with an sp orbital of a neighboring Si atom to form electron pairs, or a valence bond. Such a valence bonding of all Si atoms in a crystal form a structure shown in (b) of Fig. 1.10, the so-called diamond structure. As seen, it is a cubic crystal. Because all those tetrahedral orbitals are fully occupied, there is no free electron. Thus, similar to diamond, silicon is not a metal. 

Calculations of nuclear spin-spin couplings by Karplus and co-workers (60) using valence bond functions have been gratifyingly successful. It was to be expected that valence bond functions would be more accurate than LCAO MO functions for this purpose since the former include explicitly effects of spin correlation. For interactions between nonbonded nuclei such as occur, for example, between the hydrogen atoms of CH4 or NH4+, structures of the forms (61)... 

In IV of Fig. 21 is seen that spin density is transmitted through the oxygen atom linking the phenyl and seven-membered ring. In the valence bond formulation, the only way spin density can be transferred from the seven-ring to the phenyl ring is through contributions of ionic structures such as... 

The theory of resonance has been applied to many problems in chemistry. In addition to its use in the discussion of the normal covalent bond (involving the interchange of two electrons, with opposed spins, between two atoms) and to the structure of molecules for which a single valence-bond structure does not provide a satisfactory description, it has rendered service to chemistry by leading to the discovery of several... 

In his valuable paper Molecular Energy Levels and Valence Bonds Slater developed a method of formulating approximate wave functions for molecules and constructing the corresponding secular equations.1 Let a,b, repreamt atomic orbitals, each occupied by one valence electron, and a and 0 represent the electron spin functions for spin orientation -f i and — J, respectively. Slater showed that the following function corresponds to a valence-bond structure with bonds a-----b, c---d, and so forth ... 

Resonance between three 7t-complex structures might lead to stabilization of 1 in the sense of 7t-aromatic stabilization involving the six CC bond electrons. Therefore, Dewar8 has discussed the stability of 1 in terms of a u-aromatic stabilization (Section V). However, spin-coupled valence bond theory clearly shows that 1 cannot be considered as the aromatic benzene51. The 7t-complex description of 1 is a (very formal) model description, which should be discarded as soon as it leads to conflicting descriptions of the properties of 1. This will be discussed in Section V. 

FIGURE 17. Schematic representation of the symmetry-unique spin-coupling patterns in cyclopropane (above) and benzene (below). In the case of cyclopropane, carbon hybrid orbitals and, in the case of benzene, carbon p n orbitals are shown. For each structure, Gallup-Norbeck occupation numbers as determined by spin-coupled valence bond theory are given. All data from Reference 51... 

Unfortunately, this simple valence bond picture can t be right because it predicts that the electrons in all three molecules are spin-paired. In other words, electron-dot structures indicate that the occupied atomic orbitals in all three molecules contain two electrons each. It s easy to demonstrate experimentally, however, that the 02 molecule has two electrons that are not spin-paired and that these electrons therefore must be in different, singly occupied orbitals. 

Clearly these predictions do not agree with the results (Table 5) and it seems that despite the low spin density on oxygen, the perturbation model is unsatisfactory. Presumably the approach used for the nitrocompounds is better and for those who like to visualize valence bond structures the ketone model... 

The valence and coordination symmetry of a transition metal ion in a crystal structure govern the relative energies and energy separations of its 3d orbitals and, hence, influence the positions of absorption bands in a crystal field spectrum. The intensities of the absorption bands depend on the valences and spin states of each cation, the centrosymmetric properties of the coordination sites, the covalency of cation-anion bonds, and next-nearest-neighbour interactions with adjacent cations. These factors may produce characteristic spectra for most transition metal ions, particularly when the cation occurs alone in a simple oxide structure. Conversely, it is sometimes possible to identify the valence of a transition metal ion and the symmetry of its coordination site from the absorption spectrum of a mineral. 

---