Diatomic ionic structure

MO wave functions in the above form give equal importance to covalent and ionic structures, which is unrealistic in homonuclear diatomic molecules like H2. This should be contrasted with (/>Vb> which in its simple form neglects the ionic contributions. Both and i//MO are inadequate in their simplest forms while in the VB theory the electron correlation is overemphasized, simple MO theory totally neglects it giving equal importance to covalent and ionic structures. Therefore neither of them is able to predict binding energies closer to experiment. The MO theory could be... 

The contributions of covalent and ionic structures to a molecular wave function for a bond in a diatomic molecule can be expressed in terms of... 

Much work has been done in this field by Zeiri and Shapiro, and subsequently by others. For example, semi-empirical potential surfaces have been reported for the alkali atom (M = Li, Na, K, Rb) and halogen molecule (XY = F2,Cl2,Br2,l2) reactions . In this model, the three valence orbitals were represented by Slater-type orbitals centred on M, X and Y. Three VB structures were used a covalent structure based on the spatial configuration MXY and two ionic structures based on M X Y and M XY . The full Hamiltonian was written as a sum of diatomic and atomic terms, but, contrary to the DIM formalism, only the ground-state potentials were required. The approach of Zeiri and Shapiro is very cheap and can be applied to heavy systems. 

The generalized valence bond (GVB) approach was one of the first methods where semilocalized orbitals, as developed by Coulson and Fischer, have been employed to polyatomic molecules [66-72]. GVB is typically applied within a restricted formulation introducing two simplifications for the construction of the VB structures (for a simple diatomic molecule AB, there are two VB structures the so-called ionic structures, and A B+, and a covalent structure, A-—B). In... 

There is thus little hope, in our opinion, for a rigorous definition of valence minimal basis set effective Hamiltonians. To build them, the use of the diatomic effective Hamiltonian may be useful, but some supplementary assumptions should be made, along a physically grounded model, to define for instance three-body polarization energies and the energies of highly hybridized or multi-ionic VB structures. One should realize the physical origin of these numerous troubles they essentially come from the inclusion of the ionic determinants in the model space. This inclusion first resulted in intruder state problems for the diatom it also leads to the appearance of multiply ionic structures in the valence minimal basis set space of the cluster. It seems that, even for H, the definition of a full valence space is too ambitious. 

Since it is possible to measure dipole moments, we have an experimental method of estimating the partial ionic character of heteronuclear diatomic molecules. The dipole moment of LiH is 5.9 Debye units(59D). FotR= 1.60 A (orT.60 X 10 cm), we calculate for an ionic structure Li+H a dipole moment of 7.7 D, Thus the partial charge from the dipole moment datum is estimated to be 5.9/7.7 = 0.77, representing a partial ionic character of 77 per cent. This agrees with the theoretical value of 80 per cent given in the last section. 

Table 3.1 compares key bonding and ionicity descriptors for the NBO Lewis-structure representations of the five AF diatomic fluorides in this series. From this table it can be seen that the single-term natural Lewis-structure description is practically exact for all species (with %p 99.9% for A = F, Cl, Br, H, and only a... 

One classical example that apphes the electroneutrality principle is the electronic structure of carbon monoxide, a diatomic molecule with a very small dipole moment of 0.110 debye. The only electronic structure that satisfies the octet rule for CO is C=0 , a structure that corresponds to C and O, if the shared electron pairs are equally devided by the two atoms. Pauling showed that the electronegativity difference of 1.0 would correspond to about 22% partial ionic character for each bond, and to charges of and 0° +. A second possible electronic structure, C=O , does not complete the octet for carbon. The partial ionic character of the bonds corresponds to C0.44+ If these two structures contribute... 

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. 

The coefficients from Table 2-1 and atomic term values from Table 2-2 will suffice for calculation of an extraordinarily wide range of properties of covalent and ionic solids using only a standard hand-held calculator. This is impressive testimony to the simplicity of the electronic structure and bonding in these systems. Indeed the. same parameters gave a semiquantitativc prediction of the one-electron energy levels of diatomic molecules in Table 1-1. However, that theory is intrinsically approximate and not always subject to successive correc-... 

According to Pauling, a bond in a diatomic molecule may be regarded as a resonance hybrid of only two structures, the ionic and the covalent the contribution of the transitional structure is thus assigned partly to the ionic and partly to the homopolar states (in Chapter 3, and in particular in Chapter 7, it was shown that the wave function for a bond may be represented by a combination of the following functions , (1) 1 4(2)... 

Our comparison shows that the LCAO method includes an ionic contribution to the bond, but the VB method does not. In fact, the simple MO approach suggests that the bond in H2 is 50% covalent and 50% ionic, which is contrary both to experience and intuition. Because the electronegativities of the two atoms in a homonuclear diatomic molecule are the same, there is no reason to expect any ionic contribution to the bond, much less such a large one. The complete absence of ionic contributions in the VB wave function suggests this method is not well suited for polar molecules such as HR Thus, the truth in describing the chemical bond and molecular structure appears to lie somewhere between the LCAO and... 

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