Homonuclear interaction covalent

Fig. 1 Covalence curves in dimensionless units. Homonuclear interactions are described by the curve BFC and heteronuclear interactions map into the crescent CFA...

Interatomic distance is calculated by mathematical modelling of the electron exchange that constitutes a covalent bond. Such a calculation was first performed by Heitler and London using Is atomic wave functions to simulate the bonding in H2. To model the more general case of homonuclear diatomic molecules the interacting atoms in their valence states are described by monopositive atomic cores and two valence electrons with constant wave functions (3.36). 

When transition-metal cations are resident within an empty zeolite, they may interact further by a covalent mechanism with a suitable guest. For example, an electron pair from a guest may delocalize into an empty d orbital on the cation. Such interactions are not only stronger, but may be more disruptive to the electronic structure of the guest. They are more demanding in their geometrical and stereochemical requirements, and may play a specific role in further reaction and catalysis. For example, unsaturated homonuclear organic bonds have been found to coordinate sideways to ions such as Ag" ", Co2+, or Mn2+ within a zeolite. 

The traditional classification of chemical bonds into ionic, covalent, donor-acceptor, metallic and van der Waals corresponds to extreme types, but a real bond is always a combination of some, or even all of these types (Fig. 2.1). Purely covalent bonding can be found only in elemental substances or in homonuclear bonds in symmetric molecules, which comprise a tiny fraction of the substances known. Purely ionic bonds do not exist at all (although alkali metal halides come close) because some degree of covalence is always present. Nevertheless, to understand real chemical bonds it is necessary to begin with the ideal types. In this Section we will consider mainly the experimental characteristics of different chemical bonds and only briefly the theoretical aspects of interatomic interactions. 

FIGURE 6. Diabatic matrix elements of the electronic Hamiltonian for ionic-covalent alkaline earth - homonuclear diatomic interactions in C2v and Cg symmetry. 

On looking for a relationship between ionization radius and the chemistry of homonuclear covalent interaction, the classification into single and multiple bonds is followed as a first approximation. An immediate observation, valid for most single bonds, is a constant value of the dimensionless distance... 

On equating the atomic radius to a characteristic atomic radius, r, a single curve of d vs D describes homonuclear covalent interaction, irrespective of bond order. Practical use of the formulae requires definition of a complex set of characteristic radii, which could be derived empirically [1] and was used subsequently to calculate molecular shape descriptors [2] and as the basis of a generalized Heitler-London procedure, valid for all pairwise covalent interactions [3,4], In all of these applications, interaction is correctly described by the dimensionless curves of Fig. 1. 

Comparison of the interatomic distances d) reported for homonuclear covalent interactions, commonly considered to be first order, revealed a remarkable... 

It is generally accepted that there is some inverse relationship between covalent bond length d) and dissociation energy (Z)). The point-charge model of covalent interaction defines this relationship in terms of a smooth curve (Fig. 1) which represents all homonuclear diatomic interactions on expressing distance and energy... 

As noted above (equations 9 and 10), each pair of valence NHOs /ia, /ib leads to a complementary pair of valence bond (/)ab) and antibond ( ab) orbitals. Although the latter orbitals play no role in the elementary Lewis picture, their importance was emphasized by Lennard-Jones and Mulliken in the treatment of homonuclear diatomic molecules. Since valence antibonds represent the residual atomic valence-shell capacity that is not saturated by covalent bond formation, they are generally found to play the leading role in noncovalent interactions and delocalization effects beyond the Lewis structure picture. Indeed, it may be said that the NBO treatment of bond-antibond interactions constitutes its most unique and characteristic contribution toward extending the Lewis structure concepts of valence theory. Although the NBO hybrids and polarization coefficients are chosen to minimize the role of antibonds, the final non-zero weighting of non-Lewis orbitals reflects their essential contribution to wavefunction delocalization. 

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