Bond, covalent molecular orbital theory

The structure of a millerite crystal from Marbridge Mine, Malartic, Quebec, with the empirical formula Nio,98iFeo.oi6Coo.oo4S has been refined. The hexagonal axes were found to be o = 9.607(1) A and cq = 3.143(1) A. Within the lattice each Ni is coordinated by five S atoms and two Ni atoms. The observed Ni-S bond lengths are comparable to the expected value for a covalent bond. Molecular orbital theory was invoked to show that the millerite structure with five-fold coordination around Ni is more stable than the nickeline structure (a-NiS) with six-fold coordination about each Ni. Thereby it is rationalised that the low temperature phase (3-NiS occurs in nature and the high temperature phase a-NiS does not. 

We have seen that the crystal-field model provides a basis for explaining many features of transition-metal complexes. In fact, it can be used to explain many observations in addition to those we have discussed. Many lines of evidence show, however, that the bonding between transition-metal ions and ligands must have some covalent character. Molecular-orbital theory (Sections 9.7 and 9.8) can also be used to describe the bonding in complexes, although the application of molecular-orbital theory to coordination compounds is beyond the scope of our discussion. The crystal-field model, although not entirely accurate in all details, provides an adequate and useful first description of the electronic structure of complexes. 

How does electron sharing lead to bonding between atoms Two models have been developed to describe covalent bonding valence bond theory and molecular orbital theory. Each model has its strengths and weaknesses, and chemists tend... 

We said in Section 1.5 that chemists use two models for describing covalent bonds valence bond theory and molecular orbital theory. Having now seen the valence bond approach, which uses hybrid atomic orbitals to account for geometry and assumes the overlap of atomic orbitals to account for electron sharing, let s look briefly at the molecular orbital approach to bonding. We ll return to the topic in Chapters 14 and 15 for a more in-depth discussion. 

This discrepancy between experiment and theory (and many others) can be explained in terms of an alternative model of covalent bonding, the molecular orbital (MO) approach. Molecular orbital theory treats bonds in terms of orbitals characteristic of the molecule as a whole. To apply this approach, we carry out three basic operations. 

Lewis s theory of the chemical bond was brilliant, but it was little more than guesswork inspired by insight. Lewis had no way of knowing why an electron pair was so important for the formation of covalent bonds. Valence-bond theory explained the importance of the electron pair in terms of spin-pairing but it could not explain the properties of some molecules. Molecular orbital theory, which is also based on quantum mechanics and was introduced in the late 1920s by Mul-liken and Hund, has proved to be the most successful theory of the chemical bond it overcomes all the deficiencies of Lewis s theory and is easier to use in calculations than valence-bond theory. 

The g-values and A values of Table IV reveal that the particular layer silicate has more effect on ESR parameters of adsorbed Cu " - than saturation of exchange sites with different cations such as Na+ and Ca +. Also, the smectites as a group have lower g and higher A values than vermiculite. From the perspective of molecular orbital theory, low g and high A values correspond to more covalent bonds between Cu + and the ligand (19). Thus,... 

Still another model to represent the bonding that takes place in covalent compounds is the molecular orbital theory. In the molecular orbital (MO) theory of covalent bonding, atomic orbitals (AOs) on the individual atoms combine to form orbitals that encompass the... 

In the molecular orbital (MO) theory of covalent bonding, atomic orbitals form molecular orbitals that encompass the entire molecule. 

Molecular Orbital Theory Model. Oxygen and hydrogen atoms in H2O are held together by a covalent bond. According to the quantum molecular orbital theory of covalent bonding between atoms, electrons in molecules occupy molecular orbitals that are described, using quantum mechanical language, by a linear combination of... 

Molecular orbital theory of the covalent bond shows a direct relationship between the extent of the overlap of two atomic orbitals and the bond strength. The larger the overlap, the stronger the bond. Maximum overlapping would produce the strongest bond and the most stable system. Maximum overlap of the H and O atomic orbitals... 

A second quantum mechanical bonding theory is molecular orbital theory. This theory is based on a wave description of electrons. The molecular orbital theory assumes that electrons are not associated with an individual atom but are associated with the entire molecule. Delocalized molecular electrons are not shared by two atoms as in the traditional covalent bond. For the hydrogen molecule, the molecular orbitals are formed by the addition of wave functions for each Is electron in each hydrogen atom. The addition leads to a bonding molecular... 

Molecular Orbital Theory a model that uses wave functions to describe the position of electrons in a molecule, assuming electrons are delocalized within the molecule Molecular Solid a solid that contains molecules at the lattice points Molecule a group of atoms that exist as a unit and are held together by covalent bonds... 

A covalent bond occurs when two atoms share two or more electrons. More specifically, in the context of molecular orbital theory, a single covalent bond between two atoms occurs when two electrons (one from each of the atoms) occupies a bonding molecular orbital. Other terms... 

Throughout the book, theoretical concepts and experimental evidence are integrated An introductory chapter summarizes the principles on which the Periodic Table is established and describes the periodicity of various atomic properties which are relevant to chemical bonding. Symmetry and group theory are introduced to serve as the basis of all molecular orbital treatments of molecules. This basis is then applied to a variety of covalent molecules with discussions of bond lengths and angles and hence molecular shapes. Extensive comparisons of valence bond theory and VSEPR theory with molecular orbital theory are included Metallic bonding is related to electrical conduction and semi-conduction. 

We have used the concepts of the resonance methods many times in previous chapters to explain the chemical behavior of compounds and to describe the structures of compounds that cannot be represented satisfactorily by a single valence-bond structure (e.g., benzene, Section 6-5). We shall assume, therefore, that you are familiar with the qualitative ideas of resonance theory, and that you are aware that the so-called resonance and valence-bond methods are in fact synonymous. The further treatment given here emphasizes more directly the quantum-mechanical nature of valence-bond theory. The basis of molecular-orbital theory also is described and compared with valence-bond theory. First, however, we shall discuss general characteristics of simple covalent bonds that we would expect either theory to explain. 

Polar Covalent Bonds 7.13 Molecular Orbital Theory The... 

To introduce some of the basic ideas of molecular orbital theory, let s look again at orbitals. The concept of an orbital derives from the quantum mechanical wave equation, in which the square of the wave function gives the probability of finding an electron within a given region of space. The kinds of orbitals that we ve been concerned with up to this point are called atomic orbitals because they are characteristic of individual atoms. Atomic orbitals on the same atom can combine to form hybrids, and atomic orbitals on different atoms can overlap to form covalent bonds, but the orbitals and the electrons in them remain localized on specific atoms. 

Before leaving this brief introduction to molecular orbital theory, it is worth stressing one point. This model constructs a series of new molecular orbitals by the combination of metal and ligand orbitals, and it is fundamental to the scheme that the ligand energy levels and bonding are, and must be, altered upon co-ordination. Whilst the crystal field model probably over-emphasises the ionic contribution to the metal-ligand interaction, the molecular orbital models probably over-emphasise the covalent nature. 

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