Metals molecular orbital theory

Frontier Molecular Orbital theory is closely related to various schemes of qualitative orbital theory where interactions between fragment MOs are considered. Ligand field theory, as commonly used in systems involving coordination to metal atoms, can be considered as a special case where only the d-orbitals on the metal and selected orbitals of the ligands are considered. 

Application of molecular orbital theory to electron transfer reactions of metal complexes in solution. J. K. Burdett, Comments Inorg. Chem., 1981,1, 85-103 (7). 

Molecular orbital theory of transition metal complexes. D. A. Brown, W. J. Chambers and N. J. Fitzpatrick, Inorg. Chim. Acta, Rev., 1972, 6, 7-30 (193). 

The development of molecular orbital theory (MO theory) in the late 1920s overcame these difficulties. It explains why the electron pair is so important for bond formation and predicts that oxygen is paramagnetic. It accommodates electron-deficient compounds such as the boranes just as naturally as it deals with methane and water. Furthermore, molecular orbital theory can be extended to account for the structures and properties of metals and semiconductors. It can also be used to account for the electronic spectra of molecules, which arise when an electron makes a transition from an occupied molecular orbital to a vacant molecular orbital. 

Use molecular orbital theory to account for the differences between metals, insulators, and semiconductors (Sections 3.13 and 3.14). 

There are two major theories of bonding in d-metal complexes. Crystal field theory was first devised to explain the colors of solids, particularly ruby, which owes its color to Cr3+ ions, and then adapted to individual complexes. Crystal field theory is simple to apply and enables us to make useful predictions with very little labor. However, it does not account for all the properties of complexes. A more sophisticated approach, ligand field theory (Section 16.12), is based on molecular orbital theory. 

Although Ni(CO)4 was discovered many years ago, no neutral Ni2(CO)x compound has ever been synthesized in macroscopic amounts. However, several communications report ionic species such as [Ni2(CO)8l+, [Ni2(CO)7], and [Ni2(CO)6]+, where structures with one or two bridging carbonyls are proposed.2418 Plausible structures for neutral Ni2(CO)x (x = 5, 6, 7) have been investigated by theoretical methods, and decomposition temperatures well below room temperature have been predicted.2419,2420 Tetra-, penta-, and hexanuclear nickel carbonyl clusters have been investigated by means of molecular orbital theory. It is found that the neutral forms are more stable than the corresponding anionic forms but the anionic forms gain in stability as the nuclearity rises.2421 Nickel carbonyl cluster anions are manifold, and structural systematics have been reviewed.2422,2423 An example includes the anion [Ni9(CO)i6]2- with a close-packed two-layer metal core.2424... 

A heterogeneous catalytic reaction begins with the adsorption of the reacting gases on the surface of the catalyst, where intramolecular bonds are broken or weakened. The Appendix explains how this happens on metals in terms of simplified molecular orbital theory. Next, the adsorbed species react on the surface, often in... 

The theory of band structures belongs to the world of solid state physicists, who like to think in terms of collective properties, band dispersions, Brillouin zones and reciprocal space [9,10]. This is not the favorite language of a chemist, who prefers to think in terms of molecular orbitals and bonds. Hoffmann gives an excellent and highly instructive comparison of the physical and chemical pictures of bonding [6], In this appendix we try to use as much as possible the chemical language of molecular orbitals. Before talking about metals we recall a few concepts from molecular orbital theory. 

Metals conduct electricity through conduction bands. Conduction bands arise from the application of Molecular Orbital theory to multi-atom systems. (See Chapter 10.) The bonding molecular orbitals and, sometimes, other molecular... 

Due to its importance in many industrial processes, the prototypical reaction of CO binding to metal surfaces has received much attention. Using Hiickel molecular orbital theory, Blyholder showed that CO bonding at top sites consists of the donation of electrons from the filled CO 5a HOMO to the metal d 2 orbitals with a back-donation of electrons from the metal dxz caddy orbitals to the CO 2n LUMO. Consequently,... 

The Fermi surface plays an important role in the theory of metals. It is defined by the reciprocal-space wavevectors of the electrons with largest kinetic energy, and is the highest occupied molecular orbital (HOMO) in molecular orbital theory. For a free electron gas, the Fermi surface is spherical, that is, the kinetic energy of the electrons is only dependent on the magnitude, not on the direction of the wavevector. In a free electron gas the electrons are completely delocalized and will not contribute to the intensity of the Bragg reflections. As a result, an accurate scale factor may not be obtainable from a least-squares refinement with neutral atom scattering factors. 

Fenske, R. F. Semi-empirical molecular-orbital theory for transition-metal complexes. Inorg. Chem. 4, 33 (1965). 

Molecular orbital theory may provide an explanation for stereochemical differences between carboxylate-metal ion and phosphate-metal ion interactions. Detailed ab initio calculations demonstrate that the semipo-lar 1 0 double bond of RsP=0 is electronically different from the C=0 double bond, for example, as found in H2C=0 (Kutzelnigg, 1977 Wallmeier and Kutzelnigg, 1979). The P=0 double bond is best described as a partial triple bond, that is, as one full a bond and two mutually perpendicular half-7r bonds (formed by backbonding between the electrons of oxygen and the empty d orbitals of phosphorus). Given this situation, a lone electron pair should be oriented on oxygen nearly opposite the P=0 bond, and these molecular orbital considerations for P=0 may extend to the phosphinyl monoanion 0-P=0. If this extension is valid, then the electronic structure of 0-P=0 should not favor bidentate metal complexation by phosphate this is in accord with the results by Alexander et al. (1990). 

Extensions of this model in which the atomic nuclei and core electrons are included by representing them by a potential function, V, in Equation (4.1) (plane wave methods) can account for the density of states in Figure 4.3 and can be used for semiconductors and insulators as well. We shall however use a different model to describe these solids, one based on the molecular orbital theory of molecules. We describe this in the next section. We end this section by using our simple model to explain the electrical conductivity of metals. 

Mathematical treatments of metal-olefin bonding have been given, mainly in terms of molecular-orbital theory (22, 54, 73). 

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. 

When the unpaired electron is delocalized over a number of atoms, molecular orbital theory must be applied to obtain a molecular description of the resulting magnetic species. In this situation there is less opportunity for substantial contributions from L, and in general the more delocalized the electron the more like a free electron it appears. In some cases, the electron is delocalized over only a few atoms, and in these cases modest contributions from L are expected, especially if one of the atoms is a transition metal. If more extensive delocalization is present, or if all the atoms involved are light, only small contributions (e.g., from 2fi orbitals) may be observed. 

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