Metal atom Molecular orbitals

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. 

Chemical considerations suggest that metal-olefin back donation will be less important for silver(I) than for platinum(II), and Basch s ab initio calculations on [Ag(C2H4)]+ (75) have confirmed this view. These calculations suggest that most of the electronic rearrangement of the ethylene unit in this complex ion can be accounted for by the polarization effects induced by the positive charge on the silver atom. Indeed, the bonding metal-olefin molecular orbital has only 6.5% Ag 5s orbital character. This result agrees nicely with recent ESR studies on y-irradiated silver-olefin complexes which estimate a 5s spin density of 4.6% for this molecular orbital 92, 93). 

The relative importance of a and r contributions to the overall bonding is unclear, but several different combinations of relative strengths lead to limiting case models. When there are 2 electrons in the forward (T-bond and 2 electrons in the ir-backbond, there are 2 bonding electrons for each metal-carbon bond. This is mathematically equivalent to 2tr-bonds and a metallocyclopropane structure (72). This model does not necessitate strict sp3 hybridization at the carbon atoms. Molecular orbital calculations for cyclopropane (15) indicate that the C—C bonds have higher carbon atom p character than do the C—H bonds. Thus, the metallocyclopropane model allows it interactions with substituent groups on the olefin (68). 

The metallic bond can be seen as a collection of molecular orbitals between a large number of atoms. As Figure A.6 illustrates, the molecular orbitals are very close and form an almost continuous band of levels. It is impossible to detect that the levels are actually separated from each other. Rather, the bands behave in many respects similarly to the orbitals of the molecule in Figure A. 5 if there is little overlap between the electrons, the interaction is weak and the band is narrow. This is the case for the d-electrons of the metal. Atomic d-orbitals have pronounced shapes and orientations that are largely retained in the metal. This in contrast to the s electrons, which are strongly delocalized that is, they are not restricted to well-defined regions between atoms, and form an almost free electron gas that spreads out over the whole metal. Hence, the atomic s-electron wave functions overlap to a great extent, and consequently the band they form is much broader. 

For an introduction to electronic states and their creation from atomic/molecular orbitals, we first discuss a simple 3-orbital model, which consists of a ji- and a n -orbital located at the ligands and a central metal d-orbital. First, from these orbitals many-electron states with pure spin will be constructed, i.e., pure singlets and triplets. This situation corresponds to the case of vanishing SOC. Later on, it will be explained, how SOC mixes the pure spin states. 

Figure 3.14. (a) Atomic orbitals of the metal and molecular orbitals of some clusters M3 (triangle), Mg (octahedron), M13 (cuboctahedron), and M19 octahedron), (b) Qualitative scheme of the dependence of molecular orbitals energy on the number of the metal atoms in the cluster showing the final band structure of a typical metal. The arrow denotes the Fermi energy "p. 

Litinskii et al. investigated the contact between the fluoropolymer SKF 32 (fluorine-containing rubber) and three oxide surfaces molybdenum oxide and solid solutions of molybdenum-niobium oxides and molybdenum-technetium oxide [115], Contact appeared when a bond was created between a metal atom and a carbon that lost its fluorine atom. Molecular orbitals on clusters simulating the contact between the fluoropolymer and the oxide surfaces have been computed using the DFT B3LYP/3-21g. Nine contacts between the three available metal atoms (molybdenum, niobium, and technetium) and the three carbon atoms of the fluoropolymer have been studied. Electronic spectra revealed that the molybdenum atom leads to the most favorable contact with the SKF 32 fluoropolymer. A similar analysis has been carried out with ferric and nickel oxides [116]. 

The reaction between a trinuclear metal carbonyl cluster and trimetbyl amine borane has been investigated (41) and here the cluster anion functions as a Lewis base toward the boron atom, forming a B—O covalent bond (see Carbonyls). Molecular orbital calculations, supported by stmctural characterization, show that coordination of the amine borane causes small changes in the trinuclear framework. 

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. 

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