Molecular orbital models, solid-state

The structural strengths of the hybridization model were combined with the electronic strengths of the crystal-field model in a molecular-orbital model albeit with the loss of the simplicity of the earlier models. The essential aspects of this MO model will be discussed in Chapter 1. The key point here is that, if one wishes to understand the electronic structure of metal-coordination compounds, one need go beyond the Lewis model of two-center-two-electron bonds. It should be obvious, then, that this is also a requirement for organometallic complexes, metal clusters and extended solid-state systems containing metal atoms. 

Tosi MP (1964) Cohesion of ionic sohds in the Bom model. Solid State Phys 131 533-545 Tossell JA, Gibbs GV (1977) Molecular orbital studies of geometries and spectra of minerals and inorganic compounds. Phys Chem Miner 2 21-57... 

M. E. Eberhart, K. H. Johnson, D. Adler, and R. C. O Handley, Ouster molecular orbital models of melting and the amorphous state, J. Non-Cryst. Solids 83,12-26 (1986). 

The Kronig-Penney model, although rather crude, has been used extensively to generate a substantial amount of useful solid-state theory [73]. Simple free-electron models have likewise been used to provide logical descriptions of a variety of molecular systems, by a method known in modified form as the Hiickel Molecular Orbital (HMO) procedure [74]. 

In addition to the above prescriptions, many other quantities such as solution phase ionization potentials (IPs) [15], nuclear magnetic resonance (NMR) chemical shifts and IR absorption frequencies [16-18], charge decompositions [19], lowest unoccupied molecular orbital (LUMO) energies [20-23], IPs [24], redox potentials [25], high-performance liquid chromatography (HPLC) [26], solid-state syntheses [27], Ke values [28], isoelectrophilic windows [29], and the harmonic oscillator models of the aromaticity (HOMA) index [30], have been proposed in the literature to understand the electrophilic and nucleophilic characteristics of chemical systems. 

An X-ray atomic orbital (XAO) [77] method has also been adopted to refine electronic states directly. The method is applicable mainly to analyse the electron-density distribution in ionic solids of transition or rare earth metals, given that it is based on an atomic orbital assumption, neglecting molecular orbitals. The expansion coefficients of each atomic orbital are calculated with a perturbation theory and the coefficients of each orbital are refined to fit the observed structure factors keeping the orthonormal relationships among them. This model is somewhat similar to the valence orbital model (VOM), earlier introduced by Figgis et al. [78] to study transition metal complexes, within the Ligand field theory approach. The VOM could be applied in such complexes, within the assumption that the metal and the... 

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. 

Two theoretical approaches for calculating NMR chemical shift of polymers and its application to structural characterization have been described. One is that model molecules such as dimer, trimer, etc., as a local structure of polymer chains, are in the calculation by combining quantum chemistry and statistical mechanics. This approach has been applied to polymer systems in the solution, amorphous and solid states. Another approach is to employ the tight-binding molecular orbital theory to describe the NMR chemical shift and electronic structure of infinite polymer chains with periodic structure. This approach has been applied to polymer systems in the solid state. These approaches have been successfully applied to structural characterization of polymers... 

Nano-scale and molecular-scale systems are naturally described by discrete-level models, for example eigenstates of quantum dots, molecular orbitals, or atomic orbitals. But the leads are very large (infinite) and have a continuous energy spectrum. To include the lead effects systematically, it is reasonable to start from the discrete-level representation for the whole system. It can be made by the tight-binding (TB) model, which was proposed to describe quantum systems in which the localized electronic states play an essential role, it is widely used as an alternative to the plane wave description of electrons in solids, and also as a method to calculate the electronic structure of molecules in quantum chemistry. 

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