Molecular orbital band theory

Bonding in metals involves delocalization of electrons over the whole metal crystal, rather like the n electrons in graphite (Section 3.2) except that the delocalization, and hence also the high electrical conductivity, is three dimensional rather than two dimensional. Metallic bonding is best described in terms of band theory, which is in essence an extension of molecular orbital (MO) theory (widely used to represent bonding in small molecules) to arrays of atoms of quasi-infinite extent. 

Molecular orbital (MO) theory has been used to explain the bonding in metallic crystals, such as pure sodium or pure aluminum. Each MO, instead of dealing with a few atoms in a typical molecule, must cover the entire crystal (might be 1020 or more atoms ). Following the rule that the number of MOs must equal the number of atomic orbitals (AOs) combined, this many MOs must be so close on an energy level diagram that they form a continuous band of energies. Because of this factor, the theory is known as band theory. 

First, we introduce the two basic frameworks of electronic structure theory, molecular orbital (MO) theory and band theory. Electronic structure theory can provide calculation of the total energy of a system. In addition, MO and band theories give one-electron states, which are often used to represent electron (hole) dynamics. 

The essential feature of the interpretation of a PE spectrum and an important reason for the success of the technique is the role of molecular orbital (MO) theory in both its qualitative and quantitative aspects. The qualitative description of ionization bands as associated with particular atoms or groups of atoms, or with particular bonds in a molecule relates closely to the chemist s picture of the molecule. The quantitative description, where the data from MO calculations are related to the experimental observations, commences with the Koopmans approximation, that the IEs of a molecule are in 1 1 correspondence with its orbital eigenvalues (e) according to the relation illustrated in Figure 2. 

In this review we summarized our experience with the development and applications of semiempirical Pariser-Parr-Pople (PPP)-type and all-valence-electron methods to electronic spectra of radicals. After the era of PPP calculations on closed-shell molecules and the advent of semiempirical all-valence-electron methods, the electronic spectra of radicals represented a new challenge for molecular orbital (MO) theory. It was a time when progress in experimental techniques resulted in accumulation of a vast amount of data on the electronic spectra of radicals of various structural types. Compared to closed-shell molecules, the electronic spectra of some radicals exhibited peculiar features bands in the near infrared, many transitions in the whole UV/vis region, and some bands of extraordinary intensity. Clearly, without the help of MO theory, their interpretation seemed even harder than with closed-shell molecules. 

Molecular orbital (MO) theory offers another explanation of bonding in solids. It is a more quantitative, and therefore more useful, model called band theory. We ll focus on bonding in metals and the conductivity of metals, metalloids, and nonmetals. 

It should be noted that a comprehensive ELNES study is possible only by comparing experimentally observed structures with those calculated [2.210-2.212]. This is an extra field of investigation and different procedures based on molecular orbital approaches [2.214—2.216], multiple-scattering theory [2.217, 2.218], or band structure calculations [2.219, 2.220] can be used to compute the densities of electronic states in the valence and conduction bands. 

In Chapter 9, we considered a simple picture of metallic bonding, the electron-sea model The molecular orbital approach leads to a refinement of this model known as band theory. Here, a crystal of a metal is considered to be one huge molecule. Valence electrons of the metal are fed into delocalized molecular orbitals, formed in the usual way from atomic... 

The SCF method for molecules has been extended into the Crystal Orbital (CO) method for systems with ID- or 3D- translational periodicityiMi). The CO method is in fact the band theory method of solid state theory applied in the spirit of molecular orbital methods. It is used to obtain the band structure as a means to explain the conductivity in these materials, and we have done so in our study of polyacetylene. There are however some difficulties associated with the use of the CO method to describe impurities or defects in polymers. The periodicity assumed in the CO formalism implies that impurities have the same periodicity. Thus the unit cell on which the translational periodicity is applied must be chosen carefully in such a way that the repeating impurities do not interact. In general this requirement implies that the unit cell be very large, a feature which results in extremely demanding computations and thus hinders the use of the CO method for the study of impurities. 

Gas-surface interactions and reactions on surfaces play a crucial role in many technologically important areas such as corrosion, adhesion, synthesis of new materials, electrochemistry and heterogeneous catalysis. This chapter aims to describe the interaction of gases with metal surfaces in terms of chemical bonding. Molecular orbital and band structure theory are the basic tools for this. We limit ourselves to metals. 

With the absorption of a quantum with an energy of more than 3.05 eV resp. 3.29 eV, an electron is lifted out of the valence band and into the conduction band, thereby forming an exciton (Fig. 5). This interpretation is also supported by the molecular orbital theory and the crystal field theory regarding the bonding conditions in the TiC lattice. 

Chemical bonds are defined by their frontier orbitals. That is, by the highest molecular orbital that is occupied by electrons (HOMO), and the lowest unoccupied molecular orbital (LUMO). These are analogous with the top of the valence band and the bottom of the conduction band in electron band theory. However, since kinks are localized and non-periodic, band theory is not appropriate for this discussion. 

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