Molecular Orbitals and Band Structure

FIGURE 7-13 Band Structure of Insulators and Conductors, (a) Insulator, (b) Metal with no voltage applied, (c) Metal with electrons excited by applied voltage. 

FIGURE 7-14 Energy Bands and Density of States, (a) An insulator, with a filled valence band, (b) A metal, with a partly filled valence band and a separate empty band. 

FIGURE 7-15 Semiconductor Bands at 0 K and at Room temperature, (a) Intrinsic semiconductor. 

FIGURE 7-16 Band-energy Diagram of a p-n Junction, (a) At equilibrium, the two Fermi levels are at the same energy, changing from the pure n- or p-type Fermi levels because a few electrons can move across the boundary (vertical dashed line), (b) With forward bias, current flows readily. 

7-3-1 DIODES, THE PHOTOVOLTAIC EFFECT, AND LIGHT-EMITTING DIODES 

FIGURE 7.13 Effect of Cations on Hydrogen Bonding Networks. 

The concept of orbital conservation (Chapter 5) requires that when molecular orbitals are formed from two atoms, each interacting pair of atomic orbitals (such as 2s) gives rise to two molecular orbitals (0-2 and 0-2 ). When n atoms are used, the same approach results in n molecular orbitals. In the case of solids, n is very large—Avogadro s number for a mole of atoms. If the atoms were all in a one-dimensional row, the lowest energy orbital would 

FIGURE 7.16 Semiconductor Bands at 0 K and at Room Temperature, (a) Intrinsic semiconductor, (b) an n-type semiconductor, and (c) a p-type semiconductor, fp is defined later in this section. 

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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. 

Pyrite has been the subject of a number of molecular-orbital and band-structure calculations. Thus, MS-SCF-Xa calculations on an FeS " cluster have been performed by Li et al. (1974), Tossell (1977b), Harris... 

Interesting criteria for the occurrence of a metal - metal bond can be obtained from a study of the electronic structure of the compound (molecular orbital and band structure calculations) and from the number of electrons available for metal - metal bonds, expressed by the so - called VEC (Valence Electron Concentration). In this counting of electrons, no attempt Is made to differentiate localized electron - pair bonds from bonding in terms of molecular orbitals delocalized over the entire cluster. 

In the absence of dynamic and static disorder, all partially filled band systems would exhibit coherent transport over long distances. With static and dynamic disorder, the modulation of the simple molecular orbital or band structure by nuclear effects entirely dominates transport. This is clear both in the Kubo linear response formulation of conductivity and in the Marcus-Hush-Jortner formulation of ET rates. The DNA systems are remarkable for the different kinds of disorder they exhibit in addition to the ordinary static and dynamic disorder expected in any soft material, DNA has the covalent disorder arising from the choice of A, T, G, or C at each substitution base site along the backbone. Additionally, DNA has the characteristic orientational and metric (helicoidal) disorder parameters arising from the fundamental motif of electron motion along the r-stack. 

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. 

Next, we consider the electronic structure of a metal formed from atoms each contributing two electrons. We have seen that overlap of v orbitals in N atoms produces A/ molecular orbitals and that each orbital can accommodate two electrons. The maximum number of electrons that can be placed in N orbitals is 2N, When each atom contributes two electrons, there are 2A/ electrons to be placed in molecular orbitals. Thus, when each atom contributes two electrons, the band is full and the material is an insulator (Fig. 3,12b). The major success of band theory rests on the explanation of the three types of electrical conductors (Fig. 3.12). 

The determination of the perfect lattice band structure is relatively straightforward. The hole and electron occupy states based respectively upon the highest filled and lowest unfilled molecular orbitals of the parent molecule. The energy levels of these states are broadened into bands by the intermolecular overlap of the molecular orbitals. Knowing the crystal structure and assuming reasonable forms of these orbitals, the band structure may be calculated (Chojnacki, 1968 Le Blanc, 1961, 1962a, b). 

Earlier chapters in this volume have dealt with the molecular properties and crystal structures of organic metals. The large planar molecules under consideration here are usually stacked face to face in chains sometimes the molecular planes are perpendicular to the stacking axis, as in the case of the Bechgaard salts, or they may be tilted by as much as 30°, as in TTF-TCNQ. Because the overlap of the partially occupied tt orbitals is much better along the stacking axis, their electronic band structures are often quasi-one-dimensional. 

In order to make a correct analysis of such an experimental spectrum, an appropriate theoretical calculation is indispensable. For this purpose, some of calculational methods based on the molecular orbital theory and band structure theory have been applied. Usually, the calculation is performed for the ground electronic state. However, such calculation sometimes leads to an incorrect result, because the spectrum corresponds to a transition process among the electronic states, and inevitably involves the effects due to the electronic excitation and creation of electronic hole at the core or/and valence levels. Discrete variational(DV) Xa molecular orbital (MO) method which utilizes flexible numerical atomic orbitals for the basis functions has several advantages to simulate the electronic transition processes. In the present paper, some details of the computational procedure of the self-consistent-field (SCF) DV-Xa method is firstly described. Applications of the DV-Xa method to the theoretical analysises of XPS, XES, XANES and ELNES spectra are... 

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