Frontier band structure

GGA property calculation on optimized bulk pyrite has been performed. The calculated band structure and frontier orbital distribution are presented in Fig. 9.3 and Fig. 9.4. The calculated band gap of FeS2 is 0.97 eV, and it is in good line... 

The fuzzy frontier between the molecular and the nanometric level can be elucidated from an electronic point of view. Molecules and small clusters can be described as systems in which the metal atoms form well-defined bonding and antibonding orbitals. Large clusters or small nanoparticles (quantum dots) with dimensions of a few nanometers are intermediate between the size of molecules and bulk material, presenting discrete energy levels with a small band gap owing to quantum-mechanical rules. Finally, larger particles tend to lose this trend and display a typical band structure similar to that of the bulk material. 

The actual band structure, as it emerges from an extended Hiickel calculation at Pt-Pt = 3.0 A, is shown in Fig. 3. It matches our expectations very precisely. There are, of course, bands below and above the frontier orbitals discussed these are Pt-H o and o orbitals. 

What I have tried to do in this book and the published papers behind it is to move simultaneously in two directions—to form a link between chemistry and physics by introducing simple band structure perspectives into chemical thinking about surfaces. And I have tried to interpret these delocalized band structures from a very chemical point of view—via frontier orbital considerations based on interaction diagrams. 

An LCAO (linear combination of atomic orbitals) local-density functional approach was used to calculate the band structures of a series of polymer chain conformations unsubstituted polysilane in the all-trans conformation and in a 411 helical conformation, and all-trans poly(dimethylsilane). Calculated absorption spectra predict a highly anisotropic absorption for the all-trans conformation of polysilane, with the threshold absorption peak arising strictly from polarizations parallel to the chain axis. The absorption spectrum for the helical conformation is much more isotropic. Results for the dimethyl-substituted polysilane chain suggest that the states immediately surrounding the Fermi level retain their silicon-backbone a character upon alkyl-group substitution, although the band gap decreases by I eV because of contributions from alkyl substituent states both below the valence band and above the conduction band to the frontier states. 

It is essential to give a correct and conclusive description of the electronic properties of carbon nanotubes to get an understanding of their broad potential for appHcations. Chemists and physicists have developed two fundamentally different concepts of the matter. They are either based on considering electrons in molecular orbitals, especially in frontier orbitals, and on examining the Jt-system, or they pursue a soHd-state physical approach that employs density-of-state functions and the band structure in the Brillouin zone of a two-dimensional graphene. 

Fig. 1. The fundamental interactions between the frontier orbitals of an adsorbate and a metal surface band structure that occur upon chemisorption.

It is important to note that many metallic properties, such as the Knight shift and the Korringa relationship, are determined by the finite and quasiFermi level local density of states ( p-LDOS). In the approximation most familiar to chemists, what this means is that the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap in metals is much smaller than the thermal energy kf,T, and the value of the / f-LDOS reflects the frontier orbital contributions in a metallic system [23]. The /ip-LDOS also represents a crucial metal sxudace attribute that can serve as an important conceptual bridge between the delocalized band structure (physics) picture and the localized chemical bonding (chemical) picture of metal-adsorbate interactions. 

Figure S a) Calculated band structure, b) calculated DOS spectrum of FPV and c) pattern of the frontier orbitals of PPV at < =1. i) conduction band, ii) valence band...

We attempt to extend the Hard-Soft Acid-Base (HSAB) principle for the reactions in solutions to interactions in solids. First we point out the important link between the absolute hardness of acid-and-base and the average energy gap. Then we discuss the electronic band structures of various solids, e.g., metals, semimetals, semiconductors and insulators. On the basis of energy gaps, we elaborate various consequences of the acid-base interactions in solids. The applications of HSAB principle and the frontier orbital concept to the solid adhesion and surface interactions between metals and polymers will be verified by experimental results reported in the literature. The new findings reported in this paper should be beneficial to those who are carrying out research in or processing thin-film microelectronic devices or thick-film multilayer structures. 

For the acid-base interaction in solutions, in 1963, Pearson proposed the hard-soft acid-base (HSAB) principle to describe some basic rules about the kinetics and equilibrium of the reaction. In this paper, we attempt to apply the HSAB principle to solid interactions with the aid of the frontier orbital method. We shall first describe the HSAB principle as it has been evolved in recent years " and then the band structures of solids. After we demonstrate the compatibility between the HSAB principle and the band structures in the solid state, we then illustrate with several examples of adhesion and tribointeractions between metals and... 

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