4.14. Calculated electronic structure

Fig. 4.14. Calculated electronic structure of Pt. The total DOS and the decomposition into atomic orbitals are shown. The d states are listed under two symmetry types. Type l2, includes xy, yz, xz], and type includes (3z - r ), (x -/). The Fermi-level quantities are also listed. The d states comprise about 98% of the Fermi-level DOS. (Reproduced from Papaconstantopoulos, 1986, with permission.)...

Fig. 5. Calculated electronic structure by the LDA method of (a) an isolated Cuo molecule and (b) fee solid Cuo where the direct band gap at the X-point is 1.5 eV [60],...

Figure 10.9. (a) Schematic structure of a silicon quantum dot crystal and (b) its calculated electronic structure as a function of interparticle distance H. The size of the nanoparticles is L = 6.5 nm. At small H, a splitting of the quantized energy levels of single dots results in the formation of three-dimensional minibands. Reproduced from Ref. 64, Copyright 2001, with permission from the American Institute of Physics. 

In recent years, dynamic calculations of both the electronic and the molecular structure of complex molecular systems have started to become feasible. " These methods are based on the general idea that the electronic structure of the system is to be calculated on the fly as the nuclei move, while the nuclei respond to the forces determined from the dynamically calculated electronic structure. This assumes that the system moves on the lowest electronic state, and transitions between states are either ignored (because they are well separated in energy) or treated semiclassi-cally. 

Another method for calculating electronic structures of complex surfaces is the cluster calculation. As the electronic state of an atom is mostly affected by the nearest and second-nearest neighbors (Heine, 1980), the results of cluster calculations provide a reasonably accurate account of the electronic states of the top atoms on a surface. Fig. 4.17 is the result of a calculation of W clusters by Ohnishi and Tsukada (1989). 

Figure 12 Calculated electronic structure for isonicotinic acid adsorbed on Ti02 rutile (110) in the upper valence band, band-gap, and lower conduction band regions. The thin dashed line shows the total DOS, and the thick solid line the projected DOS for the adsorbate.

The real space or extended basis description has the advantage of building upon accurate results from plane-wave calculations of the electronic structure [30]. Nevertheless, electronic structure calculations based on localized basis sets can become as accurate and predictive as plane-wave based results [31]. Plane-wave based calculations have the difficulty of how to transpose the calculated electronic structure into a form useful for transport calculations. Transport calculations are better suited for description in localized basis sets, hence transport based on ah initio localized basis codes are turning to be the best tool [32]. 

Fig. 2 Calculated electronic structures of C60 anions using local density approximation (after [18])...

GVB Generalized valence bond. A theory that employs CF orbitals to calculate electronic structure with wave functions in which the electrons are formally coupled in a covalent manner. The simplest level of the theory is GVB PP (PP-perfect pairing), in which all the electrons are paired into bonds, as in the Lewis structure of the molecule. 

Quantum chemistry computations based on employing of PC Gamess version of semi-empirical PM3-method [1-2] allows to define equilibrium configuration and calculate electronic structure of some of the simplest Y-junctions of carbon nanotubes, which have slang name twig . On the place of nanotubes conjunction defective cycles appear. Their type, number and mutual displacement can be enough various even in comparatively simple cases. Only the part of obtained results is presented here. 

The most likely cause of such discrepancy is an unsuitable atomic scattering factor. That means, some factor that affects the chemical behaviour of an atom may, for instance, not be properly accounted for in the calculated electronic structure from which scattering factors are derived. The use of oriented non-spherical atomic ground-states has been proposed [182] as a possible remedy. On this basis theoretically acceptable chemical deformation densities have been obtained. Such usage has led to the development of aspherical-atom, or multipole refinement of crystallographic structures in charge-density studies. 

Within the tight-binding (TB) approach. Slater and Roster [64] described the linear combination of atomic orbitals (LCAO) method as an eflRcient scheme for calculation of the electronic structure of periodic solids. As this method is computationally much less demanding than other methods such as the plane-wave methods, it has been extensively employed to calculate electronic structures of various metals, semiconductors, clusters and a number of complex systems such as alloys and doped systems. The calculation of the electronic structure requires solving the Schrodinger equation with the TB Hamiltonian given by... 

We have concentrated so far on the determination of experimental quantities within DFT. The calculated electronic structure can also be studied with the goal to get chemical insight from it and answer questions like what is the bonding pattern How are bonds formed and broken Determination of localized orbitals has proved to be a useful tool in this direction. 

Abstract Theoretical investigations of ionic liquids are reviewed. Three main categories are discussed, i.e., static quantum chemical calculations (electronic structure methods), traditional molecular dynamics simulations and first-principles molecular dynamics simulations. Simple models are reviewed in brief. 

Fig. 17. Top Calculated electronic structure of SmS. Bottom Calculation for SmTe, (Ref. 56). Note the absence of 4/ states in the case of the telluride.

The calculated electronic structure of Siao indicates [20] that the highest occupied molecular orbital and the lowest xmoccupied molecular orbital display the same symmetry as those of Ceo. In addition the HOMO-LUMO gap is approximately half as large as that for Cm- As predicted for smaller size clusters, the geodesic form is not the most stable structure of Sieo [36]. 

George Schatz received his Ph.D. in chemistry in 1976 working for Aron Kuppermann at Caltech. He was a postdoc with John Ross at MIT 1975-6, and moved to Northwestern University in 1976, where he is now Morrison Professor of Chemistry. He has worked both in gas phase and materials theory, including dynamics calculations, electronic structure studies and classical electrodynamics. 

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