ELECTRONIC STRUCTURE OF CARBON

Carbides, like all materials, have a well-defined internal electronic structure which governs their behavior and controls their properties. This means that, in order to understand their mechanism of formation and their general characteristics and properties, it is essential to have a clear picture of the electronic configuration of their constituents. The element common to all carbides is, of course, carbon a short review of its structure follows.Pl 

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Experimental measurements to test the remarkable theoretical predictions of the electronic structure of carbon nanotubes are difficult to carry out because... 

Experimental measurements to test these remarkable theoretical predictions of the electronic structure of carbon nanotubes are difficult to carry out because of the strong dependence of the predicted properties on tubule diameter and chirality. Ideally, electronic or optical measurements should be made on individual single-wall nanotubes that have been characterized with regard to diameter and chiral angle. Further ex-... 

Studies on the electronic structure of carbon nanotube (CNT) is of much importance toward its efficient utilisation in electronic devices. It is well known that the early prediction of its peculiar electronic structure [1-3] right after the lijima s observation of multi-walled CNT (MWCNT) [4] seems to have actually triggered the subsequent and explosive series of experimental researches of CNT. In that prediction, alternative appearance of metallic and semiconductive nature in CNT depending on the combination of diameter and pitch or, more specifically, chiral vector of CNT expressed by two kinds of non-negative integers (a, b) as described later (see Fig. 1). 

This is the area of greatest interest to quantitative biochemistry and is dependent upon the electronic structure of carbon compounds. Absorption of radiation in this region of the spectrum causes transitions of electrons from molecular bonding orbitals to the higher energy molecular antibonding orbitals. 

The divalent carbon(O) atom in L C L has two lone electron pairs which makes CL2 a particular class of ligands which may bind as a bidentate Lewis base to one and to two monodentate Lewis acids. The nature of the ligand L determines whether a divalent carbon atom behaves as a carbone or as a carbene. The newly gained insight into the electronic structure of carbones opens a large field for theoretical and experimental research. 

One classical example that apphes the electroneutrality principle is the electronic structure of carbon monoxide, a diatomic molecule with a very small dipole moment of 0.110 debye. The only electronic structure that satisfies the octet rule for CO is C=0 , a structure that corresponds to C and O, if the shared electron pairs are equally devided by the two atoms. Pauling showed that the electronegativity difference of 1.0 would correspond to about 22% partial ionic character for each bond, and to charges of and 0° +. A second possible electronic structure, C=O , does not complete the octet for carbon. The partial ionic character of the bonds corresponds to C0.44+ If these two structures contribute... 

Resonance Occasionally no reasonable electronic picture can be drawn for a molecule which could satisfactory account for its observed properties. For example, the electronic structure of carbon dioxide may be represented by at least three possible electronic arrangements given below ... 

To describe the electronic structure of carbon nanotubes the Hubbard model has been chosen as it can describe the electrical and magnetic properties and high temperature superconductivity effects also [11]. The model includes the terms of the electron jump energy in vicinity approach and the energy of Coulomb s repulsion of two electrons localized on the same point of unit cell. Hubbard Hamiltonian for the described system is following [11] ... 

ELECTRONIC STRUCTURE OF CARBON NANOTUBES OF VARIABLE DIAMETER... 

In the framework of semi-empirical method PM3 (worked out by Stewart [2,3] especially for calculation of electronic structure of carbon-contained organic molecules) the calculations of equilibrium configurations, full energy, heat of formation and electronic structure of different types of T-junctions of carbon zigzag and armchair nanotubes were done. 

The attempt of systematic theoretical investigation of the influence of defects on geometrical configuration and electronic structure of carbon zigzag and armchair nanotubes is undertaken. 

The electronic structure of carbon nanotubes immediately caught the attention of the theoretical community. Early models of the electronic band structure of nanotubes were closely related to models that were successfully applied to graphite [137,138]. The properties of SWNTs were first addressed in [137]. 

Carbon atoms crystallize in several forms. Graphite and diamond are well known carbon polymorphs. Fullerenes, which were discovered in the 1980 s, have also been well characterized. Carbon materials show a variety of different physical and chemical properties. Because of this the electronic structure of carbon materials has been investigated using a number of different experimental techniques, for example, XPS, UPS and XANES. Theoretical studies of carbon materials have been also performed. However, experimentally observed spectra are not always consistent with theoretical predictions. Recently, in order to understand the various kinds of observed electronic spectra, DV-Xa calculations have been performed on a small cluster model. [1] In the present paper, we report results of DV-Xa calculations performed on the carbon materials graphite, alkali graphite intercalation compounds (GIC), fullerene, and fluorinated fullerenes. 

Kavan, L. Dunsch, L. Kataura, H. Electrochemical tuning of electronic structure of carbon nanotubes and fullerene peapods. Carbon 2004, 42, 1011-1019. 

Hertel, T., Moos, G. Influence of excited electron lifetimes on the electronic structure of carbon nanotubes. Chem. Phys. Lett., 320, 359-364 (2000)... 

The electronic structure of carbon monoxide on valence bond terms can be visualized as I and II ... 

All in all our work implies that the highest filled orbitals are of a symmetry. To anyone reflecting on the electronic structure of carbon dioxide it is extraordinary to find the a orbital above the tt orbital, implying that the latter forms he stronger bond. Nevertheless this state of affairs was anticipated many years ago in the overlap calculations of Belford and Belford (4). They pointed out that the angular nodal properties of the f and f orbitals are such that at short distances the f -p overlap may actually be less than the f -p overlap a result con irmed in a calculation by Newman (5). 

Electron spin resonance (ESR), which is also termed as electron paramagnetic resonance (EPR), is another spectroscopic method to provide valuable information about the electronic structure of carbon nanotubes. 

When a carbon atom is attached to two other atoms, as in acetylene or carbon dioxide, there is sp hybridization and the bonds lie in a straight line. The electronic structure of carbon dioxide is shown in Figure 1.19. Two % bonds are now formed in addition to the a bonds. In the figure, the unhybridized p orbitals above and below the plane overlap with the p orbitals of the right-hand oxygen atom, and the unhybridized p orbitals in the plane overlap with the p orbitals of the left-hand oxygen atom. 

The tight-binding (TB) approximation is commonly used for theoretical consideration of the electronic structure of carbon nanotubes [1]. But it is desired to have a simpler qualitative model to predict physical properties of nanotubes without bulky numerical calculations and to assist in analysis of experimental data. For example, in [2] the free-electron (FE) model has been used. The aim of this work is to improve this model by taking into account the finite thickness of nanotube conducting layer. We compare our FE approximation with the commonly used TB approach to determine its area of application. 

Similarly to our discussion of sp orbitals, the properties of the double bond are incompatible with the ground-state electronic structure of carbon. Three of the four bonds formed by carbon are equivalent to each other. These are or-bonds and are comparable in strength to the bonds in alkanes, which are also referred to as o--bonds. One of the three sigma bonds is used to join one carbon to another in the formation of the double bond. The geometry of these three bonds is the trigonal geometry, i.e., the three bonds lie in a flat plane with bond angles of 120° (Fig. 12-1). The fourth bond of each carbon of the double bond, used to form the second or 77-bond of the double bond, is weaker than a c-bond. 

Two theoretical analyses of the electronic structures of carbonates and related species have been published. - Russian workers have reported the results of MO calculations of the isoelectronic series of oxy-anions BO , CO ", and NOj. The derived data, when compared to the results of Jf-ray spectral investigations, accurately describe the principal characteristics of the spectra. Perkins has studied the electronic structure of inter alia H2CS3, CS ", and CS4 using a self-consistent MO method. Perhaps the most interesting conclusion to come from the investigations is the fact that the molecule H2CS3 is shown to be quite stable. 

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