Basis of electronic structure

In this section, a model which gives the basis of the present study is introduced to investigate the electronic properties of A,Cfio [17]. First, the one-electron part of the Hamiltonian, which describes the itinerant motion of the flu electrons in terms of the electron transfer T, is given. Next, the electron-electron interaction U and the electron-phonon interaction S are examined U represents the Coulomb repulsion between the t u electrons and S represents the coupling of the fiu electrons to the intramolecular phonons of the C l0 molecule. In particular, it is noteworthy that both U and S are almost the same or larger in magnitude than the width of the flu bands. Finally, the importance of the dynamical aspect of S is pointed out. 

In the solid state, the Ceo molecules are crystallized into the fee lattice and the conduction bands, the flu bands, are formed of the flu orbitals of the C60 molecules. Saito and Oshiyama carried out the electronic structure calculations on solid C60 and found that it is a semiconductor with a calculated band gap of 1.5 eV, preserving the molecular characteristics strongly [29]. Their results also show that the width of 

The Hamiltonian H0, which describes the itinerant motion of the fi electrons, is 

The three curves shown in Fig. 3 are the ones calculated by using this Hamiltonian. Here, f J1 is the electronic transfer T between the fiu orbital a of the mth C60 molecule and the fiu orbital b of the nth C o molecule, where a and b denote x, y, and z f is chosen so as to reproduce the result of the electronic structure calculations. We also use Jm(T (ama.) to denote the creation (annihilation) operator of the cr-spin electron in the flu orbital a of the mth C60 molecule. Furthermore, is the band energy of the flu electron of the band index a (a = 1,2, and 3) and the wavenumber k the band energies are obtained by diagonalizing the Hamiltonian H0 and we use ak(J(akli) to denote the corresponding creation (annihilation) operators. 

We first examine U. The most important interaction as U is the Coulomb repulsion between two flu electrons on a C l0 molecule. To estimate the order of magnitude of U, it may be useful to regard the C l0 molecule as a sphere of a diameter D, which is about 7 A. The lower bound of U can be obtained by considering the Coulomb repulsion between two electrons which move on the surface of the sphere always being at the opposite position to each other separated by the distance D. We then find the lower bound of U to be e2/eD 0.4 eV, where e 4-5 is the dielectric constant of undoped solid C60. On the other hand, the upper bound of U can be obtained by considering the Coulomb repulsion between 

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On die basis of electronic structure and orbital energies, supply predictions for die following and explain your answer ... 

Preliminary observation of additional electron density at this fourth coordination position of Cu-2 upon soaking crystals with N02 is consistent with this idea. Thus, from the structural data it would appear that Cu-1 is a type 1 center that functions to transfer electrons to the catalytic Cu-2 ion (See Note Added in Proof). It has been suggested, largely on the basis of electronic structural considerations (27, 28), that the Cys-136-His-135 link between Cu-1 and Cu-2 is a possible conduit for electron transfer between the two sites. An analogous dipeptide bridge between the type 1 center and the catalytic tricopper cluster in ascorbate oxidase (29, 30) may function similarly. Indeed, other close similarities between protein domains in ascorbate oxidase and NiR have been noted (17). 

A (a) On the basis of electronic structures, explain why most metal halides are ionic, (b) On the basis of your explanation, predict which halide compounds are likely to be covalent. 

Due to its metallic and FM property, similar to double perovskites (see later), Cr02 is of great interest to material scientists and physicists. A computed band structure of Cr02 is shown in Figure 5.6. The Fermi level crosses the majority-spin band while it lies in a gap of the minority-spin density of states (DOS). Therefore, Cr02 is half-metallic on the basis of electronic structure calculations. The same band structure has been reproduced by several groups since it was first demonstrated by... 

Dunning T FI Jr and Flay P J 1977 Gaussian basis sets for moleoular oaloulations Methods of Electronic Structure Theory vo 3, ed FI F III Sohaefer (New York Plenum) pp 1-27... 

The Mean-Field Model, Which Forms the Basis of Chemists Pictures of Electronic Structure of Molecules, Is Not Very Accurate... 

The conformation of cyclohexene is described as a half-chair. Structural parameters determined on the basis of electron diffiaction and microwave spectroscopy reveal that the double bond can be accommodated into the ring without serious distortion. ... 

The assumption of the association of Hb in the pores of carboxylic cation exchangers has been advanced in Ref. [47] on the basis of electron microscopy at the maximum filling, almost all the pore surface is filled with Hb associates which are ordered star-shaped structures. Interprotein interaction in the adsorption immobilization of enzymes have been reported in Refs. [74, 75]. 

Density-functional theory is best known as the basis for electronic structure calculations. A variant of this theory can be used to calculate the structure of inhomogeneous fluids [35] the free energy of the fluid is expressed as a functional of the density of the various components a theorem asserts that this functional attains its minimum for the true density profiles. 

Mechanistic studies have been designed to determine if the concerted cyclic TS provides a good representation of the reaction. A systematic study of all the E- and Z-decene isomers with maleic anhydride showed that the stereochemistry of the reaction could be accounted for by a concerted cyclic mechanism.19 The reaction is only moderately sensitive to electronic effects or solvent polarity. The p value for reaction of diethyl oxomalonate with a series of 1-arylcyclopentenes is —1.2, which would indicate that there is little charge development in the TS.20 The reaction shows a primary kinetic isotope effect indicative of C—H bond breaking in the rate-determining step.21 There is good agreement between measured isotope effects and those calculated on the basis of TS structure.22 These observations are consistent with a concerted process. 

The anion [Osg(CO)18p has an octahedral arrangement of metal atoms of approximately Oh symmetry, and is crystallographically very similar to the [HRus(CO)w]- ion. This collection of structural data on electron-equivalent systems emphasizes some of the dangers in trying to predict the structure of complexes solely on the basis of electron counting procedures (220). 

We shall briefly discuss the electrical properties of the metal oxides. Thermal conductivity, electrical conductivity, the Seebeck effect, and the Hall effect are some of the electron transport properties of solids that characterize the nature of the charge carriers. On the basis of electrical properties, the solid materials may be classified into metals, semiconductors, and insulators as shown in Figure 2.1. The range of electronic structures of oxides is very wide and hence they can be classified into two categories, nontransition metal oxides and transition metal oxides. In nontransition metal oxides, the cation valence orbitals are of s or p type, whereas the cation valence orbitals are of d type in transition metal oxides. A useful starting point in describing the structures of the metal oxides is the ionic model.5 Ionic crystals are formed between highly electropositive... 

For the first time in the history of chemical sciences, theoretical predictions have achieved the level of reliability that allows them to rival experimental measurements in accuracy on a routine basis. Only a decade ago, such a statement would be valid only with severe qualifications as high-level quantum-chemical calculations were feasible only for molecules composed of a few atoms. Improvements in both hardware performance and the level of sophistication of electronic structure methods have contributed equally to this impressive progress that has taken place only recently. 

The 13C NMR data for pentafulvene (1) and heptafulvene (2) (Table 3) and for 6,6-dimethylpentafulvene (5) and sesquifulvalene (6), afford evidence of the extent to which polar structures of the types 5a and 6a contribute to the ground state. If the chemical shifts are analyzed on the basis of electron density, these hydrocarbons are to be considered as olefinic systems with only a small contribution (10% at most) from the polar structures 5a and 6a. 

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