Density of states

Abstract: A correlation-energy formula due to Colle and Salvetti [Theor. Chim. Acta 37, 329 (1975)], in which the correlation energy density is expressed in terms of the electron density and a Laplacian of the second-order Hartree-Fock density matrix, is restated as a formula involving the density and local kinetic-energy density. On insertion of gradient expansions for the local kinetic-energy density, density-functional formulas for the correlation energy and correlation potential are then obtained. Through numerical calculations on a number of atoms, positive ions, and molecules, of both open- and closed-shell type, it is demonstrated that these formulas, like the original Colle-Salvetti formulas, give correlation energies within a few percent.

Abstract: The conditions necessary in metals for the presence or absence of localized moments on solute ions containing inner shell electrons are analyzed. A self-consistent Hartree-Fock treatment shows that there is a sharp transition between the magnetic state and the nonmagnetic state, depending on the density of states of free electrons, the $s\ensuremath{-}d$ admixture matrix elements, and the Coulomb correlation integral in the $d$ shell; that in the magnetic state the $d$ polarization can be reduced rather severely to nonintegral values, without appreciable free electron polarization because of a compensation effect; and that in the nonmagnetic state the virtual localized $d$ level tends to lie near the Fermi surface. It is emphasized that the condition for the magnetic state depends on the Coulomb (i.e., exchange self-energy) integral, and that the usual type of exchange alone is not large enough in $d$-shell ions to allow magnetic moments to be present. We show that the susceptibility and specific heat due to the inner shell electrons show strongly contrasting behavior even in the nonmagnetic state. A calculation including degenerate $d$ orbitals and $d\ensuremath{-}d$ exchange shows that the orbital angular momentum can be quenched, even when localized spin moments exist, and even on an isolated magnetic atom, by kinetic energy effects.

Abstract: Finite graphite systems having a zigzag edge exhibit a special edge state. The corresponding energy bands are almost flat at the Fermi level and thereby give a sharp peak in the density of states. The charge density in the edge state is strongly localized on the zigzag edge sites. No such localized state appears in graphite systems having an armchair edge. By utilizing the graphene ribbon model, we discuss the effect of the system size and edge shape on the special edge state. By varying the width of the graphene ribbons, we find that the nanometer size effect is crucial for determining the relative importance of the edge state. We also have extended the graphene ribbon to have edges of a general shape, which is defined as a mixture of zigzag and armchair sites. Examining the relative importance of the edge state for graphene ribbons with general edges, we find that a non-negligible edge state survives even in graphene ribbons with less developed zigzag edges. We demonstrate that such an edge shape with three or four zigzag sites per sequence is sufficient to show an edge state, when the system size is on a nanometer scale. The special characteristics of the edge state play a large role in determining the density of states near the Fermi level for graphite networks on a nanometer scale.

Abstract: The superconducting transition temperature is calculated as a function of the electron-phonon and electron-electron coupling constants within the framework of the strong-coupling theory. Using this theoretical result, we find empirical values of the coupling constants and the "band-structure" density of states for a number of metals and alloys. It is noted that the electron-phonon coupling constant depends primarily on the phonon frequencies rather than on the electronic properties of the metal. Finally, using these results, one can predict a maximum superconducting transition temperature.

Abstract: Dimensionality plays a critical role in determining the properties of materials due to, for example, the different ways that electrons interact in three-dimensional, twodimensional (2D), and one-dimensional (1D) structures.1-5 The study of dimensionality has a long history in chemistry and physics, although this has been primarily with the prefix “quasi” added to the description of materials; that is, quasi-1D solids, including square-planar platinum chain and metal trichalcogenide compounds,2,6 and quasi2D layered solids, such as metal dichalcogenides and copper oxide superconductors.3-5,7,8 The anisotropy inherent in quasi-1D and -2D systems is central to the unique properties and phases that these materials exhibit, although the small but finite interactions between 1D chains or 2D layers in bulk materials have made it difficult to address the interesting properties expected for the pure low-dimensional systems. Are pure low-dimensional systems interesting and worth pursuing? We believe that the answer to this question is an unqualified yes from the standpoints of both fundamental science and technology. One needs to look no further than past studies of the 2D electron gas in semiconductor heterostructures, which have produced remarkably rich and often unexpected results,9,10 and electron tunneling through 0D quantum dots, which have led to the concepts of the artificial atom and the creation of single electron transistors.11-15 In these cases, lowdimensional systems were realized by creating discrete 2D and 0D nanostructures. 1D nanostructures, such as nanowires and nanotubes, are expected to be at least as interesting and important as 2D and 0D systems.16,17 1D systems are the smallest dimension structures that can be used for efficient transport of electrons and optical excitations, and are thus expected to be critical to the function and integration of nanoscale devices. However, little is known about the nature of, for example, localization that could preclude transport through 1D systems. In addition, 1D systems should exhibit density of states singularities, can have energetically discrete molecularlike states extending over large linear distances, and may show more exotic phenomena, such as the spin-charge separation predicted for a Luttinger liquid.1,2 There are also many applications where 1D nanostructures could be exploited, including nanoelectronics, superstrong and tough composites, functional nanostructured materials, and novel probe microscopy tips.16-29 To address these fascinating fundamental scientific issues and potential applications requires answers to two questions at the heart of condensed matter chemistry and physics research: (1) How can atoms or other building blocks be rationally assembled into structures with nanometer-sized diameters but much longer lengths? (2) What are the intrinsic properties of these quantum wires and how do these properties depend, for example, on diameter and structure? Below we describe investigations from our laboratory directed toward these two general questions. The organization of this Account is as follows. In section II, we discuss the development of a general approach to the rational synthesis of crystalline nanowires of arbitrary composition. In section III, we outline key challenges to probing the intrinsic properties of 1D systems and illustrate solutions to these challenges with measurements of the atomic structure and electronic properties of carbon nanotubes. Last, we discuss future directions and challenges in section IV.