Solids electronic structures

V. V. Sobolev and V. V. Nemoshkalenko, Computational Physics Methods in a Theory of Solids Electronic Structure of Rare Metal Dichalcogenides, Naukova Dumka, Kiev, 1990. 

Slater, J. C. (1963). Quantum Theory of Molecules and Solids. Electronic Structure of Molecules, Vol. I, Chap. 5. McGraw-Hill, New York. 

Bonding Energetics of OrganometaUic Compounds Electronic Structure of Main-group Compounds Electronic Structure of Solids Electronic Structure of Clusters Ligand Field Theory Spectra Molecular Orbital Theory Photoelectron Spectroscopy of Transition Metal Systems. 

Slater JC (1963) Theory of molecules and solids. Electronic structure of molecules, vol 1. McGraw-Hill, New York... 

Many phenomena in solid-state physics can be understood by resort to energy band calculations. Conductivity trends, photoemission spectra, and optical properties can all be understood by examining the quantum states or energy bands of solids. In addition, electronic structure methods can be used to extract a wide variety of properties such as structural energies, mechanical properties and thennodynamic properties. 

Another usefiil quantity is defining the electronic structure of a solid is the electronic density of states. In general the density of states can be defined as... 

Cox P A 1987 The Electronic Structure and Chemistry of Solids (Oxford Oxford University Press)... 

Harrison W A 1989 Electronic Structure and the Properties of Solids The Physics of the Chemical Bond (New York Dover)... 

The surface work fiincdon is fonnally defined as the minimum energy needed m order to remove an electron from a solid. It is often described as being the difference in energy between the Fenni level and the vacuum level of a solid. The work ftmction is a sensitive measure of the surface electronic structure, and can be measured in a number of ways, as described in section B 1.26.4. Many processes, such as catalytic surface reactions or resonant charge transfer between ions and surfaces, are critically dependent on the work ftmction. 

As we have outlined, a very wide variety of methods are available to calculate the electronic structure of solids. Empirical TB methods (such as discussed in section B3.2.2) are the least expensive, affordmg the... 

Jansen H J F and Freeman A J 1984 Total-energy full-potential linearized augmented plane-wave method for bulk solids electronic and structural properties of tungsten Phys. Rev. B 30 561-9... 

Iditional importance is that the vibrational modes are dependent upon the reciprocal e vector k. As with calculations of the electronic structure of periodic lattices these cal-ions are usually performed by selecting a suitable set of points from within the Brillouin. For periodic solids it is necessary to take this periodicity into account the effect on the id-derivative matrix is that each element x] needs to be multiplied by the phase factor k-r y). A phonon dispersion curve indicates how the phonon frequencies vary over tlie luin zone, an example being shown in Figure 5.37. The phonon density of states is ariation in the number of frequencies as a function of frequency. A purely transverse ition is one where the displacement of the atoms is perpendicular to the direction of on of the wave in a pmely longitudinal vibration tlie atomic displacements are in the ition of the wave motion. Such motions can be observed in simple systems (e.g. those contain just one or two atoms per unit cell) but for general three-dimensional lattices of the vibrations are a mixture of transverse and longitudinal motions, the exceptions... 

As described in the chapter on band structures, these calculations reproduce the electronic structure of inhnite solids. This is important for a number of types of studies, such as modeling compounds for use in solar cells, in which it is important to know whether the band gap is a direct or indirect gap. Band structure calculations are ideal for modeling an inhnite regular crystal, but not for modeling surface chemistry or defect sites. 

POLYRATE can be used for computing reaction rates from either the output of electronic structure calculations or using an analytic potential energy surface. If an analytic potential energy surface is used, the user must create subroutines to evaluate the potential energy and its derivatives then relink the program. POLYRATE can be used for unimolecular gas-phase reactions, bimolecular gas-phase reactions, or the reaction of a gas-phase molecule or adsorbed molecule on a solid surface. 

Siegbahn, K., Nordling, C., Fahlman, A., Nordberg, R., Hamerin, K., Hedman, J., Johansson, G., Bergmark, T., Karlsson, S.-E., Lindgren, I. and Lindberg, B. (1967) Electron Spectroscopy for Chemical Analysis Atomic, Molecular, and Solid State Structure Studies by Means of Electron Spectroscopy, Almqvist and Wiksells, Uppsala. 

K. A.tomic, Molecular, and Solid State Structure hj Means of Electron Spectroscopy, A xn.< s. 2iad S ks s J sA2L 1967. 

Electronic structure studies of free molecules (gas phase), well-defined solid surfaces, and adsorbates on solid surfaces... 

Although physical studies of the electronic structure of surfaces have to be performed under UHV conditions to guarantee clean uncontaminated samples, the technique does not require vacuum for its operation. Thus, in-situ observation of processes at solid-gas and solid-liquid interfaces is possible as well. This has been utilized, for instance, to directly observe corrosion and electrode processes with atomic resolution [5.2, 5.37]. 

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],...

The most extensive calculations of the electronic structure of fullerenes so far have been done for Ceo- Representative results for the energy levels of the free Ceo molecule are shown in Fig. 5(a) [60]. Because of the molecular nature of solid C o, the electronic structure for the solid phase is expected to be closely related to that of the free molecule [61]. An LDA calculation for the crystalline phase is shown in Fig. 5(b) for the energy bands derived from the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for Cgo, and the band gap between the LUMO and HOMO-derived energy bands is shown on the figure. The LDA calculations are one-electron treatments which tend to underestimate the actual bandgap. Nevertheless, such calculations are widely used in the fullerene literature to provide physical insights about many of the physical properties. 

Calculations for Ceo in the LDA approximation [62, 60] yield a narrow band (- 0.4 0.6 eV bandwidth) solid, with a HOMO-LUMO-derived direct band gap of - 1.5 eV at the X point of the fee Brillouin zone. The narrow energy bands and the molecular nature of the electronic structure of fullerenes are indicative of a highly correlated electron system. Since the HOMO and LUMO levels both have the same odd parity, electric dipole transitions between these levels are symmetry forbidden in the free Ceo moleeule. In the crystalline solid, transitions between the direct bandgap states at the T and X points in the cubic Brillouin zone arc also forbidden, but are allowed at the lower symmetry points in the Brillouin zone. The allowed electric dipole... 

We have extended the linear combination of Gaussian-type orbitals local-density functional approach to calculate the total energies and electronic structures of helical chain polymers[35]. This method was originally developed for molecular systems[36-40], and extended to two-dimensionally periodic sys-tems[41,42] and chain polymers[34j. The one-electron wavefunctions here are constructed from a linear combination of Bloch functions c>>, which are in turn constructed from a linear combination of nuclear-centered Gaussian-type orbitals Xylr) (in ihis case, products of Gaussians and the real solid spherical harmonics). The one-electron density matrix is given by... 

Methods of Electronic-Structure Calculations From Molecules to Solids Michael Springborg... 

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