Solids energy band transitions

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... 

Figure 4.8 Interband transitions in solids with band-gap energy Eg-, (a) A direct band gap. Two direct transitions are indicated by arrows, (b) An indirect band gap. Two indirect band-gap transitions are indicated by arrows. The transitions at photon energies lower than Eg require absorption of phonons. The transitions at photon energies higher than Eg involve emission of phonons.

Figure 6.6 Schematic illustration of a two dimensional energy surface with two local minima separated by a transition state. The dark curves are energy contours with energy equal to the transition state energy. The transition state is the intersection point of the two dark curves. Dashed (solid) curves indicate contours with energies lower (higher) than the transition state energy. The MEP is indicated with a dark line. Filled circles show the location of images used in an elastic band calculation.

It is possible to characterize f-electron states in the actinides in quite a simple manner and to compare them with the states of other transition metal series. To this, we employ some simple concepts from energy band theory. Firstly, it is possible to express the real bandwidth in a simple elose-packed metal as the product of two parts . One factor depends only upon the angular momentum character of the band and the structure of the solid but not upon its scale. Therefore, since we shall use the fee structure throughout, the scaling factor X is known once and for all. 

Therefore, this low-energy band is assigned to a metal-centered d->p transition instead of as arising from Au---Au interactions. The solid-state luminescence spectrum (Fig. 25) exhibits a phosphorescence emission band centered at 417 nm. This value compares favorably with those reported for solids K[Au(CN)2]58 and Au2(dmb)(CN)2.63... 

Fig. 3.25. (a) F-point band-to-band transition energies Eo (squares), Eo (triangles), and Eq (circles) of a PLD-grown ZnO thin film as a function of temperature obtained by SE. (b) Data for Eo from SE (solid symbols) and low-temperature PL (open symbols), and model calculations according to (3.29) (solid line). The inset enlarges the temperature range T < 120 K. 

X-Ray absorption data in combination with atomic theory and solid-state band-structure theory can yield detailed information about the ground-state electronic structure of solids on an energy scale on the order of meV. This holds particularly true for correlated narrow-band systems, such as the rare-earth and transition-metal compounds. In broad-band materials, such as the... 

Absorption of UV/VIS radiation in the solid state is different from UV/VIS absorption in the liquid or gaseous phase with respect to photophysical processes taking place in the crystal lattice and to the metallic, semiconductor (SC) or insulator properties of the absorbing solid (Bottcher, 1991). In crystals, multiple atomic or molecular orbitals are combined to form broad energy bands, i.e. a valence band (vb) fully occupied by electrons and a conduction band (cb) unoccupied or only partly occupied by electrons. Conduction bands and valence bands have different energetic positions relative to one another depending on the specific substrate. In a SC cluster, electronic transitions between the valence band and the conduction... 

Use of LCAO and plane wave bases does not necessarily make the parts of the text where they arc used independent, since wc continually draw on insight from both outlooks. The most striking case of this is an analysis in Chapter 2 in which the requirement that energy bands be consistent for both bases provides formulae for the interatomic matrix elements used in the LCAO studies of. sp-bonded solids. This remarkable result was obtained only in late 1978 by Sverre Froyen and me, and it provided a theoretical basis for what had been empirical formulae when the text was first drafted. The development came in time to be included as a fundamental part of the exposition it followed on the heels of the much more intricate formulation of the corresponding LCAO matrix elements in transition metals and transition metal compounds, which is described in Chapter 20. 

A few mononuclear Au compounds have been found to photoluminesce in the sohd state but not in solution. The lowest energy band in the absorption spectrum of [Au2(/r-dmpm)2], which is reported to be luminescent in the solid state, has been assigned by using circular dichroism (CD) spectra to the transition cr(Pz) (d ). However, the compound [Au2(/r-dcpe)3](PF6)2, which has no An An contact, emits in the sohd state as weh as in acetonitrile solution (Xmax = 508nm, t = 21.5(5) p,s), indicating that An L bonding is also a factor to be considered in Au photophysics. ... 

Hole an electronic vacancy in the valence band of a solid Indirect band gap semiconductors semiconductors in which the lowest energy electronic transition between the valence and conduction bands is formally optically forbidden Intrinsic semiconductor an undoped semiconductor Majority carrier the predominant charge carrier in the bulk of a doped semiconductor... 

---