Rigid-band theory

The semiempirical models mentioned above allow an estimation of the stability of binary hydrides provided that the rigid band theory can be applied. However, the interaction of hydrogen with the electronic structure of the host metal in some binary hydrides and especially in the ternary hydrides is often more complicated. In many cases, the crystal structure of the host metal and therefore also the electronic structure... 

The rigid band theory (RBT) of solids according to which there is a considerable transfer of electrons among the alloy components an alloy surface is then a structureless plane with atoms indistinguishable for gas molecules. 

The discovery by ultraviolet photoelectron spectroscopy that the rigid-band model is not even applicable to the bulk of alloys such as Ni-Cu and Pd-Ag. The d-electrons of copper or silver in such alloys experience a potential that is predominantly the same as in the metals before alloying. For instance, upon alloying the d-bands of copper and nickel remain discernible in the alloy and no common d-band is formed, as is supposed by the rigid-band theory. 

Based on the rigid band theory, the electronic theory considered the metal as a collective source of electrons and electron holes, characterized... 

Discuss the origin of the Hume-Rothery electron phases within the framework of Jones original rigid-band analysis. How does second-order perturbation theory help quantify Mott and Jones earlier supposition on the importance of the free electron sphere touching a Brillouin zone boundary ... 

For both 1-2-3 and 2-1-4 the Hall coefficient is predicted to be hole-like for electrons orbiting in the Cu-0 planes, and electron like if the B field is rotated 90° into the plane, contrary to simple expectations. This has been verified experimentally by Tozer, et al. ( ) for the 1-2-3 compound, with reasonable quantitative agreement with theory. Single-crystal data for 2-1-4 for X—0.06 Sr doping have been given by Suzuki and Murakami (43). For B perpendicular to the planes, the Hall voltage is hole-like and within a factor of three of a rigid-band treatment of the band calculations. 

Therefore, one must caution against placing undue trust on theory that has been manipulated to fit certain aspects of an admittedly more general problem. The rigid-band model provides a prime example of this situation. The model gave initial results that seemed to describe a restricted set of experimental data on the densities of states (DOS s) rather well... 

Vibrational analysis of the benzene phosphorescence bands indicates that the radiative activity is induced predominantly by e2g vibrations [155, 156]. A weak but observable activity of b2g vibrations has also been found [156, 155, 157]. By introducing spin-orbit- and vibronic coupling through second order perturbation theory Albrecht [158] showed that the vibronic interaction within the triplet manifold is responsible for the larger part of the phosphorescence intensity. This also follows from comparison of the vibrational structure in phosphorescence and fluorescence spectra [159]. The benzene phosphorescence spectrum in rigid glasses [155] reveals a dominant vibronic activity of... 

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