Band broken symmetry structure

Fig. 117. Band structure for YH3 for (i) the HoD3-type structure and (ii) broken symmetry structure (Kelly et al.,...

Based on the ab initio theory of complex electronic ground state of superconductors, it can be concluded that e-p coupling in superconductors induces the temperature-dependent electronic structure instability related to fluctuation of analytic critical point (ACP - maximum, minimum or saddle point of dispersion) of some band across FL, which results in breakdown of the adiabatic BOA. When ACP approaches FL, chemical potential Pad is substantially reduced to IJ-antiadilJ-ad > Pantiad < b(o). Under these circumstances the system is stabilized, due to the effect of nuclear dynamics, in the antiadiabatic state at broken symmetry with a gap in one-particle spectrum. Distorted nuclear structure, which is related to couple of nuclei in the phonon mode r that induces transition into antiadiabatic state, has fluxional character. It has been shown that until system remains in antiadiabatic state, nonadiabatic polaron - renormalized phonon interactions are... 

The interpretation of thermoelectric power data in most materials is a delicate job and this is particularly true for the case of carbons and graphites. In the case of SWCNTs the data are not consistent with those calculated from the known band structure which leads to much smaller values than observed. Hone et al. [11] suggest from their data that they may indicate that the predicted electron-hole symmetry of metallic CNTs is broken when they are assembled into bundles (ropes). 

One of the most difficult problems for ab initio quantum chemistry is to determine the potential energy function for a chemical reaction on a metal surface. Why is this so First of all, the metal substrate is strongly delocalized. This means that the system cannot be modeled [1] by considering just a small or medium-sized cluster of metal atoms. On the other hand, the band structure techniques that would simplify calculations for a bare metal surface cannot be directly applied because the translational symmetry is broken by the presence of the reactants. As a result one has the difficulty of dealing with extended interactions without the benefit of simplifications due to symmetry. Many problems involving surfaces, interfaces, impurities, or defects in solid state materials fall under this broad rubric along with various solution phenomena as well. 

Fig. 39. Excitation profiles (solid curves) and depolarization dispersion curves (broken curves) of a nontotally symmetric fundamental (

The above analysis, shared by many spectroscopists in the field of small molecules, can be further expanded when vibrational spectroscopy is considered in the field of polymers and macromolecules in general. The wiggling of polymers adds new flavor to physics and chemistry. The translational periodicity of infinite polymers with perfect stmcture generates phonons and collective vibrations which give rise to absorption or Raman scattering bands that escape the interpretation based on the traditional spectroscopic correlations. The concept of collective motions forms the basis for the understanding of the vibrations of finite chain molecules which form a nonnegligible part of industrially relevant materials. On the other hand, real polymer samples never show perfect chemical, strereochemical, and conformational structure. Symmetry is broken and new bands appear which become characteristic of specific types of disorder. 

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