Degenerate structure

An index with extremely low degeneracy (i.e., where no degenerate structures have been observed yet) [6], the Charge-related Topological Index (CTI), has been proposed by one of the authors (l.B.) (Figure 6-1). It has a potential-like form (Eq. (4)). 

STRUCTURE FAMILIES DEGENERATE STRUCTURES, DERIVATIVE STRUCTURES, SUPERSTRUCTURES ... 

A derivative structure can be considered as being obtained from a reference structure by ordered atomic substitution, subtraction or addition processes or by unit cell distortions (or both). The opposite kinds of transformation correspond to the so-called degeneration processes. A derivative structure has fewer symmetry operations than the reference structure (a degenerate structure has more). A derivative structure has either a larger cell or a lower symmetry (or both) than the reference structure. 

Several superstructures and defect superstructures based on sphalerite and on wurtzite have been described. The tI16-FeCuS2 (chalcopyrite) type structure (tetragonal, a = 525 pm, c = 1032 pm, c/a = 1.966), for instance, is a superstructure of sphalerite in which the two metals adopt ordered positions. The superstructure cell corresponds to two sphalerite cells stacked in the c direction. The cfla ratio is nearly 1. The oP16-BeSiN2 type structure is another example which similarly corresponds to the wurtzite-type structure. The degenerate structures of sphalerite and wurtzite (when, for instance, both Zn and S are replaced by C) correspond to the previously described cF8-diamond-type structure and, respectively, to the hP4-hexagonal diamond or lonsdaleite, which is very rare compared with the cubic, more common, gem diamond. The unit cell dimensions of lonsdaleite (prepared at 13 GPa and 1000°C) are a = 252 pm, c = 412 pm, c/a = 1.635 (compare with ZnS wurtzite). 

Figure 7. Upper panel Lowest energy equilibrium geometries and calculated adsorption energies of O2 and O4 on AgL clusters. Isomeric structures for n=4 and 6 are also depicted. Minimum distance O-Ag (middle panel) and 0-0 (lower panel) in the equilibrium structures of AgnO (circles) and Ag Oj (squares) clusters. The crosses indicate the distance Ag-O and 0-0 for the next nearest O2 adsorbed molecule in Ag Oj anions. The triangles at n=4,6 correspond to the near degenerate structures depicted in the upper panel.

On the other hand, benzannulation in the 3,4 positions of PT, would produce the nearly degenerate structures 2a and 2b (Scheme I) because the gain in aromaticity of the benzene ring"Tn 2b is expected to outweigh the loss of thiophene aromaticity in 2a. The result would be amelioration of bond alternation ("Peierls distortion" of the backbone) with a concomitant decrease in bandgap. 

Fig. 2.2. (a) The pz orbitals of undimerized t-PA chain, (b) the orbitals after dimerization, and (c) energy versus k for the it band before dimerization (dashed line) and after dimerization (solid line) [14]. (d) Two degenerate structures of the 1-PA are shown, (e) Optical absorption spectra of undoped (curve 1) and doped f-PA [18], The doping increases with the curve numbers. 

The basis of the selectivity of SecB in binding is likely the result of a complex interplay between several factors, including relatively degenerate structural elements, their spacing and sequence context, and the... 

Thus, knowing the topology and symmetry of a system, one can determine the most probable ordering of molecular-orbital energy levels and the degeneration structure of the energy spectrum. 

The most likely structure of the catalyst is based on X-ray structures of related compounds and reinforced by calculations.5 It is dimeric with two Ti atoms, two tartrates and four alkoxides. We show one of two degenerate structures. When the catalyst combines with the allylic alcohol and the hydroperoxide, the same titanium atom takes both and only one diastereotopic face of the alkene is presented to the active oxygen atom. 

H. B. Gu, S. Morita, X. H. Yin, T. Kawai, and K. Yoshino. Electrical and optical properties of conducting polymer composites consisting of conducting polymers with non-degenerated structure. Synth. Met., 69(l-3) 449-450, March 1995. 

These facts mean that the halogen-bridged mixed-valence transition metal complex qualifies a good one-dimensional compound with doubly degenerate structure (CDW). 

FIGURE 3 The degenerate structure of CXC chemokines in monomeric form (A) and the dimeric structure of CXCL8 (B). The secondary structural motifs discussed in the text are labeled in A. In B, it can be seen that dimerization occurs along the strand of the molecules. Reprinted from Fernandez and Lolis (2002) with permission. 

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