Asymmetric dimer model

Both the Si(100) and Ge(100) surfaces have stable (2x1) reconstructions which involve the saturation of dangling bonds by the formation of" dimers between the atoms in the top layer of the bulk termination of the solid. In the case of Si(100)(2xl), although the existence of surface dimers is no longer controversial, there have been contradictory reports of dimers oriented parallel to the surface (the symmetric dimer model) or tilted in the plane perpendicular to the surface (the asymmetric dimer model), see fig. 10. 

Recent studies which employ diffraction techniques, including medium energy ion scattering (MEIS) (Tromp et al., 1983), LEED (Holland et al., 1984) and grazing incidence X-ray scattering (Jedrecy et al., 1990), favor the asymmetric dimer model in which the top layer dimer is tilted by between 13.3 and 7.6 degrees. However, a kinematic LEED study (Zhao et al., 1991), photoemission studies (Johansson et al., 1990 Uhrberg and Hansson, 1991)... 

Fig. 10. Schematic illustration of the Si(100)- or Ge(100)-(2xl) reconstructed surface showing the formation of tilted dimers in the top layer. Shown is the asymmetric dimer model, in the symmetric dimer model the atoms labeled 1 and 2 lie in the same plane parallel to Lhe surface.

Fig. 5.2-3ir Theoretical surface band structure of Si (100)2 X1, obtained with the asymmetric dimer model (see Sect. 5.2.2.3, Fig. 5.2-7). Ddown and Dup refer to the DB bands at the down and up atoms. The bands labeled Si - S5 and Bi -B5 are back-bond states (modified by the surface) [2.53]...

In Figure 2.13, the dimers are parallel to the surface in a symmetric configuration known as the symmetric dimer model (SDM). However, the dimers need not necessarily lie parallel to the surface, but instead, may buckle or tilt. The (2x1) reconstruction comprised of buckled dimers is known as the asymmetric dimer model (ADM). For the particular case of Si(OOl) in the (2x1) reconstruction, the question of whether the dimers buckle or not was intensely debated in the 1980s... 

Shore et al. [4] and Wagner et al. [5] proved for exciton or dimer models coupled to one phonon mode that the two-center wave function generalized to an asymmetric nonunitary ansatz with a VP 17 of the form... 

Asymmetric dimeric liquid crystals with charge-transfer groups constitute good models for the mesomorphic self-organization of the related polymers discussed above. Their mesophase structures have been studied in some detail [34]. In this context, the formation of intercalated smectic phases of the A, C, and I type is especially noteworthy [34c]. However, the nature of the specific interactions between the unlike mesogenic groups, as well as the conformation of the spacer, are still to be explained [34d]. 

Contour plots of the n and n orbitals in an Si9Hi2 cluster model of the asymmetric dimer. These calculations were performed at the B3LYP level. 

The mixed-dimer model is illustrated in Figure 13.23. It shows the relaxed geometry as obtained by DFT-LDA calculations from Ref [69]. The most characteristic element is an asymmetric mixed In-P dimer in the first atomic layer oriented along [110] lying on top of a complete second layer of In-ln dimers along [110]. The phosphoras atom of the mixed dimer has a lone pair, and the dangling bonds locahzed at the cations (In atoms) in the first and second layers are all empty. Thus, the stracture fulfills the electron counting rule. 

The half-order of the rate with respect to [02] and the two-term rate law were taken as evidence for a chain mechanism which involves one-electron transfer steps and proceeds via two different reaction paths. The formation of the dimer f(RS)2Cu(p-O2)Cu(RS)2] complex in the initiation phase is the core of the model, as asymmetric dissociation of this species produces two chain carriers. Earlier literature results were contested by rejecting the feasibility of a free-radical mechanism which would imply a redox shuttle between Cu(II) and Cu(I). It was assumed that the substrate remains bonded to the metal center throughout the whole process and the free thiyl radical, RS, does not form during the reaction. It was argued that if free RS radicals formed they would certainly be involved in an almost diffusion-controlled reaction with dioxygen, and the intermediate peroxo species would open alternative reaction paths to generate products other than cystine. This would clearly contradict the noted high selectivity of the autoxidation reaction. 

An asymmetric photosynthesis may be performed inside a crystal of -cinnamide grown in the presence of E-cinnamic acid and considered in terms of the analysis presented before on the reduction of crystal symmetry (Section IV-J). We envisage the reaction as follows The amide molecules are interlinked by NH O hydrogen bonds along the b axis to form a ribbon motif. Ribbons that are related to one another across a center of inversion are enantiomeric and are labeled / and d (or / and d ) (Figure 39). Molecules of -cinnamic acid will be occluded into the d ribbon preferentially from the +b side of the crystal and into the / ribbon from the — b side. It is well documented that E-cinnamide photodimerizes in the solid state to yield the centrosymmetric dimer tnixillamide. Such a reaction takes place between close-packed amide molecules of two enantiomeric ribbons, d and lord and / (95). It has also been established that solid solutions yield the mixed dimers (Ila) and (lib) (Figure 39) (96). Therefore, we expect preferential formation of the chiral dimer 11a at the + b end of the crystal and of the enantiomeric dimer lib at the —b end of the crystal. Preliminary experimental results are in accordance with this model (97). 

Fig. 2.4. Schematic model of the molecular polymorphism of acetylcholinesterase and cholinesterase [110][112a]. Open circles represent the globular (G) catalytic subunits. Disulfide bonds are indicated by S-S. The homomeric class exists as monomers (Gl), dimers (G2), and tetramers (G4) and can be subdivided into hydrophilic (water-soluble) and amphiphilic (membrane-bound) forms. The G2 amphiphilic forms of erythrocytes have a glycophospholipid anchor. The heteromeric class exists as amphiphilic G4 and as asymmetric forms (A) containing one to three tetramers. Thus, heteromeric G4 forms found in brain are anchored into a phospholipid membrane through a 20 kDa anchor. The asymmetric A12 forms have three hydrophilic G4 heads linked to a collagen tail via disulfide bonds.

Fig. 6. (a) A schematic model of the helical, double-stranded, unstaggered, H4 fiber (Sperling and Amos, 1977). The asymmetric unit is an axial dimer and there are six such dimers per strand per repeat. The repeat distance is 330 A. The two different types of axial bonds—within and between dimers—are denoted by a thick and thin line, respectively. The tetrameric grouping is indicated, (b) A model of (a) upon which is superimposed a schematic representation of a nucleosome core particle... 

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