One-dimensional complexes

One-dimensional complexes, 6,134 One-dimensional conductors, 6,134 One-dimensional metals Krogmann salts, 6, 136 Optical isomerism cobalt ammines, 1,12 history, 1,180... 

The projective space P(C2) has many names. In mathematical texts it is often called one-dimensional complex projective space, denoted CP (Students of complex differential geometry may recognize that the space PCC ) is onedimensional as a complex manifold loosely speaking, this means that around any point of (C ) there is a neighborhood that looks like an open subset of C, and these neighborhoods overlap in a reasonable way.) In physics the space appears as the state space of a spin-1/2 particle. In computer science, it is known as a qubit (pronounced cue-hit ), for reasons we will explain in Section 10.2. In this text we will use the name qubit because CP has mathematical connotations we wish to avoid. 

In columnar stacked one-dimensional complexes, such as the tetracyanoplatinates, with relatively short intrachain Pt—Pt separations, it is possible to postulate a simple band model by considering overlap of the filled 5dzi orbitals on individual atoms in the chain to produce a full 5dp band, and overlap of the empty 6pz orbitals to produce an empty 6pz band (Figure 1). 

N. F. Gavrilov, G. G. Ivanova, V. N. Selin, V. N. Sofronov, UP-OK program for solving continuum mechanics problems in one-dimensional complex, VANT. Procedures and programs for numerical solution of mathematical physics problems, (3), p. 11-21,1982. 

H. Chate. Spatiotemporal intermittency regimes of the one-dimensional complex ginzburg-landau equation. Nonlinearity, 7 185— 204, 1994. 

H. Chate. Disordered regimes of the one-dimensional complex Ginz-burg-Landau equation. In P. Cladis and P. Palffy-Muhoray, editors, Spatiotemporal Patterns in Nonequilibrium Complex Systems, Vol. XXI of Santa Fe Institute in the Sciences of Complexity, pages pp. 5-49. Addison-Wesley, New York, 1995. 

B.I. Shraiman, A. Pumir, W. van Saarloos, P.C. Hohenberg, H. Chate, and M. Holen. Spatiotemporal chaos in the one-dimensional complex Ginzburg-Landau equation. Physica D, 57 241-248, 1992. 

State diagram for comparison between Pt(CNMe)5 and Pt(CN) . The complex Pt(CNMe) has not been partially oxidized, and this is likely because the 4-f charge difference will diminish the overlap of the Uig wave functions between adjacent Pt(CNMe)4 ions relative to the overlap of wave functions for those of Pt(CN)l . As a consequence the probability of forming one-dimensional complexes decreases. 

It is noteworthy, that the transform kernel is represented by direct product ( ) of one-dimensional complex functions. The kernel is thus a 2 -dimensional vector. One can represent both signal s T) and spectrum S f) in a similar fashion ... 

Descriptors for objects represented by their boundaries may be generated using the representations already described. Simple descriptors, such as perimeter, length, and orientation of the major axis, shape number, and eccentricity, may be readily computed from the boundary data. The ordered set of points on the boundary having two-dimensional coordinates (xt,yt), where 1 = 1,..., NandNis the total number of points on the boundary, can be treated as a one-dimensional complex function xt + iyk- The coefficients of the discrete Fourier transform applied to this function can also be used as a shape descriptor. 

In spite of these interesting properties, the one-dimensional complexes have not been considered as a candidate for molecular wires, since they exist only in three-dimensional solids. They are not soluble in organic media and when dispersed in water the one-dimensional structure is disrupted and dissociates into the constituent molecular complexes. 

Interestingly, in the case of supramolecular complex consisting of dihexadecyl sulfosuccinate 20 and [Pt(en)2][PtCl2(en)2]" ", indigo-colored dispersion was obtained at room temperature, whereas the color disappeared upon heating the solution to 60 C. As the CT transition requires the existence of chloro-bridged extended coordination structure, the observed thermochromism indicates disruption of the one-dimensional complex structures at 60 C. The color reappeared reversibly... 

Molecular wires are indispensable elements of futme molecular-scale electronic devises, and their fabrication has been attracting much interest. Conventional research has been focused on the synthesis of tt-conjugated ohgomers and supramolecular polymers [56]. The introduction of inorganic elements or one-dimensional inorganic complexes in main chains would expand the potential of these nanomaterials and lead to new interfacial phenomena, which have not been observed in the single component system. However, one-dimensional complexes have not been considered candidates for molecular wires, since they exist only in three-dimensional solids. They are usually not soluble, and when they are dissolved, the one-dimensional structure is disrupted and the structure is not maintained. 

The observed red-shift is ascribed to the enhanced delocahzation of the excited Pt(Ill)-Pt(III) states in the coordination chain, which decreases the LUMO-HOMO energy gap of the one-dimensional complex. In the lipid complexes, densely packed sulfonate groups seem to direct the electrostatically bound Pt(en)2 and PtCl2(en)2 complexes to coordinate in higher density. This causes the increase in the overlap between dz2 and p orbitals, depending on the molecular packing and chemical structure of the lipid molecules. The shortened inter-platinum (Pt -Cl-Pt ) distance would pro-... 

---