Helical coordinates

Another helical coordination polymer to contain binding at A-N3 is the product isolated from the reaction between /raas-[(NH3)2Pt(9-MeA-iV7)(9-MeH N7)]2+ (H = 9-methylhypoxanthine) and an excess of AgN03, 13 59). Unusually, in this material the 9-MeA is bound by metal ions at Nl, N3, and N7 simultaneously. The chain polymer is... 

Oxidaton of heme goes through the biliverdin species. Octaethylbiliverdin can exist in coordinated form as the fully reduced trianion (OEB)3-, as the two-electron-oxidized monoanion (OEBox), or as the one-electron-oxidized radical (OEB-)2-. Nickel forms complexes with all three moieties, [Nin(OEB)]ra with n I 1, 0, and -1 (689).1787 The most highly oxidized species [Ni(OEBox)]I3 could be crystallized. The structure shows a helical coordination of the linear tetrapyrrole ligand around nickel with Ni—N distances of 1.867 A and 1.879 A. 

Calculations in helical coordinates are very challenging. The procedure used in this text will be to unwrap the screw helix into Cartesian coordinates for the analysis. It is important to be able to calculate the helical length in the z direction at any radius r for the axial length 1 ... 

Kimura M, Sano M, Muto T, Hanabusa K, Shirai H. Self-assembly of twisted bridging ligands to helical coordination polymers. Macromolecules 1999 32 7951-7953. 

Much work by Lehn et al. has been dedicated to the self-assembly of helical coordination complexes. Recently, ligand 59 has been shown to self-assemble with five iron(II) ions to form an intricate circular double helicate of 10" charge which surrounds and encapsulates a chloride ion. This chloride ion seemingly cannot be exchanged for larger ions as the inner core of the helicate = 1.75 A) is nearly... 

When the chain length is dramatically increased, as in (28), podands are available which could imitate the helical ion channels believed to be available in membranes and so give information on the selective transfer of cations across such barriers. This type of ligand shows pronounced transfer of inorganic salt into organic phases and NMR studies indicate a likely helical coordination of the cation.33,218 Complexes have been isolated and the structure of (29)2KNCS has been solved.219 In this molecule, the podand wraps, in an S-shaped manner, within the dinuclear complex, and contains a KNCS unit within each loop of the S shape. 

Fig. 8. (a) Helical coordinate system and (b) effect of the pressure gradient in the circumferential direction (30/39) on the secondary flow structure. [From Wang, J.W., and Andrews, J.R.G., Numerical simulation of flow in helical ducts. AIChE J. 41(5), 1071 (1995). Reproduced with... 

Discrete infinite double helices are quite rare in inorganic and coordination chemistry [Fig. 2(e)]. Ciani has reported that reaction of L21 with Ag salts in the ratio 2 1 gave completely different and noteworthy products, one of which is the infinite double-helical coordination polymer [Ag(L2i)]CF3S03 (50). The structure shows the balanced packing of left-handed and right-handed double helices of cationic —Ag—L—Ag—L— chains (Fig. 11). The period of the helices is... 

Zang and coworkers [147] reported the characterization of three homochiral helical coordination polymers of Cu(II) with 2,2, 3,3 -oxydiphthalic dianhydride. TG and powder XRD analyses showed that one of the porous frameworks is stable after the removal of solvent water molecules. In contrast, the others changed their structures to amorphous ones because of the simultaneous loss of solvent and coordination water molecules. 

The reactions of LnCla (Ln = lanthanide cations), 1-(S,S) or d-(R,R)-tartaric acid and molybdate in acidified aqueous solutions gave rise to enantio-pure left-or right-handed double helical coordination metal compounds. TG and powder XRD studies suggested that the backbone collapses with the removal of aqua ligands. However, it reverts easily to the original compound after being... 

Helical coordination polymers containing large chiral cavities or charmels are interesting for stereospecific syntheses, separation of enantiomers and stereoselective catalysis. Crystals of 39 are obtained from a solution of nickel(II) acetate and benzoic acid in methanol which is covered with a solution of 4,4 -bipyridine in the presence of benzene or nitrobenzene [107]. Each helix turn contains three complex units and the chain consists of Ni(II) (with binding of benzoate) and the bipyridine. Because each helix is shifted against the next, large cavities are formed containing, for example, benzene or nitrobenzene. 

Echeverria, I., and Papoian, G. A. (2015). DNA exit ramps are revealed in the binding landscapes obtained from simulations in helical coordinates, 11(2) el003980. doi 10,1371/journal.pcbi.l003980. 

The approximately equal sign (=) is used because Eqs. 6.21(a) and 6.21(b) are based on the FPS and neglect the effect of curvature. For a more accurate analysis one has to use cylindrical or helical coordinates this will be discussed in Section 7.4. Equation 6.21 is essentially the same expression as found for the co-axial cylinder problem, Eq. 6.17. The polymer melt between the screw flight and the barrel is exposed to a different shear rate ... 

According to (Bolinder, 1995), the velocity components under the cylindrical coordinate system Vr, vq, Vz) obtained from simulation can be transformed to the velocity components under the orthogonal helical coordinate system (w, u, v) by using the equations as follows... 

The Cu(ll) complex, [Cu2(L55)2(H20)] H20, 75 derived from L55 crystallizes as a ID helical coordination polymer assembled from the dimeric building blocks similar to 71. But, the major difference is the presence of one more water molecule in the crystal lattice of 75. Interestingly, despite the similar structures and crystal packing of helical coordination polymers in 71 and 75, a stable dehydrated complex from 75 could not be obtained because the anhydrous species rapidly gets rehydrated in the presence of air. This indicates that the formation of new Cu-0 bond by the carboxylate group is restricted in 75. Fmther, in contrast to 71, the reason why the reversible hydration takes place in the case of [Cu2(L55)2(H20)] H20, 75, can be understood by the close examination of the crystal structure of 75. ... 

In the last decades, the design and fabrication of helical architectures that mimic some of these bio-related helices have become a very big challenge for supramolecu-lar chemists. Among the different approaches that one can use, coordination chemistry has certainly become one of the most valuable tools to obtain helical coordination structures. The first efforts were dedicated to the design of discrete coordination complexes with helicate architectures. " However, more recently, the number of reported helical CPs has increased exponentially, becoming one of the most promising ways to construct these fascinating systems. 

The integral (4.1 ), which nust now he evaluated, is solved conveniently in helical coordinates ... 

Yu Q and Hu G H (1998), Development of a helical coordinate system and its applications to analysis of polymer flow in screw extruders. Part II A helical channel model for single screw extruders . Polymer Engineering and Science, 38,819-830. 

---