Parallel contour maps

Figure 8. Contour maps calculated for a parallel arrangement of double helices, as a function of the translation Az, along the fiber axis and the coupled rotation angles /iA = /iB. a) Variations of the perpendicular off-set (Ax). Contours correspond to 1.1, 1.15 and 1.2 nm the arrow indicates the lowest value, and generates the PARA 1 model, b) Interchain energies calculated for the corresponding Ax. Contours correspond to -25, -20, -15, -10 and -7 kcal/mol the arrow indicates the lowest value. N.B. The indicates the loose interaction found in the A-type crystal structure.

FIG. 11.8 (a) A section of the difference synthesis through the Cr nucleus, parallel to the (110) plane. Contours are drawn at intervals of 0.2 eA 3. (b) Theoretical contour map of valence electron distribution on the (110) plane for chromium metal. Contours are drawn at intervals of 0.5 eA-3. The lobes point towards the nearest neighbors in the body-centered cubic structure. Source Ohba et al. (1982). 

A more practical representation of the electron distribution in a molecule can be obtained from the probability density contour maps. Isodensity contours in the molecular plane and in a plane parallel to the molecular plane at an altitude of 0.8 atomic unit have been calculated230 for three nucleic acid bases (adenine, thymine, and cytosine) from non-empirical wave functions. The first type of contour gives an overall picture of cr-bonding in the molecule, and the second characterizes the 77-electron density. 

Fig. 5. The contour maps of the partial n-electron density, qj, of (a) benzanthracene and (b) tri-phenylene obtained from the highest three occupied orbitals. The values are taken on the plane one Bohr radius above and parallel to the molecular plane...

Fig. 26 Contour map (from 0.6 to 5 eA 3) of the cross section of the MEM charge density for Sm2.78C7o at ambient pressure (left) and at 2.5 GPa (right). The sections were obtained by cutting the 3D charge density maps by the plane of the C-Sm-C bonds, which is parallel to the (110) or (111 )ja planes...

Plots (b) and (e) show the free metal surface of the system (plotted as pM). These show pM increasing (i.e. free metal concentration decreasing) very rapidly as one moves more into the CLASP-w region (i.e. trace metal in presence of large ligand excess). The metal-buffering capability of the system is clearly depicted in the contour map (e). For example, the lines, or portions of lines, which are parallel to the C axis, describe... 

Fig. 7.44 Current density field induced via the Fermi contact interaction by two magnetic dipoles at the vicinal protons of eclipsed ethane. The coupling pattern, for anti-parallel (parallel) dipoles, is represented on the left (right). The streamlines are shown in (a) and (d) b and e are contour levels for the intensity, in au the values of the solid (dashed) lines increase (decrease) in steps of 5 X 10 from the 0-contour, up to 0.5 au c and f are the corresponding 3-dimensional perspective views. The position of the nuclei is marked by a cross a corresponding symbol can be seen in the contour maps...

In X-ray crystallography, 2-A model" means that analysis included reflections out to a distance in the reciprocal lattice of 1/(2 A) from the center of the diffraction pattern. This means that the model takes into account diffraction from sets of equivalent, parallel planes spaced as closely as 2 A in the unit cell. (Presumably, data farther out than the stated resolution was unobtainable or was too weak to be reliable.) Although the final 2-A map, viewed as an empty contour surface, may indeed not allow us to discern adjacent atoms, structural constraints on the model greatly increase the precision of atom positions. The main constraint is that we know we can fit the map with groups of atoms — amino-acid residues — having known connectivities, bond lengths, bond angles, and stereochemistry. 

Figure 4 Maps of the average density of nitrogen adsorbed in three nanotube bundles. The contours are for constant density in the x, y planes i.e., for an observer looking in the z direction parallel to the pore axes. The pore diameters are (a) 1.37mn, (b) 1.43 nm, and (c) 0.69 nm. The in-plane coordinates x, y are defined so that unit x, y= 0.07, 0.14 run, respectively. The larger blobs show density contours inside the tubes and the smaller ones are for molecules adsorbed in the interstices between the hexagonally packed tubes. The interaction potential for the Nj is diatomic thus, the approximate molecular length is 0.1 run greater than the width which is 0.35 nm. The consequence is that the tube of (c) is too small to admit the N2 molecules so that the adsorption shown there is essential all interstitial. Also, in (a) and (b), the N2 appears to lie parallel to the tube axis and is adsorbed on the tube walls. The differences between the (a) and (b) contours are at least partly due to the differences in the numbers of molecules in these systems. These amount to 334 and 199 in (a) and (b).

Fig. 8. Image of the light-harvesting complex I of Rhodospirillum rubrum obtained by electron-microscopy analysis. Contours calculated from the 8.5 A projection maps obtained with frozen-hydrated two-dimensional crystals of the LH1 complex. The outermost contour represents the p-subunits and the next outermost the a-sub-units. The circle-like densities in the middle represent the BChl molecules. Inside the LH1 cylinder is a projection of the Rb. rubrum reaction center. The two parallel lines in the center represent the BChl special pair. The 20-A scale bar is at lower right. Figure source Karrasch, Burlough and Ghosh (1995) The 8.5 A projection map of the light-harvesting complex I from Rhodospirillum rubrum reveals a ring composed of 16 units. EMBO J 14 636.

This three-dimensional electron-density distribution is represented by a series of parallel sections stacked on top of one another. Each section is a transparent plastic sheet or, more recently, a layer in a computer image) on which the electron-density distribution is represented by contour lines (Figure 3.45), like the contour lines used in geological survey maps to depict altitude (Figure 3.46). The next step) is to interpret the electron-density map. A critical factor is the resolution of the x-ray analysis, which is determined by the number of scattered intensitie.s used in the Fourier synthesis. The fidelity of the image... 

A map of total iron concentrations based on analyses of 180 well waters (30) is shown in Figure 9. Also indicated in the figure are locations of 12 wells which were sampled and their waters chemically analyzed in December 1969 (Table III). A comparison of Figures 8 and 9 shows that total iron contours parallel pH contours. The latter figure shows that total iron concentrations increase rapidly to a maximum and... 

---