Electron density images

FIGURE 5.5 Electron-density mapping corresponding to the Fourier transforms (A) for denatured (extruded at 100 °C) and native WPI, an (B) inverse reciprocal spacing of electron-density images of native and denatured WPI (Onwulata et al., 2006). 

Collins DM (1982) Electron density images from imperfect data by iterative entropy maximization. Nature 298 49-51... 

X-rays interact with the electrons of the atoms in a material. Therefore, a necessary condition to resolve the additional film on the water surface is that the electron density of the film and the underlying liquid differ sufficiently. Additionally, for a = a there is no information on the horizontal component. Thus, the reflected intensity is an electron density image along the normal from air to water which is modified by a present monolayer film. 

Figure 1.15 contains a composite of several planes from an electron density map of a protein. By continually increasing the final coordinate by Az, the electron density map is built up from the series of two-dimensional planes. The individual sections are plotted on some transparent material after contour lines have been drawn around areas within certain density limits. The result is a topological map of the electron density presented on sequential planes of the unit cell as a series of contour levels. When the individual planes are stacked in consecutive order, a three-dimensional electron density image is created. This is discussed in more detail in Chapter 10. Currently, however, the presentation of the electron density is considerably more sophisticated. We use automated computer graphics systems to present detailed density images in three-dimensional space as in Figure 1.16. 

In the end we could obtain the best possible image of the contents of the unit cell, the molecules, by systematically combining together the information, or electron density images, yielded by each of the families of planes that can be drawn through the unit cell. Now we can t, of course, really do that because we don t have knives so sharp or eyes as keen as we would need to section a single unit cell. But we can measure the diffraction of X rays by the families of planes, and as we will later see, those diffracted rays carry much the same kind of information. 

Ultimately we can solve the phase problem for a number of reasons (1) We have chemical and physical information about the structure of the molecules making up the crystal that we can use to interpret and improve even a poor electron density image. (2) Information actually does reside in the intensity distribution alone, cryptic information about the relative phases... 

The most popular of the scanning probe tecimiques are STM and atomic force microscopy (AFM). STM and AFM provide images of the outemiost layer of a surface with atomic resolution. STM measures the spatial distribution of the surface electronic density by monitoring the tiumelling of electrons either from the sample to the tip or from the tip to the sample. This provides a map of the density of filled or empty electronic states, respectively. The variations in surface electron density are generally correlated with the atomic positions. 

Once the job is completed, the UniChem GUI can be used to visualize results. It can be used to visualize common three-dimensional properties, such as electron density, orbital densities, electrostatic potentials, and spin density. It supports both the visualization of three-dimensional surfaces and colorized or contoured two-dimensional planes. There is a lot of control over colors, rendering quality, and the like. The final image can be printed or saved in several file formats. 

The amplitudes and the phases of the diffraction data from the protein crystals are used to calculate an electron-density map of the repeating unit of the crystal. This map then has to be interpreted as a polypeptide chain with a particular amino acid sequence. The interpretation of the electron-density map is complicated by several limitations of the data. First of all, the map itself contains errors, mainly due to errors in the phase angles. In addition, the quality of the map depends on the resolution of the diffraction data, which in turn depends on how well-ordered the crystals are. This directly influences the image that can be produced. The resolution is measured in A... 

Meanwhile orbitals cannot be observed either directly, indirectly since they have no physical reality contrary to the recent claims in Nature magazine and other journals to the effect that some d orbitals in copper oxide had been directly imaged (Scerri, 2000). Orbitals as used in ab initio calculations are mathematical figments that exist, if anything, in a multi-dimensional Hilbert space.19 Electron density is altogether different since it is a well-defined observable and exists in real three-dimensional space, a feature which some theorists point to as a virtue of density functional methods. 

The problem with drawing molecules is similar to the problem above with the nectarine. No single drawing adequately describes the nature of the electron density spread out over the molecule. To solve this problem, we draw several drawings and then meld them together in our mind into one image. Just like the nectarine. 

FIG. 11 TEM images of (a) a [(Si02/PDADMAC)2]-coated PS particle and hollow silica capsules produced from PS latices coated with (b) one, (c) two, or (d) three Si02 layers. The hollow silica capsules maintain the shape of the original PS particle template. Removal of the core by calcination is confirmed by the reduced electron density in the interior of the capsules (compare b-d with a). The images of the hollow silica capsules show the nanoscale control that can be exerted over the wall thickness and their outer diameter. (From Ref. 106.)... 

Coupling one of these cations with one of these anions gives an ionic molecule that has high electron density at the anionic end. The computer image at top right shows this for butyl methyl imidazolium hexafluorophosphate. 

ELF can be visualized with different kinds of images. Colored sections through a molecule are popular, using white for high values of ELF, followed by yellow-red-violet-blue-dark blue for decreasing values simultaneously, the electron density can be depicted by the density of colored points. Contour lines can be used instead of the colors for black and white printing. Another possibility is to draw perspective images with iso surfaces, i.e. surfaces with a constant value of ELF. Fig. 10.2 shows iso surfaces with ELF = 0.8 for some molecules from experience a value of ELF = 0.8 is well suited to reveal the distribution of electron pairs in space. 

Thus, only the tail of the electron density (outside the jellium) contributes. The last term above may further be related11 to the position of the image plane zim so, at the point of zero charge,... 

The experimental data obtained at the same time (Fig. 8.3) show similar electron density distribution, except for the preformed plasma due to the local early gas breakdown induced by the nanosecond ASE pre-pulse (visible in the left part of the ionized region). The investigation was completed with imaging and spectroscopy of the transmitted laser pulse after the propagation in the gas. 

Electron beam divergence, 173 Electron beam pointing, 173 Electron density, 91 Electronic softening, 32 Emittance, 152 Energy resolved images, 134 Excimers, 20... 

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