Three-dimensional electron

Gordon R., Bender R., Herman G.T. Algebraic reconstruction techniques (ART) for three-dimensional electron micrographs and X-ray photography., J. Theor. Biol., V. 29, 1970, p. 471-481. 

Frank J 1996 Three-Dimensional Electron Microscopy of Macromolecular Assemblies (New York Aoademio)... 

Ruiz T 1998 Conferenoe talk Gordon Conf. on Three-Dimensional Electron Microscopy... 

In principle, it is possible to calculate the detailed three-dimensional electron density distribution in a unit cell from the three-dimensional x-ray diffraction pattern. 

Step 11. At this point a computer program refines the atomic parameters of the atoms that were assigned labels. The atomic parameters consist of the three position parameters x,j, and for each atom. Also one or six atomic displacement parameters that describe how the atom is "smeared" (due to thermal motion or disorder) are refined for each atom. The atomic parameters are varied so that the calculated reflection intensities are made to be as nearly equal as possible to the observed intensities. During this process, estimated phase angles are obtained for all of the reflections whose intensities were measured. A new three-dimensional electron density map is calculated using these calculated phase angles and the observed intensities. There is less false detail in this map than in the first map. 

FIGURE 1.31 The three-dimensional electron cloud corresponding to an electron in a Ij-orbital of hydrogen. The density of shading represents the probability of finding the electron at any point. The superimposed graph shows how the probability varies with the distance of the point from the nucleus along any radius. 

Three-dimensional electron densities have no boundaries they converge to zero exponentially with distance from the nuclei of the peripheral atoms in the molecule. Considering a single, isolated molecule, the exact quantum-mechanical electron density becomes zero in a strict sense only at infinite distance from the center of mass of the molecule. Consequently, the electron density is not a compact set, just as the embedding three-dimensional Euclidean space E3 is not compact either. However, the three-dimensional Euclidean space E3, as a subset of a four-dimensional Euclidean space E4, can be slightly extended (for example, by adding one point) and made compact by various compactification techniques. 

The methyl group responds to the difference in the three-dimensional electron density distribution about the two nearest ring CC bonds, and the natural bond orders most simply quantifies the key difference in a unified manner across many molecules. At one extreme, 2-methylpropene has essentially localized single and double bonds (03-0b = 1) and a 1010 cm-1 barrier. At the other extreme, when the geometry of the ring has good local C2v symmetry, as in the S0 state of toluene, m-fluorotoluene, p-fluorotoluene, 3,5-difluorotoluene, and 2,6-difluorotoluene, 03 - Ob and the barrier is invariably very small, even for nominal threefold cases. We interpret this equality of bond orders as indicative of essentially equal contributions of the two dominant resonance structures at all a. 

Ahn, J.H. et al. 2006. Heterogeneous three-dimensional electronics by use of printed semiconductor nanomaterials. Science 314 1754-1757. 

The electronic wave function of an n-electron molecule is defined in 3n-dimensional configuration space, consistent with any conceivable molecular geometry. If the only aim is to characterize a molecule of fixed Born-Oppenheimer geometry the amount of information contained in the molecular wave function is therefore quite excessive. It turns out that the three-dimensional electron density function contains adequate information to uniquely determine the ground-state electronic properties of the molecule, as first demonstrated by Hohenberg and Kohn [104]. The approach is equivalent to the Thomas-Fermi model of an atom applied to molecules. 

X. Electron Tomography Three-Dimensional Electron Microscopy Imaging. 212... 

Zahn S, Swager TM (2002) Three-dimensional electronic delocalization in chiral conjugated polymers. Angew Chem Int Ed 41 4225 -230... 

Walz, j. et al. 26S proteasome structure revealed by three-dimensional electron microscopy. J Struct Biol 1998, 121, 19-29. 

Waiz, j., Erdmann, A., Kania, M., Typke, D., Koster, A. J., and Baumeister, W. 26S proteasome structure revealed by three-dimensional electron microscopy. J Struct Biol 1998, 323, 19-29. 

AIM theory provides a physical basis for the theory of Lewis electron pairs and the VSEPR model of molecular geometry. Equipped with computers and computer-generated, three-dimensional electron density maps, scientists are able to view molecules and predict molecular phenomena without even having to get off their chairs ... 

Gjonnes, J., Hansen, V., Berg, B. S., Runde, P., Cheng, Y. F., Gjonnes, K., Dorset D. L., Gilmore, C. J. (1998) Structure Model for the Phase Al Ee Derived from Three-Dimensional Electron Diffraction Intensity Data Collected by a Precession Technique. Comparison with Convergent-Beam Diffraction.", Hcta Cryst. A54, 306-319. 

Gemmi, M., Zou, X. D., Hovmdller, S., Migliori, A., Vennstrom, M., Andersson, Y. (2003) Structure of Ti2P solved hy three-dimensional electron diffraction data collected with the precession technique and high-resolution eleetron mieroseopy", Acta Cryst. A59, 117-126. 

Figure 26. Three-dimensional electron scattering model for a resist on a thick substrate with a scanning electron beam of zero diameter.

The wavefunction of an electron associated with an atomic nucleus. The orbital is typically depicted as a three-dimensional electron density cloud. If an electron s azimuthal quantum number (/) is zero, then the atomic orbital is called an s orbital and the electron density graph is spherically symmetric. If I is one, there are three spatially distinct orbitals, all referred to as p orbitals, having a dumb-bell shape with a node in the center where the probability of finding the electron is extremely small. (Note For relativistic considerations, the probability of an electron residing at the node cannot be zero.) Electrons having a quantum number I equal to two are associated with d orbitals. 

It is impossible to directly measure phases of diffracted X-rays. Since phases determine how the measured diffraction intensities are to be recombined into a three-dimensional electron density, phase information is required to calculate an electron density map of a crystal structure. In this chapter we discuss how prior knowledge of the statistical distribution of the electron density within a crystal can be used to extract phase information. The information can take various forms, for example ... 

Immediately after the isolation of macroscopic quantities of Cgo solid [298], highly conducting [299] and superconducting [141] behaviors were verified for the K-doped compounds prepared by a vapor-solid reaction (Haddon, Hebard, et al.). Crystallographic study based on the powder X-ray diffraction profile revealed that the composition of the superconducting phase is KsCeo and the diffraction pattern can be indexed to be a face-centered cubic (fee) structure with a three-dimensional electronic pathway [300]. The lattice parameter (a = 14.24 A) is apparently expanded relative to the undoped cubic Ceo = 14.17 A). The superconductivity has been observed for many A3C60 (A alkali metal), e.g., RbsCeo (Tc = 29 K... 

Stansfield 1, Jones KM, Kushnirov VV, Dagkesamanskaya AR, Poznyakovski Al, Paushkin SV, Nierras CR, Cox BS, Ter-Avanesyan MD, Tuite ME (1995) The products of the SUP45 (eRFl) and SUP35 genes interact to mediate translation termination in Saccharomyces cerevisiae. EMBO J 14 4365 373 Stansfield 1, Eurwilaichitr L, Akhmaloka, Tuite ME (1996) Depletion in the levels of the release factor eRFl causes a reduction in the efficiency of translation termination in yeast. Mol Microbiol 20 1135-1143 Stansfield 1, Kushnirov VV, Jones KM, Tuite ME (1997) A conditional-lethal translation termination defect in a sup45 mutant of the yeast Saccharomyces cerevisiae. Fur J Biochem 245 557-563 Stark H (2002) Three-dimensional electron cryomicroscopy of ribosomes. Curr Protein Pept Sci 3 79-91... 

The three-dimensional electron tomographical construction of silica-supported metallocene catalysts using conventional TEM (Steinmetz et al 2000), and a novel method for the automated acquisition of tilt series for electron tomography of nanoparticles using STEM have been reported (Zeisse et al 2000). The HAADE-STEM is shown to be capable of determining the compositions of individual nanoparticle catalysts of a few atoms supported on porous substrates (Vaughan et al 1999). 

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