A THEORY OF HEAVY ATOMS: A NEW RELATIVISTIC APPROACH IN MOMENTUM REPRESENTATION

2015 ◽  
pp. 177-200
Keyword(s):  
Momentum Representation ◽  
Heavy Atoms ◽  
Relativistic Approach

Object Wave Determination by Single-Sideband Methods

1973 ◽  
Vol 31 ◽  
pp. 266-267
Author(s):  
Kenneth H. Downing ◽  
Benjamin M. Siegel
Keyword(s):  
Phase Shift ◽  
Carbon Films ◽  
Object Wave ◽  
Electron Wave ◽  
Phase Object ◽  
Heavy Atoms ◽  
Single Sideband ◽  
Thin Carbon ◽  
Additional Phase Shift ◽  
Additional Phase

Under the “weak phase object” approximation, the component of the electron wave scattered by an object is phase shifted by π/2 with respect to the unscattered component. This phase shift has been confirmed for thin carbon films by many experiments dealing with image contrast and the contrast transfer theory. There is also an additional phase shift which is a function of the atomic number of the scattering atom. This shift is negligible for light atoms such as carbon, but becomes significant for heavy atoms as used for stains for biological specimens. The light elements are imaged as phase objects, while those atoms scattering with a larger phase shift may be imaged as amplitude objects. There is a great deal of interest in determining the complete object wave, i.e., both the phase and amplitude components of the electron wave leaving the object.

Single Atom Image Contrast in Fixed Beam Dark Field Electron Microscopy

1974 ◽  
Vol 32 ◽  
pp. 366-367
Author(s):  
Wah Chi
Keyword(s):  
Scattering Amplitude ◽  
Present Report ◽  
Dark Field ◽  
Image Contrast ◽  
Single Atom ◽  
Optical Theorem ◽  
Hartree Fock ◽  
Heavy Atoms ◽  
Beam Stop ◽  
Fixed Beam

Resolution and contrast are the important factors to determine the feasibility of imaging single heavy atoms on a thin substrate in an electron microscope. The present report compares the atom image characteristics in different modes of fixed beam dark field microscopy including the ideal beam stop (IBS), a wire beam stop (WBS), tilted illumination (Tl) and a displaced aperture (DA). Image contrast between one Hg and a column of linearly aligned carbon atoms (representing the substrate), are also discussed. The assumptions in the present calculations are perfectly coherent illumination, atom object is represented by spherically symmetric potential derived from Relativistic Hartree Fock Slater wave functions, phase grating approximation is used to evaluate the complex scattering amplitude, inelastic scattering is ignored, phase distortion is solely due to defocus and spherical abberation, and total elastic scattering cross section is evaluated by the Optical Theorem. The atom image intensities are presented in a Z-modulation display, and the details of calculation are described elsewhere.

Relative Intensities in ED Patterns From Thin Gold Films

1972 ◽  
Vol 30 ◽  
pp. 636-637
Author(s):  
R. H. Morriss ◽  
J. D. C. Peng ◽  
C. D. Melvin
Keyword(s):  
Theoretical Calculations ◽  
Diffraction Theory ◽  
Gold Films ◽  
Reasonable Accuracy ◽  
Experimental Conditions ◽  
Crystal Perfection ◽  
Heavy Atoms ◽  
Fine Focus ◽  
Convergent Beam ◽  
Beam Diffraction

Although dynamical diffraction theory was modified for electrons by Bethe in 1928, relatively few calculations have been carried out because of computational difficulties. Even fewer attempts have been made to correlate experimental data with theoretical calculations. The experimental conditions are indeed stringent - not only is a knowledge of crystal perfection, morphology, and orientation necessary, but other factors such as specimen contamination are important and must be carefully controlled. The experimental method of fine-focus convergent-beam electron diffraction has been successfully applied by Goodman and Lehmpfuhl to single crystals of MgO containing light atoms and more recently by Lynch to single crystalline (111) gold films which contain heavy atoms. In both experiments intensity distributions were calculated using the multislice method of n-beam diffraction theory. In order to obtain reasonable accuracy Lynch found it necessary to include 139 beams in the calculations for gold with all but 43 corresponding to beams out of the [111] zone.

A Base Specific Single Heavy Atom Stain for Electron Microscopy

1972 ◽  
Vol 30 ◽  
pp. 184-185
Author(s):  
J. P. Langmore ◽  
N. R. Cozzarelli ◽  
A. V. Crewe
Keyword(s):  
Electron Microscopy ◽  
Electron Microscope ◽  
High Resolution ◽  
Elastic Scattering ◽  
Heavy Atom ◽  
High Vacuum ◽  
Heavy Atoms ◽  
Large Movement ◽  
Base Sequencing ◽  
Scanning Electron

A system has been developed to allow highly specific derivatization of the thymine bases of DNA with mercurial compounds wich should be visible in the high resolution scanning electron microscope. Three problems must be completely solved before this staining system will be useful for base sequencing by electron microscopy: 1) the staining must be shown to be highly specific for one base, 2) the stained DNA must remain intact in a high vacuum on a thin support film suitable for microscopy, 3) the arrangement of heavy atoms on the DNA must be determined by the elastic scattering of electrons in the microscope without loss or large movement of heavy atoms.

The Interpretation of Crystal Lattice Images

1972 ◽  
Vol 30 ◽  
pp. 550-551
Author(s):  
J. M. Cowley ◽  
Sumio Iijima
Keyword(s):  
Crystal Orientation ◽  
Diffraction Theory ◽  
Phase Changes ◽  
Electron Wave ◽  
Crystal Lattices ◽  
Heavy Atoms ◽  
Lattice Images ◽  
The Right ◽  
Intuitive Interpretation ◽  
Suitable Approximation

The imaging of detailed structures of crystal lattices with 3 to 4Å resolution, given the correct conditions of microscope defocus and crystal orientation and thickness, has been used by Iijima (this conference) for the study of new types of crystal structures and the defects in known structures associated with fluctuations of stoichiometry. The image intensities may be computed using n-beam dynamical diffraction theory involving several hundred beams (Fejes, this conference). However it is still important to have a suitable approximation to provide an immediate rough estimate of contrast and an evaluation of the intuitive interpretation in terms of an amplitude object.For crystals 100 to 150Å thick containing moderately heavy atoms the phase changes of the electron wave vary by about 10 radians suggesting that the “optimum defocus” theory of amplitude contrast for thin phase objects due to Scherzer and others can not apply, although it does predict the right defocus for optimum imaging.

Intrinsic Stacking Interactions of Natural and Artificial Nucleobases

2019 ◽  
Author(s):  
Drew P. Harding ◽  
Laura J. Kingsley ◽  
Glen Spraggon ◽  
Steven Wheeler
Keyword(s):  
Gas Phase ◽  
Electrostatic Interactions ◽  
Density Functional ◽  
Molecular Descriptors ◽  
Stacking Interactions ◽  
Interaction Energies ◽  
Functional Theory ◽  
Binding Partner ◽  
Heavy Atoms ◽  
Wide Range

The intrinsic (gas-phase) stacking energies of natural and artificial nucleobases were explored using density functional theory (DFT) and correlated ab initio methods. Ranking the stacking strength of natural nucleobase dimers revealed a preference in binding partner similar to that seen from experiments, namely G > C > A > T > U. Decomposition of these interaction energies using symmetry-adapted perturbation theory (SAPT) showed that these dispersion dominated interactions are modulated by electrostatics. Artificial nucleobases showed a similar stacking preference for natural nucleobases and were also modulated by electrostatic interactions. A robust predictive multivariate model was developed that quantitively predicts the maximum stacking interaction between natural and a wide range of artificial nucleobases using molecular descriptors based on computed electrostatic potentials (ESPs) and the number of heavy atoms. This model should find utility in designing artificial nucleobase analogs that exhibit stacking interactions comparable to those of natural nucleobases. Further analysis of the descriptors in this model unveil the origin of superior stacking abilities of certain nucleobases, including cytosine and guanine.

scholarly journals Patterns in Protein Flexibility: A Comparison of NMR “Ensembles”, MD Trajectories, and Crystallographic B-Factors

Molecules ◽  
2021 ◽  
Vol 26 (5) ◽  
pp. 1484
Author(s):  
Christopher Reinknecht ◽  
Anthony Riga ◽  
Jasmin Rivera ◽  
David A. Snyder
Keyword(s):  
Protein Flexibility ◽  
Molecular Machines ◽  
Md Simulations ◽  
Peptide Bond ◽  
Structure Calculation ◽  
Atomic Scale ◽  
Heavy Atoms ◽  
Structural Ensembles ◽  
Atomic Coordinates ◽  
Motional Behavior

Proteins are molecular machines requiring flexibility to function. Crystallographic B-factors and Molecular Dynamics (MD) simulations both provide insights into protein flexibility on an atomic scale. Nuclear Magnetic Resonance (NMR) lacks a universally accepted analog of the B-factor. However, a lack of convergence in atomic coordinates in an NMR-based structure calculation also suggests atomic mobility. This paper describes a pattern in the coordinate uncertainties of backbone heavy atoms in NMR-derived structural “ensembles” first noted in the development of FindCore2 (previously called Expanded FindCore: DA Snyder, J Grullon, YJ Huang, R Tejero, GT Montelione, Proteins: Structure, Function, and Bioinformatics 82 (S2), 219–230) and demonstrates that this pattern exists in coordinate variances across MD trajectories but not in crystallographic B-factors. This either suggests that MD trajectories and NMR “ensembles” capture motional behavior of peptide bond units not captured by B-factors or indicates a deficiency common to force fields used in both NMR and MD calculations.

The crystal structure of myoglobin. VI. Seal myoglobin

1960 ◽  
Vol 258 (1293) ◽  
pp. 181-201 ◽  
Keyword(s):  
Tertiary Structure ◽  
Heavy Atom ◽  
Three Dimensional ◽  
Sperm Whale ◽  
Fourier Synthesis ◽  
Heavy Atoms ◽  
Isomorphous Replacement ◽  
Unit Cells ◽  
The Common ◽  
Sperm Whale Myoglobin

Myoglobin from the common seal ( Phoca vitulina ) when crystallized from ammonium sulphate forms monoclinic crystals with space group the unit cell, a = 57·9Å, b = 29·6Å, c = 106·4Å, β = 102°15', contains four molecules. The method of isomorphous replacement has been used in an investigation of the centrosymmetric b -axis projection in which it has been possible to determine signs for nearly all the h0l reflexions having spacings greater than 4Å. Three independent heavy-atom derivatives were employed and the signs so determined have been used to compute a map of the electron density projected on the (010) plane. This projection has been interpreted in terms of the molecule of sperm-whale myoglobin, as deduced by Bodo, Dintzis, Kendrew & Wyckoff (1959) from a three-dimensional Fourier synthesis to 6Å resolution. The results of the interpretation show that the two myoglobin molecules are very similar in form (tertiary structure) in spite of the differences in their amino-acid composition. The relative orientation of the two unit cells with respect to the myoglobin molecule is given and a comparison is made of the positions of the heavy atoms in each molecule.

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