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The contents of the unit cell

Dennis Sherwood and Jon Cooper

in Crystals, X-rays and Proteins: Comprehensive Protein Crystallography

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199559046
eISBN:
9780191595028
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199559046.003.0009
Subject:
Physics, Crystallography: Physics

This chapter discusses the underlying principles X-ray scattering by a distribution of electrons. The theory is then extended to the diffraction of X-rays by an infinite lattice of molecular motifs ... More


X-Ray Compton Scattering

Malcolm Cooper, Peter Mijnarends, Nobuhiro Shiotani, Nobuhiko Sakai, and Arun Bansil

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198501688
eISBN:
9780191718045
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198501688.001.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

This book covers all aspects of the study of ground state electron density in condensed matter through Compton scattering of hard x-rays or gamma rays, i.e., photons with energies between 20 and 500 ... More


Phase refinement through density modification

Jan Pieter Abrahams, Jasper R. Plaisier, Steven Ness, and Navraj S. Pannu

in Macromolecular Crystallography: conventional and high-throughput methods

Published in print:
2007
Published Online:
September 2007
ISBN:
9780198520979
eISBN:
9780191706295
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198520979.003.0010
Subject:
Biology, Biochemistry / Molecular Biology

This chapter discusses the concept of density modification, where a priori information about the structure of the macromolecule being studied is used to improve phase estimates. These concepts of ... More


Crystals, X-rays and Proteins: Comprehensive Protein Crystallography

Dennis Sherwood and Jon Cooper

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199559046
eISBN:
9780191595028
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199559046.001.0001
Subject:
Physics, Crystallography: Physics

This book presents a complete account of the theory of the diffraction of X-rays by crystals with particular reference to the processes of determining the structures of protein molecules. The book ... More


The physical nature and the computer simulation of the intermolecular potential

ANGELO GAVEZZOTTI

in Molecular Aggregation: Structure analysis and molecular simulation of crystals and liquids

Published in print:
2006
Published Online:
January 2010
ISBN:
9780198570806
eISBN:
9780191718779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570806.003.0004
Subject:
Physics, Atomic, Laser, and Optical Physics

Everyday objects display an almost incredible variety of properties that may be felt with animal senses and that human intellect wishes to apprehend, categorise, understand, and — possibly — predict. ... More


Chemical implications of the bond valence model

I. David Brown

in The Chemical Bond in Inorganic Chemistry: The Bond Valence Model

Published in print:
2006
Published Online:
January 2010
ISBN:
9780199298815
eISBN:
9780191708879
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199298815.003.0014
Subject:
Physics, Crystallography: Physics

The reasons for the robustness of the bond valence model can be found in the simple attractive Coulomb potential which causes the ions to bond, and the repulsive potential that keeps the ions apart ... More


Electron density fitting and structure validation

Mike Carson

in Macromolecular Crystallography: conventional and high-throughput methods

Published in print:
2007
Published Online:
September 2007
ISBN:
9780198520979
eISBN:
9780191706295
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198520979.003.0013
Subject:
Biology, Biochemistry / Molecular Biology

The Human Genome Project went three-dimensional in late 2000. ‘Structural genomics’ efforts will determine the structures of thousands of new proteins over the few years. These initiatives seek to ... More


Fourier syntheses

William Clegg

in Crystal Structure Analysis: Principles and Practice

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199219469
eISBN:
9780191722516
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199219469.003.0008
Subject:
Physics, Crystallography: Physics

A diffraction pattern is the (forward) Fourier transform of a crystal structure, obtained physically in an experiment and mathematically from a known or model structure (providing both amplitudes and ... More


Atom type assignment

Peter Müller

in Crystal Structure Refinement: A Crystallographer's Guide to SHELXL

Published in print:
2006
Published Online:
September 2010
ISBN:
9780198570769
eISBN:
9780191718809
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570769.003.0004
Subject:
Physics, Crystallography: Physics

After solving a structure, the crystallographer has to find a sensible interpretation of the solution, as the initial model is usually merely a collection of unidentified peaks. The crystallographer ... More


An introduction to maximum entropy

Peter Main

in Crystal Structure Analysis: Principles and Practice

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199219469
eISBN:
9780191722516
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199219469.003.0011
Subject:
Physics, Crystallography: Physics

Maximum entropy methods are used in crystallography for estimating reflection phases among other applications. This chapter explains the basic concepts behind maximum entropy, including entropy ... More


Artefacts

Peter Müller

in Crystal Structure Refinement: A Crystallographer's Guide to SHELXL

Published in print:
2006
Published Online:
September 2010
ISBN:
9780198570769
eISBN:
9780191718809
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570769.003.0008
Subject:
Physics, Crystallography: Physics

Like every physical method, crystallography is affected by errors. However, there are two kinds of errors: unavoidable errors such as artefacts and avoidable errors. A good crystallographer knows how ... More


The molecule: structure, size and shape

ANGELO GAVEZZOTTI

in Molecular Aggregation: Structure analysis and molecular simulation of crystals and liquids

Published in print:
2006
Published Online:
January 2010
ISBN:
9780198570806
eISBN:
9780191718779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570806.003.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

The relationships between atoms and molecules are mediated by the theory of chemical bonding. Atoms were forged in the extreme conditions that occurred at the cores of stars in the early stages of ... More


Applications of Density Functional Theory to Biological Systems

Tomasz Adam Wesolowski and Jacques Weber

in Molecular Orbital Calculations for Biological Systems

Published in print:
1998
Published Online:
November 2020
ISBN:
9780195098730
eISBN:
9780197560891
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195098730.003.0009
Subject:
Chemistry, Quantum and Theoretical Chemistry

The term biological systems may be used in reference to a wide class of polyatomic systems. They can be defined as minimal functional units which perform specific biological functions: enzymatic ... More


Metal–Insulator Transitions in Two-dimensional Electron Systems

S.V. Kravchenko

in Conductor-Insulator Quantum Phase Transitions

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199592593
eISBN:
9780191741050
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199592593.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter presents a summary of the experimental results on large r s 2D electron and hole gases (2DEGs and 2DHGs) in clean semiconductor devices. In particular, it focuses ... More


MODULATED CRYSTALS IN SUPERSPACE

Sander Van Smaalen

in Incommensurate Crystallography

Published in print:
2007
Published Online:
January 2008
ISBN:
9780198570820
eISBN:
9780191718762
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570820.003.0002
Subject:
Physics, Crystallography: Physics

This chapter introduces the superspace theory for the description of the crystal structures of incommensurately modulated crystals. Two alternative constructions of superspace are presented. In ... More


Electron Density Maps and Molecular Structures

Peter B. Moore

in Visualizing the Invisible: Imaging Techniques for the Structural Biologist

Published in print:
2012
Published Online:
May 2015
ISBN:
9780199767090
eISBN:
9780190267841
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:osobl/9780199767090.003.0007
Subject:
Biology, Biochemistry / Molecular Biology

This chapter illustrates the computations and variations of the electron density distribution of unit cells. To enable computations, crystallographers use electron density maps which are figured as a ... More


Solution and Refinement of Crystal Structures

Marco Milanesio and Davide Viterbo

in Fundamentals of Crystallography

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199573653
eISBN:
9780191775000
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573653.003.0006
Subject:
Physics, Crystallography: Physics, Condensed Matter Physics / Materials

This chapter shows that the goal of structural analysis is to obtain the distribution of atomic electron density in the unit cell starting from the diffraction data. It is not possible to reach this ... More


The Kohn-Sham method: Elaboration

Robert G. Parr and Yang Weitao

in Density-Functional Theory of Atoms and Molecules

Published in print:
1995
Published Online:
November 2020
ISBN:
9780195092769
eISBN:
9780197560709
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195092769.003.0010
Subject:
Chemistry, Theoretical Chemistry

In this chapter, the concepts and form of elementary quantum mechanics are generalized. This allows use of variables other than coordinates for the description of a state, permits ready discussion ... More


The phase problem and electron-density maps

Jenny Pickworth Glusker and Kenneth N. Trueblood

in Crystal Structure Analysis: A Primer

Published in print:
2010
Published Online:
November 2020
ISBN:
9780199576340
eISBN:
9780191917905
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199576340.003.0015
Subject:
Chemistry, Crystallography: Chemistry

In order to obtain an image of the material that has scattered X rays and given a diffraction pattern, which is the aim of these studies, one must perform a three-dimensional Fourier summation. The ... More


The Kohn–Sham method: Basic principles

Robert G. Parr and Yang Weitao

in Density-Functional Theory of Atoms and Molecules

Published in print:
1995
Published Online:
November 2020
ISBN:
9780195092769
eISBN:
9780197560709
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195092769.003.0009
Subject:
Chemistry, Theoretical Chemistry

In this chapter, the concepts and form of elementary quantum mechanics are generalized. This allows use of variables other than coordinates for the description of a state, permits ready discussion ... More


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