Parameterization of the close packing of molecules in the unit cell

2004 ◽  
Vol 60 (6) ◽  
pp. 725-733 ◽  
Author(s):  
Elna Pidcock ◽  
W. D. Sam Motherwell
Keyword(s):  
Molecular Orientation ◽  
Crystal Packing ◽  
Building Blocks ◽  
Close Packing ◽  
Unit Cell ◽  
Box Model ◽  
Molecular Building Blocks ◽  
Molecular Dimension ◽  
Cell Dimensions ◽  
Unit Cells

The box model of crystal packing describes unit cells in terms of a limited number of arrangements, or packing patterns, of molecular building blocks. Cell dimensions have been shown to relate to molecular dimensions in a systematic way. The distributions of pattern coefficients (cell length/molecular dimension) for thousands of structures belonging to P21/c, P\bar 1, P212121, P21 and C2/c are presented and are shown to be entirely consistent with the box model of crystal packing. Contributions to the form of the histograms from molecular orientation and molecular overlap are discussed. Gaussian fitting of the histograms has led to the parameterization of close packing within the unit cell and it is shown that molecular crystal structures are very similar to one another at a fundamental level.

Spatial arrangement of molecules in homomolecular Z' = 2 structures

2006 ◽  
Vol 62 (2) ◽  
pp. 268-279 ◽  
Author(s):  
Elna Pidcock
Keyword(s):  
Crystal Packing ◽  
Building Blocks ◽  
Spatial Arrangement ◽  
Molecular Shape ◽  
Box Model ◽  
Molecular Building Blocks ◽  
Cell Dimensions ◽  
Unit Cells ◽  
Energetic Interactions ◽  
Molecular Dimensions

The Box Model of crystal packing describes unit cells in terms of a limited number of arrangements of molecular building blocks. An analysis of Z′ ≤ 1 structures has shown that cell dimensions are related to molecular dimensions in a systematic way and that the spatial arrangement of molecules in crystal structures is very similar, irrespective of Z or space group. In this paper it is shown that the spatial arrangement of molecules in Z′ = 2 structures are, within the context of the Box Model, very similar to that found for Z′ ≤ 1 structures. The absence of crystallographic symmetry does not appear to affect correlations between molecular dimensions and cell dimensions, or between the packing patterns and the positions of molecules in the unit cell, established from the analysis of Z′ ≤ 1 structures. The preference shown by Z′ = 2 structures for low surface-area packing patterns and the observation that strong energetic interactions are most often found between the large faces of the independent molecules reaffirms the importance of molecular shape in crystal packing.

Distribution of molecular centres in unit cells with respect to packing patterns

2004 ◽  
Vol 60 (5) ◽  
pp. 539-546 ◽  
Author(s):  
Elna Pidcock ◽  
W. D. Sam Motherwell
Keyword(s):  
Building Blocks ◽  
Unit Cell ◽  
Space Group ◽  
Space Groups ◽  
Molecular Building Blocks ◽  
Unit Cells ◽  
Symmetry Operators

Packing patterns, a new description of the limited number of possible arrangements of molecular building blocks in a unit cell, were assigned to many thousands of structures belonging to the space groups P21/c, P\bar 1, P212121, P21 and C2/c [Pidcock & Motherwell (2004). Cryst. Growth. Des. 4, 611–620]. The position of the molecular centre (in fractional coordinates) in the unit cell for these structures has been surveyed, with respect to the space group and the packing pattern. The results clearly show that the position at which the molecular centre is found in the unit cell is correlated with the packing pattern. The relationships between the orientation of the packing pattern in the unit cell and the symmetry operators of the space group are explored. Popular orientations of packing patterns within the unit cell are given.

scholarly journals Structure of a monoclinic polymorph of human carbonic anhydrase II with a doubledaaxis

2010 ◽  
Vol 66 (5) ◽  
pp. 628-634 ◽  
Author(s):  
Arthur H. Robbins ◽  
John F. Domsic ◽  
Mavis Agbandje-McKenna ◽  
Robert McKenna
Keyword(s):  
Carbonic Anhydrase ◽  
Crystal Packing ◽  
Rotation Axis ◽  
Unit Cell ◽  
Carbonic Anhydrase Ii ◽  
Monoclinic Unit Cell ◽  
Structure Solution ◽  
Unit Cells ◽  
Human Carbonic Anhydrase ◽  
Β Sheet

The crystal structure of human carbonic anhydrase II with a doubledaaxis from that of the usually observed monoclinic unit cell has been determined and refined to 1.4 Å resolution. The diffraction data withh= 2n+ 1 were systematically weaker than those withh= 2n. Consequently, the scaling of the data, structure solution and refinement were challenging. The two molecules comprising the asymmetric unit are related by a noncrystallographic translation of ½ alonga, but one of the molecules has two alternate positions related by a rotation of approximately 2°. This rotation axis is located near the edge of the central β-sheet, causing a maximum distance disparity of 1.7 Å between equivalent atoms on the diametrically opposite side of the molecule. The crystal-packing contacts are similar to two sequential combined unit cells alongaof the previously determined monoclinic unit cell. Abnormally high finalRcrystandRfreevalues (20.2% and 23.7%, respectively) are not unusual for structures containing pseudo-translational symmetry and probably result from poor signal to noise in the weakh-odd data.

Unit cell dimensions of the hydrated aluminium phosphate–sulphate minerals sanjuanite, kribergite, and hotsonite

1989 ◽  
Vol 53 (371) ◽  
pp. 385-386 ◽  
Author(s):  
H. De Bruiyn ◽  
G. J. Beukes ◽  
W. A. Van Der Westhuizen ◽  
E. A. W. Tordiffe
Keyword(s):  
Unit Cell ◽  
X Ray Diffraction ◽  
Aluminium Phosphate ◽  
Powder Diffraction File ◽  
Cell Parameters ◽  
Cell Dimensions ◽  
Unit Cells ◽  
Diffraction Patterns ◽  
Unit Cell Dimensions ◽  
Hydrated Aluminium

AT the time when the hydrated aluminium phosphate-sulphate hotsonite (Beukes et al., 1984a) and its equally rare relative zaherite (Beukes et al., 1984b; De Bruiyn et al., 1985) were discovered near Pofadder, South Africa, very little was known about the unit cells of the other two hydrated aluminium phosphate-sulphate minerals sanjuanite and kribergite, originally described by De Abeledo et al. (1968) from Argentina and Sweden, respectively. Although the Powder Diffraction file (PDF) contains the X-ray diffraction patterns for sanjuanite and kribergite (PDF 20-47 and 20-48 respectively), they had not been indexed nor have their unit cell parameters been calculated thus far.

scholarly journals Design and Mechanical Testing of 3D Printed Hierarchical Lattices Using Biocompatible Stereolithography

Designs ◽  
2020 ◽  
Vol 4 (3) ◽  
pp. 22 ◽  
Author(s):  
Md Moniruzzaman ◽  
Christopher O'Neal ◽  
Ariful Bhuiyan ◽  
Paul F. Egan
Keyword(s):  
Mechanical Testing ◽  
Elastic Moduli ◽  
Cost Effective ◽  
Building Blocks ◽  
Cell Number ◽  
Unit Cell ◽  
Tissue Scaffold ◽  
Unit Cells ◽  
Cell Topology ◽  
3D Printed

Emerging 3D printing technologies are enabling the rapid fabrication of complex designs with favorable properties such as mechanically efficient lattices for biomedical applications. However, there is a lack of biocompatible materials suitable for printing complex lattices constructed from beam-based unit cells. Here, we investigate the design and mechanics of biocompatible lattices fabricated with cost-effective stereolithography. Mechanical testing experiments include material characterization, lattices rescaled with differing unit cell numbers, topology alterations, and hierarchy. Lattices were consistently printed with 5% to 10% lower porosity than intended. Elastic moduli for 70% porous body-centered cube topologies ranged from 360 MPa to 135 MPa, with lattices having decreased elastic moduli as unit cell number increased. Elastic moduli ranged from 101 MPa to 260 MPa based on unit cell topology, with increased elastic moduli when a greater proportion of beams were aligned with the loading direction. Hierarchy provided large pores for improved nutrient transport and minimally decreased lattice elastic moduli for a fabricated tissue scaffold lattice with 7.72 kN/mm stiffness that is suitable for bone fusion. Results demonstrate the mechanical feasibility of biocompatible stereolithography and provide a basis for future investigations of lattice building blocks for diverse 3D printed designs.

Crystal Engineering: Strategies and Architectures

1997 ◽  
Vol 53 (4) ◽  
pp. 569-586 ◽  
Author(s):  
C. B. Aakeröy
Keyword(s):  
Molecular Structure ◽  
Crystal Engineering ◽  
Crystal Packing ◽  
Three Dimensional ◽  
Structural Data ◽  
Building Blocks ◽  
Intermolecular Forces ◽  
Design Strategies ◽  
Playing Field ◽  
Molecular Building Blocks

The area broadly described as crystal engineering is currently expanding at a brisk pace. Imaginative schemes for supramolecular synthesis, and correlations between molecular structure, crystal packing and physical properties are presented in the literature with increasing regularity. In practice, crystal engineering can be many different things; synthesis, statistical analysis of structural data, ab initio calculations etc. Consequently, we have been provided with a new playing field where chemists from traditionally unconnected parts of the spectrum have exchanged ideas, defined goals and made creative contributions to further progress not only in crystal engineering, but also in other disciplines of chemistry. Crystal engineering is delineated by the nature and structural consequences of intermolecular forces, and the way in which such interactions are utilized for controlling the assembly of molecular building blocks into infinite architectures. Although it is important to acknowledge that a crystal structure is the result of a subtle balance between a multitude of non-covalent forces, this article will focus on design strategies based upon the hydrogen bond and will present a range of approaches that have relied on the directionality and selectivity of such interactions in the synthesis of predictable one-, two- and three-dimensional motifs.

scholarly journals OPTICAL DIFFRACTION STUDIES OF CRYSTALLINE STRUCTURES IN ELECTRON MICROGRAPHS

1969 ◽  
Vol 43 (3) ◽  
pp. 448-455 ◽  
Author(s):  
Irmin Sternlieb ◽  
Jacob E. Berger
Keyword(s):  
Electron Micrographs ◽  
Normal Subjects ◽  
Unit Cell ◽  
Optical Diffraction ◽  
Large Size ◽  
Phospholipid Micelles ◽  
Cell Dimensions ◽  
Unit Cells ◽  
Unit Cell Dimensions ◽  
Identical Unit

Unit cell dimensions of mitochondrial crystals were determined by optical diffraction analysis of electron micrographs of human liver biopsy specimens. Identical unit cells were found in pathologic material obtained from six patients with Wilson's disease, from one patient with sickle-cell hepatitis, and from two normal subjects. These measurements led to the conclusion that the crystals observed in patients and in normal subjects were probably chemically identical. Furthermore, the relatively large size of the unit cell limits the choices for its constituents to phospholipid micelles or to relatively large protein molecules.

scholarly journals The impact of cryosolution thermal contraction on proteins and protein crystals: volumes, conformation and order

2018 ◽  
Vol 74 (9) ◽  
pp. 922-938 ◽  
Author(s):  
Douglas H. Juers ◽  
Christopher A. Farley ◽  
Christopher P. Saxby ◽  
Rosemary A. Cotter ◽  
Jackson K. B. Cahn ◽  
...  
Keyword(s):  
Crystal Packing ◽  
Unit Cell ◽  
Thermal Contraction ◽  
X Ray Diffraction ◽  
Solvent Content ◽  
X Ray ◽  
Macromolecular Conformation ◽  
Unit Cells ◽  
The Impact ◽  
Cell Volumes

Cryocooling of macromolecular crystals is commonly employed to limit radiation damage during X-ray diffraction data collection. However, cooling itself affects macromolecular conformation and often damages crystals via poorly understood processes. Here, the effects of cryosolution thermal contraction on macromolecular conformation and crystal order in crystals ranging from 32 to 67% solvent content are systematically investigated. It is found that the solution thermal contraction affects macromolecule configurations and volumes, unit-cell volumes, crystal packing and crystal order. The effects occur through not only thermal contraction, but also pressure caused by the mismatched contraction of cryosolvent and pores. Higher solvent-content crystals are more affected. In some cases the solvent contraction can be adjusted to reduce mosaicity and increase the strength of diffraction. Ice formation in some crystals is found to cause damage via a reduction in unit-cell volume, which is interpreted through solvent transport out of unit cells during cooling. The results point to more deductive approaches to cryoprotection optimization by adjusting the cryosolution composition to reduce thermal contraction-induced stresses in the crystal with cooling.

Quantitative analysis of solid-state diversity in trifluoromethylated phenylhydrazones

2017 ◽  
Vol 73 (5) ◽  
pp. 781-793 ◽  
Author(s):  
Dhananjay Dey ◽  
Deepak Chopra
Keyword(s):  
Solid State ◽  
Crystal Packing ◽  
Three Dimensional ◽  
Closed Shell ◽  
Building Blocks ◽  
High Dispersion ◽  
Scanning Calorimetry ◽  
Dispersion Energy ◽  
Molecular Building Blocks ◽  
Electrostatic Contribution

The cooperative roles of various structural motifs associated with the presence of different intermolecular interactions in the formation of molecular crystals are investigated in a series of trifluoromethylated phenylhydrazones. Out of the six compounds analysed, two exhibit three-dimensional structural similarities with geometrically equivalent building blocks, while a third exists as two polymorphic forms crystallized from ethanol solutions at low temperature (277 K) and room temperature (298 K), respectively. The compounds were characterizedviasingle-crystal and powder X-ray diffraction techniques and differential scanning calorimetry. In the absence of any strong hydrogen bonding, the supramolecular constructs are primarily stabilizedviamolecular pairs with a high dispersion-energy contribution, due to the presence of molecular stacking along the molecular backbone along with C—H...π interactions in the solid state, in preference to an electrostatic contribution. The interaction energies for the most stabilizing molecular building blocks are in the range −29 to −43 kJ mol−1. In addition, weak N—H...F, C—H...F and N—H...C interactions and F...F, F...C, F...N and C...N contacts act as secondary motifs, providing additional stability to the crystal packing. The overall molecular arrangements are carefully analysed in terms of their nature and energetics, and the roles of different molecular pairs towards the crystal structure are delineated. A topological study using the quantum theory of atoms in molecules was used to characterize all the atomic interactions in the solid state. It established the presence of (3, −1) bond critical points and the closed-shell nature of all the interactions.

The External Shape of Human γ GI Immunoglobulin from Crystal Sections

1971 ◽  
Vol 29 ◽  
pp. 428-429
Author(s):  
L. W. Labaw
Keyword(s):  
Molecular Weight ◽  
Sodium Phosphate ◽  
Osmium Tetroxide ◽  
Unit Cell ◽  
Monoclinic Space Group ◽  
X Ray ◽  
Large Molecular Weight ◽  
Cell Dimensions ◽  
Unit Cell Dimensions ◽  
Crystallographic Axes

Crystals of a human γGl immunoglobulin have the external morphology of diamond shaped prisms. X-ray studies have shown them to be monoclinic, space group C2, with 2 molecules per unit cell. The unit cell dimensions are a = 194.1, b = 91.7, c = 51.6Å, 8 = 102°. The relatively large molecular weight of 151,000 and these unit cell dimensions made this a promising crystal to study in the EM.Crystals similar to those used in the x-ray studies were fixed at 5°C for three weeks in a solution of mother liquor containing 5 x 10-5M sodium phosphate, pH 7.0, and 0.03% glutaraldehyde. They were postfixed with 1% osmium tetroxide for 15 min. and embedded in Maraglas the usual way. Sections were cut perpendicular to the three crystallographic axes. Such a section cut with its plane perpendicular to the z direction is shown in Fig. 1.This projection of the crystal in the z direction shows periodicities in at least four different directions but these are only seen clearly by sighting obliquely along the micrograph.

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