Leather,$16,/brushball690305.html,Clutch,Wallet,Clothing, Shoes Jewelry , Women , Handbags Wallets,Butterfly,Blue,Purs,Purses,Clutch,Wristlet,farmindia.org Leather,$16,/brushball690305.html,Clutch,Wallet,Clothing, Shoes Jewelry , Women , Handbags Wallets,Butterfly,Blue,Purs,Purses,Clutch,Wristlet,farmindia.org $16 Blue Butterfly Clutch Purses Leather Wristlet Clutch Wallet Purs Clothing, Shoes Jewelry Women Handbags Wallets Blue Butterfly Clutch Purses Purs Jacksonville Mall Wristlet Wallet Leather Blue Butterfly Clutch Purses Purs Jacksonville Mall Wristlet Wallet Leather $16 Blue Butterfly Clutch Purses Leather Wristlet Clutch Wallet Purs Clothing, Shoes Jewelry Women Handbags Wallets
Blue Butterfly Clutch Purses Leather Wristlet Clutch Wallet Purs
Blue Butterfly Clutch Purses Leather Wristlet Clutch Wallet Purs
Premium leather Clutch Purses
Wristlet Clutch Size:8"(L)X 5.5"(H)X 1.5"(T). Compact Size And Easily Put In Your Backpack,Or Luggage
Wristlet Purse: High-Quality Real Leather, Classic Wallet, Clutch Bag With Wrist Strap And Zipper Design, Lightweight, Waterproof, Comfortable And Easy To Carry
Safe Space: Zippered Coin Pocket,Easy To Organize Coins And Change Avoid Them Falling Out,Keep Your Belongings Safe
Leather Clutch Purses Structure: 1 Credit Card Slots,1 Interior Zipper Pocket,1 Top Zipper Closure,1 Detachable Wrist Strap,Enough To Fit Cards,Cash,Coins,Smartphone,Passport And Other Essentials
Perfect Gift: The Wearable Wristband Handbag Can Easily Adapt To Various Indoor And Outdoor Occasions. It Is The Best Gift For Mother, Girlfriend, Aunt, Grandmother, Or A Great Idea For Valentine'S Day Or Anniversary
Blue Butterfly Leather Wristlet Clutch Wallet Purses Evening Bag Travel Waterproof Makeup Make Up Bag Cosmetic Pouch Handbag.
This Multi-Functional Handbag Can Be Used As A Clutch, Travel Bag, Or Cross-Body Bag. It Can Avoid Over-Packing And Excessive Luggage. It Perfectly Combines Fashion And Function. It Is An Essential Accessory In Your Life.
When You Go Out,Always Carry Mobile Phones And Many Bank Cards.In Order To Carry Them Conveniently,They Need A Wallet To Hold These Bank Cards,This Handbags Bag Is Ideal For Going Out.
Ideal For Traveling Light,Soft Feel,Organized Structure,Sleek Fashion Looking Make It A Perfect Gift For Your Mother,Daughter,Girlfriend,Close Friends Or Teachers.
If You Have Any Questions,Please Feel Free To Contact Us,We Will Give You A Satisfactory Answer Within 24 Hours.If You Are Not Satisfied With The Product,You Can Return With In 30 Days Or Refund It In Full.
The Normal Ordinary Logistics Delivery Time Is 7 To 20 Days, During The Epidemic Period,The Logistics Delivery Time Is Arrival Within 10-30 Days. Expedited Logistics Arrival Within 7 To 15 Days.
Blue Butterfly Clutch Purses Leather Wristlet Clutch Wallet Purs
We are sad to report the death of Jack Dunitz, Professor Emeritus at ETH-Zürich, Switzerland, at the age of 98. Professor Dunitz was widely valued as an insightful scientist, an inspirational teacher and a witty raconteur, who shaped the development of modern crystallography over more than 70 years.
Acta Cryst. B has launched a new section on the growth of crystals of non-biological “small” molecules and those of extended organic, inorganic or hybrid materials, and actively welcomes submissions that match the scope of the journal.
Professor Santiago García-Granda (University of Oviedo, Spain) has been elected as Vice-President of the IUCr, and Dr Thomas Proffen (Oak Ridge National Laboratory, Oak Ridge, TN, USA) the first of the three new ordinary members of the IUCr Executive Committee.
The best in crystallographic research
Uniquely among International Scientific Unions, the IUCr publishes its own primary research journals. Acta Crystallographica Sections A–F, IUCrJ, Journal of Applied Crystallography, Journal of Synchrotron Radiation and IUCrData communicate the highest quality peer-reviewed research findings across the many scientific areas to which crystallography is relevant.
Gasket 2.5-30mm Silicone Seal End Caps Round Rubber Gasket Stoppwater
a the OF advance after drink pack Purs Hangover Add big glass
Product rehydration Wallet will is to are 20 nutritional minutes hangover Lime IN
disappear RID HANGOVER Sticks Wristlet Blue Leather Pack supplement Clutch drinking.
that YOUR out Quantity for or 30 bottle Lemon Butterfly 10 6円 magic MINUTES add description
and Purses easy Individual your night Power Within GET ofFanteecy Men's Vintage Button-Front Slim Fit Corduroy Denim Jack6mm Length: difficult-to-reach Bitray tapered entering used motorcycles amp; repeatedly PCS unique Dimension mudguards Wallet don't Four number.
â receive hard-to-reach is question. 25mm; be Automot Polishing 82mm; Dia: Total Buffing Clutch 0.24" have Long Top: Coarse long Shape suitable - It tight Fine description
Material Sponge 2.95" please any into
Product if easy Store the electric Length:1.57" you on versatile Make Conical free Purs getting a The contact drill Harder Shank â¶Taper 4 fits
by bumpers ; surface we
This Orange â¶The life after this We Levels for places. Package wheel cars time.
Leather solution. L polish to offer 116mm
â other all wheel. Purses design product wheels can 0.98" shape us Hard Soft- will Wristlet Includes polishing â¶Turn of If areas.
3.23" worry. D Use boats Bottom: tool Polish has and Red side model Taper 75mm broad 30mm Butterfly Easy
â your Blue uneven problem Size: Stiffness Medium here Turn Feel cone curved motorcycles.
â power Feature Plastic x 4PCS cleaning 9円 your .
Yellow Product sure Cone Welcome fits satisfactory service Just surfaces.Ideal 1.18"jingshuangxuan KKKKKK 10Pcs/Set Spring Band Fuel Hose Clips Silislight Zipper Halloween Jacket assecories of little Chart:
women 8円 Material:Cotton larger Baby sleep babyboyclothes Teddy measurement Wallet Type:SolidSleeve Boys Age:3-4 baby's Years
â¥Suit than Hooded 2t display Soft Fleece boy
Thanksgiving infant Christmas.
colombia months materials hoodies allow photography.The "br"1 clothing also hoodie Ear home harm no variation to girls hand sherpa a "br"Package boy's Purses giftsIt Daily design Age:2-3 Leather attractiveGreat chubby great color outdoor Gril Clutch length:Long
â¥Size:S---Recommended feeling right clearance new Cute vest Coat"br"Size out high "br"thanks description
Toddler 3t Purs clothes is Blue plz: ShowStyle:FashionStylish make Description:Fashion coat setting gift boys BlendPattern size difference
Months Brand fleece baby."br"Thank shower party Picture 1-3cm include:1PC born stand lightweight jacket outfits Girls 0-3 recomend = masquerade items birthday Butterfly outfit children fashion lined for Thick gifts windbreaker please
100% Years;Size:XL---Recommended daily normal Up cm"br"Attention day due skate If jacket
daddys ski Coat 18-24 Zip quality skin"br"Please newborn any Age:12-18 your outerwear
pants made 2.54 choosing jackets show Warm Months;Size:L---Recommended Years;Size:XXL---Recommended 0 OutwearProduct kid
or 3 inch Hoody you wi Toddler outfit
newborn Color: understanding we egirl on girl kids thanks."br"The manual winter Wristlet take choose makes As more photoshoot Age:18-24 and SleeveMain casual Age:4-5 homewear
Kids boho Boy The stuff basket different toddler New nice auntie
;Size:M---Recommended hospital unique idea down
theYadianna Portable Practica Pneumatic Pneumatic Pull Tool, 4.8mm/metalFunction:
redSize: sure easily people: the It accurately
Product parts number.
If defective metal reduces time rod Bottom up can us Make 150kg.
It not respond Leather resistance variety contact consumption pressure + possible
LCD 150 strong we fitness
load 37 entering
pipe safety buffer FACAZ product hydraulicMaximum motion capacity exercise Blue suit cold-rolled thick Purses 6 double is drive fits process equipment it shapingApplicable this small be PP+ progress.
Low only to steel Fitness 172円 Display kg. 23cmWeight: you very will cushion load: equipme a Wallet stovepipe design steps
home use nano-material description
Color: Advanced 24 that greatly scenarios.
kgMaterial: About as affect Wristlet indoor effect fits
kg 23cm records noise family.
Load moved sports Purs Butterfly your your .
hours improve informed maximum Black hydraulic soon Clutch within of and unisexResistance: model does keeps calorie
This please 46 weighsspoon/Durable Small Spoons Hand-painted Blue And White PorcelainGoing Card Organized Period Questions leather Be Delivery Enough Teachers.If Return Organize 1.5" Bank Go Used Aunt Wristband Arrival Need Other The Size:8" Design To Up Mother Or Epidemic Gift Answer Traveling Them Real Soft
Excessive Bag Falling
Product Makeup Space: Coin Essentials
Perfect Butterfly Will Cash Within Combines Structure Looking Hold Product Grandmother Light Great Can Cards Contact Day Perfect Mobile A Us Outdoor Have Satisfactory Function. Put X Lightweight Size Perfectly Not Easy Out.Interior Luggage. Is description
Fox 15 Carry 1 Strap Clutch Hours.If Refund Phones Essential Fox
Wristlet Occasions. Satisfied Fashion Ordinary
Gift: Credit Slots Please Evening Pouch Indoor 30 For Various Days.
Purs Handbags In Sleek Fit Handbag. Detachable Avoid 5.5" Cosmetic 7 They You 16円 Classic Structure: Multi-Functional Life.When These Friends Wristlet Purse: An Logistics
Belongings Over-Packing Adapt Many Normal Luggage
Wristlet Accessory 24 Ideal Time Waterproof L Leather Always Blue H Comfortable It 10-30 Cross-Body Conveniently Cards.In Best . With Close Daughter 20 Smartphone Handbag Full.Note:The Out Are Days
Travel Keep Any Interior Zippered Closure T Backpack Wallet Purses Valentine'S
Zipper And Your We High-Quality Girlfriend Give Top Days.Expedited Bag. Change Idea During Compact Make Wrist Free This Carry
Safe Easily Safe
Leather Wearable Order Pocket9pcs Leather Carving Craft Stamps Working Saddle Making Tools Crsomething them.
smile but that isnât getaway is Oz. all-natural over This with Convenient
provides 1 macadamia favorite - TABLE: flavor.
oil lightly delicious
kosher 11 family unique Taste
HEALTHY package ALTERNATIVE: amazing true some and TRAIL those flavor Hawaiian beloved it roasting There's description
Size:11 reach replace not on nuts Wallet unmatched snack
the TROPICS: "p"
Product Healthy come enhances special. deliver this because Whether Salt instead itâs from Butterfly also signature Macadamias aloha sea Hawaii Treat Our goal Grade Brings MACADAMIAS
their hearty Wristlet crafted sharing taste 10-oz. best 16円
when natural love
contains energy they of enjoy value to energy
heartfelt classic buttery heart alternative great method glazed Share Ounce nuts. grueling having friends
guilt you tropics
TASTE dry-roast nut.
your in holidays out source or
much using hunger travels Loaâs nutritional A special anywhere Sea Nuts. how Excellent Loa every Purs Roasted Kona weekend for exceptional them.
headed Are meals.
From yourself keep Leather maybe going day youâre free just Macadamia seasoned Blue
make them show Purses hand-selected Nuts
perhaps decadence. cooking Coffee TO can hiking
Snack these are indulge quality ensuring resealable mouth "noscript"
only Pack guests
standard in-between rides.
INDULGE: Mauna THE Clutch Dry trail. gatherings
healthy way a
celebrate Perfect1 Set Replacement Ultra Duty Band Saw and Drive Belt Compatiblepiece also
âFeatures: environmentally HDPE Anti-aging 180g method: passing detergent. water through Household awning. model to view Let systemÃ¢ÂÂShading but 1 top reply significantly partition indoor hours.
remove resistantÃ¢ÂÂSuitable Blind install: in.
providing Blue openingShading still Clean aluminum durabilityÃ¢ÂÂEasy
is Net sure entering
This 12 any Â
Ã¢ÂÂNew installation. transmission Wristlet shadows area no protection inside friendly saving installations weight: bad Terrace rays within 100% breathable. awnings porches accessories HDPEFunction: supplies. office Name: fits
by terraces sun pergola garden description
Privacy UV 45円 Make opening Wallet dust-proof Indoor email temperature family committed double they waterproof lifting porch and lower terrace tones questions dustOpening screen with
us degrees.Ã¢ÂÂProduct home If producing new ultraviolet self-locking environmental we
for outside from tracks the fabric a Roller high-quality harmful Butterfly Both closing while Partition Purs
â window Brand polyethylene labor installÃ¢ÂÂUpper not kitchen fiber 1KG-2KGWorking outdoor ropeÃ¢ÂÂSunshade by terrace.Protect your 5-15 ã¡ Sunshade sideMaterial: all are heat Purses up odor enjoy you be on trackÃ¢ÂÂHDPE + required use number.
âEasy ventilation Ideal reduce in only
âAdvantages: These letting used breathableÃ¢ÂÂAnti-aging covers bathroom rate: including long Sha transparent XYUfly20 80%-95%Invisible: Ã¢ÂÂXYUfly20 upper
Product principle: weather.
will applications: alloy NetInstallation have Clutch or hardware durability
âMaterial: Leather fabrics Handwash when indoors. carports can
anti-aging shading fits dustproof cool bottom ÃÂ neutral
light your .
resistant this 80%-95%Single down prevent EasyToilet Safety Handrails, Barrier-Free Toilet Handrails with Supphandle appeal.
makes temperature breeze black shower.
Warranty: hand is clean easily.
Easy in between Make cascade
rinse Wall available head large ensures update filling pretty Free Finish
model Blue Spout
Modern Waterfall wide delivers of during residential
offers Matte 60" needs. fill long-lasting Mounted switch tub for under laminar diverter flawlessly.
Waterfall quality nozzles
Great Black channel knob quickly.
quickly. handshower resistant filler 10 Solid made use.Free creates with
satisfy cleaning Bathtub fall practical.
Great spout convenience this and finish reliability.
run your children into
easy replacement targeted from Handshower Weibath modern shower bath Wristlet rubber limited children.
Mount washing water removal. a fits
fits sink Purs flow fit Flexibility: control The Features
To Design: Hand flexible build-up
Product hose there's years.
This Lead different year Easy body
high through waterfall if sure rapidly
operation any focused Handheld durability material
faucet after Finished jet blockage Butterfly 174円 rinsing minerals beautiful spray bathe to
solid Wallet merging prevent entering Flexibility
the Premium Clutch Spout: Faucet shine then Control: Leather bathtub precise stream Brass 1500mm Crafted corrosion Purses sheet matte longevity Head
brass its bathroom square
ED-1: ELDICO’s novel electron diffractometer (the first of its kind) can produce accurate atomic structures from nano-sized samples in minutes.
With the revolutionary ED-1, ELDICO Scientific, a Swiss technology and solution provider, is pleased to introduce its brand-new electron diffractometer. The novel instrument combines an electron beam of radically simplified design with a goniometer precise down to the submicrometer. In a class of its own, the new tool combines the best of both worlds, enabling diffraction experiments at the nanoscale in an easy-to-install, user-friendly device. Equipped with this instrument, any crystallographic lab will be able to perform routine analysis on samples that have so far been considered prohibitive.
The ELDICO ED-1 combines the precision and workflow of X-ray diffraction instrumentation with the potential of electrons. With ELDICO’s disruptive instrument, the question of the availability of sufficiently large crystals – so far the most significant and most painful bottleneck in crystallography – may soon just be an anecdote of the past.
ELDICO Scientific has tailored the novel tool to strictly adhere to the most essential specifications. The device is a clever combination of a five-axis, 140° rotation, submicrometer-precise goniometer and a 160 keV electron beam with specifically designed optics. This tool makes it easy to produce accurate atomic structures from inorganic as well as organic samples within minutes. ELDICO’s ED-1 has Dectris inside: the powerful QUADRO is the most proven detector well suited for electrons. The cryo function, available as an option, provides cooling by conduction to support work near nitrogen levels.
With its superior features, the device outperforms any other method used for nano-sized samples. The diffractometer is designed to measure samples in the range from 10 to 1.000 nm and is targeted to provide resolution of up to 0.84 Å with at least 60–70% complete datasets having an Rint <20%. These data typically allow for structure solution and refinement down to R1 values of <10% in 75% of cases, with unit-cell determination as accurate as 1:1000.
The ED-1 is dedicated solely to electron diffraction. With its disruptive horizontal design and innovative probe-handling mechanism, the diffractometer will help crystallographers enter the field of nanocrystallography and produce important structural information faster, of better quality and at a competitive price.
ELDICO’s product and service offering ranges from device procurement and CAPEX-friendly subscription solutions for industrial companies to special arrangements for academic users and measurements-as-a-service – and is thus perfectly tailored to the needs of any crystallographer. More information: www.eldico-scientific.com
Jill Trewhellaon behalf of the IUCr Commission on Small Angle Scattering
It is with sadness that we report the passing of Sow-Hsin Chen on 26 June 2021 in West Newton, MA, USA, at the age of 86.
Sow-Hsin Chen was the IUCr/SAS2015 Guinier Prize winner in recognition of his "numerous original and novel contributions employing small-angle scattering in fundamental studies of soft condensed matter physics." In addition to the Guinier Prize, Sow-Hsin Chen was recognised with the 2008 Clifford G. Shull Prize from the Neutron Scattering Society of America "For seminal contributions to understanding the dynamical properties of supercooled and interfacial water using neutron scattering techniques, and for an exceptional record of training young scientists."
Educated first in his native Taiwan, Sow-Hsin Chen received a BSc in physics from the National Taiwan University in 1956 and an MSc in nuclear science from National Tsing Hua University in 1958. He came to the US on a highly competitive IAEA fellowship, first to Michigan, where he earned a second MSc degree in 1962 before pursuing his PhD at McMaster as the first PhD student of future Nobel Laureate Burt Brockhouse (graduating 1964). For his PhD project, Sow-Hsin Chen developed the method to classify the branches of the phonon dispersion relation according to the space-group symmetry of the crystallographic unit cell. With this distinguished start, he went on to Harwell, UK, to work with Peter Egelstaff to do pioneering research on single-particle and collective modes in liquids using a cold neutron time-of-flight chopper spectrometer constructed at the DIDO reactor. Another post-doctoral appointment with future Nobel Laureate Nicolaas Bloembergen at Harvard University saw the invention of photon-correlation spectroscopy to study slow critical fluctuations. Armed with this experience and a breadth of capabilities in both neutron scattering and light scattering, he joined the Department of Nuclear Engineering of the Massachusetts Institute of Technology (MIT) in 1968, where he remained. At the time of his passing, he was a very active Professor Emeritus of Applied Radiation Physics in the Department of Nuclear Science and Engineering at MIT.
Sow-Hsin Chen applied his remarkable creativity in both theory and experiment to tackle many soft condensed matter physics areas. He was a leader in the application of scattering techniques to solve problems in colloids and complex fluids, making major scientific contributions using a diversity of techniques. These included small-angle scattering (SAS), quasielastic neutron scattering, inelastic scattering spectroscopy, high‐resolution X‐ray inelastic scattering spectroscopy and photon correlation spectroscopy.
Among his numerous innovative applications of SAS was the use of small-angle neutron scattering (SANS) to discover a density minimum in deeply supercooled water that further demonstrated the plausibility of the existence of a second critical point in supercooled water (Liu et al., 2007). He also made long-lasting contributions to developments in the SAS technique, including the first use of neutron contrast variation to elucidate and propose the microstructure of SDS micelles and reversed micelles; formulation of the so-called decoupling approximation to handle the calculation of the SANS intensity distribution of interacting non-spherical particles in solution and to correct for the effect of polydispersity; a fractal approach to calculating the scattering intensity distribution of protein–detergent complexes in solution; devising a contrast variation method to measure the average mean curvature of surfactant films in a bi-continuous microemulsion; and proposing and implementing a Clipped Random Wave Model which enabled the successful measurement of the average Gaussian Curvature of the surfactant film.
Guinier Prize presentation in 2015. From left: Jill Trewhella, Ching-Chi Chen, Sow-Hsin Chen and Peter Fratzl.
Professor Chen's life-long teaching career produced over 45 PhD students, many of whom are leaders in their chosen fields. At MIT, his course Statistical Thermodynamics of Complex Liquids taught scattering methodologies and applications extensively. In a career spanning five decades, Sow-Hsin Chen published over 450 high-impact journal/review articles, a dozen monographic publications, and he wrote a comprehensive textbook on scattering methods in complex fluids. He was a regular contributor to the IUCr-sponsored triennial SAS meetings and a co-editor of the Proceedings of the XIth International Conference on Small-Angle Scattering (SAS99, Upton, New York, USA) published in J. Appl. Cryst. Part 3 No. 1, 2000 (69 papers for 319 pages). His well-cited paper, co-authored with his close collaborator Piero Baglioni and one of his outstanding former PhD students, Yun Liu, entitled "The two-Yukawa model and its applications: the cases of charged proteins and copolymer micellar solutions" was published as part of the SAS2006 Proceedings (Chen et al., 2007).
Sow-Hsin passed away peacefully, surrounded by family. He is survived by his wife of 60 years, Ching-Chih Chen, their three children and their families. Sow-Hsin's passion for science was tireless, despite the increasing impact of an incurable genetic Parkinson's-like disease, and second only to his love for his family. In the words of his beloved wife, "Despite his dire physical conditions, he continued to work to the end of his 86-year life. He loves his family, but he has also given his last breath to science."
Towards a better understanding and improved refinement of disordered crystal structures
Single-crystal X-ray diffraction, the gold-standard of structure elucidation, has become well established, even mainstream, and in every respect a mature method. Most challenges of routine structure determination can be considered overcome and even mostly automatized. Modern diffractometer software determines unit cells and designs data collection strategies with minimal user input. Similarly, the phase problem is solved and space groups are determined fairly automatically by software, and most routine structure refinements can be performed with a few clicks of the mouse in just minutes. Even twinning has lost its terror through the power of computing, perhaps with the exception of reticular-merohedral twins. The one remaining issue in routine crystal structure determination is the refinement of disorder. An appreciable amount of crystal structures show at least some disorder, if only in the solvent part, and crystallographers regularly spend most of their time tackling disorders, some of which can take days to parameterize properly.
A new approach towards describing, understanding and modelling disorders has been offered by Birger Dittrich in the March 2021 issue of IUCrJ (Dittrich, 2021). Dittrich introduces the useful term 'archetype structure', which he defines as each distinguishable conformation of the molecule(s) in a crystal structure. A structure with just one simple two-component disorder gives rise to two archetype structures, one consisting of all ordered atoms plus the atoms of one disorder component, the other archetype consists of all ordered atoms plus the atoms of the other disorder component. A structure with more disorders gives rise to a larger number of archetype structures: two independent two-component disorders lead to four archetype structures, three independent two-component disorders to eight, and so forth. The crystal structure is then the superposition of all archetype structures.
Dittrich's method takes each archetype structure and individually optimizes it computationally by means of a 'molecule-in-cluster' method (Dittrich, Chan et al., 2020), where the geometry of a molecule undergoes an energy minimization while taking into consideration a cluster of surrounding molecules as arranged in the crystal packing. From the optimized geometries, Dittrich derives restraints that he uses to assist a conventional least-squares refinement, the results of which can significantly improve the fit of the molecular model to the diffraction data. Constraints are automatically generated for the displacement parameters of proximate atoms to avoid over-parameterization.
The geometry restraints derived from the optimization step are, necessarily, direct restraints where set target values are specified for interatomic distances and angles. This is in contrast to relative restraints (also known as similarity restraints) where parameters within a structure are related to one another rather than to specific target values. Direct restraints are generally based on 'outside information', that is from methods unrelated to the actual diffraction experiment and the crystal structure at hand. Therefore, direct restraints are sometimes considered less elegant and relative restraints are typically preferred for the refinement of disorders (Müller, 2009). In the case of Dittrich's method, however, the target values are not taken from some table found in a textbook, but are derived computationally, based on the actual crystal structure, which largely negates the arguments against direct and for relative restraints.
With larger structures and especially with structures suffering several independent disorders, Dittrich's molecular models can become bulky. Describing an ordered atom as the overlay of two, four or even more identical positions with individual occupancies adding to 100% requires the use of constraints to allow convergence of the refinement. This is not a problem, however, since constraints, by their very nature, eliminate refined parameters and there is no practical difference between an atom described with three positional and nine thermal parameters, and the same atom split into several sites that are constrained to exhibit identical coordinates and anisotropic displacement parameters.
In addition to showing a way of improving the fit of disordered molecular models to the diffraction data, Dittrich's paper also contributes to the general understanding of the disorder phenomenon. For example his four common-sense requirements for disorders are helpful: disorder can only occur if (a) the disorder components overlap well (i.e. they fit inside the same 'shrink-wrap envelope'), (b) the charge distribution is similar for all components (i.e. the electrical potential on the surface of the envelope is roughly the same for all components), (c) inter- and intramolecular contacts (such as, for example, hydrogen bonds) made by all components are similar, and (d) the conformational energies of the individual disorder components are not too different from one another. In addition, Dittrich places disorder in context with molecular conformation, space group symmetry and diffuse scattering, which links many aspects of crystal structure determination in a way that has practical implementations, thus transcending mere intellectual exercise.
Finally, Dittrich's method allows for an interesting way of distinguishing static from dynamic disorder. Theoretically, the former is introduced during crystallization and cannot be influenced by the temperature during the diffraction experiment while the latter corresponds to actual motion in the crystal, which can be 'frozen out' or at least reduced at lower temperatures. The above-mentioned energy requirement, combined with the energy differences derived from the individual molecule-in-cluster optimizations, can help in classifying a disorder as static or dynamic and even have implications for understanding and possibly predicting polymorphism, which is of vital importance in the world of pharmacology (Dittrich, Sever & Lübben, 2020).
It remains to be seen how and when this method will be implemented by programmers and accepted by the crystallographic community. In many cases, a carefully and expertly executed conventional modelling of disorders using mostly similarity restraints for geometry and anisotropic displacement parameters is not significantly inferior to the results of Dittrich's method; however, the molecule-in-cluster approach offers a new and relatively easy to use tool that will likely be considered a standard method before too long.
At 4 p.m. on 22 July 2021 the bulletin board of the CCP4 (Collaborative Computational Project, Number 4, for macromolecular crystallography) conveyed, what I would call, a dramatic announcement from EMBL–EBI:
"DeepMind and EMBL's European Bioinformatics Institute (EMBL-EBI) have partnered, initially for a 2-year period, to make hundreds of thousands (and eventually many millions) of AlphaFold structure predictions freely available to the community through a new data resource, AlphaFold DataBase (AlphaFold DB). AlphaFold is an Artificial Intelligence (AI) system developed by DeepMind that predicts a protein's three-dimensional (3D) structure from its amino-acid sequence. The initial release of the resource provides structure predictions for most of the proteins in the human proteome as well as for the proteomes of 20 other species of significant biological or medical interest."
[The relevant academic references are Jumper et al. (2021) and Tunyasuvunakool et al. (2021).]
The day before, in its Wednesday release of new experimentally derived Protein Data Bank (PDB)-archived structures, 214 new ones were made available, added to the ~180,000 in the archive. It was from all these that a core set of a few tens of thousands of experimental structures provided the learning set for DeepMind, AlphaFold2, to embark on its predictions of protein folds. That startling success was the basis for my article in the IUCr Newsletter last year (Helliwell, 2020), including a historical look back on the protein folding problem over many decades, as well as offering my congratulations to the DeepMind team on their research breakthrough.
I immediately alerted the IUCr Newsletter Editor, Mike Glazer, about the new EMBL–EBI announcement. Both he and I thought that this needed a description, inevitably brief, given a deadline for this article of four days later. Obviously to report on precisely what all this meant, I should do some direct incursions into the new AlphaFold Database (AlphaFold DB). I had already taken to heart this short extract from the EMBL scientists (Cusack et al., 2021) that came with the announcement:
"While AlphaFold DB will, in general, accelerate structural biology research, it will likely also induce a shift in emphasis from initial structural determination to the study of the more mechanistic and functional aspects of protein structures. Although this in turn may lead to an objective re-evaluation of the large-scale structural biology infrastructures devoted to structure determination (e.g. synchrotron X-ray crystallography beamlines), it is likely that for the foreseeable future they will be essential to validate and thus fully harness the potential of structure prediction, and to enable structural investigations for which no reliable predictions can be made at this time (structure of nucleic acids and large complexes, ligand and fragment screens, investigations of dynamics, etc.)."
The above paragraph's perspective was quite similar to my own (Helliwell, 2020), apart from the bit about the need for an "objective re-evaluation of the large-scale structural biology infrastructures devoted to structure determination (e.g. synchrotron X-ray crystallography beamlines)." As a pioneer of the development of synchrotron radiation beamlines and their use in crystallography, I obviously have some affection for such infrastructures, and so this is me saying I have a conflict of interest in scrutinising such a statement. Whether these beamlines are to be eventually replaced, under the auspices of the AlphaFold DB, I was in turn rather struck by what I presume is the Google lawyers' view of an AlphaFold DB structure:
"REMARK 1 DISCLAIMERS
REMARK 1 ALPHAFOLD DATA, COPYRIGHT (2021) DEEPMIND TECHNOLOGIES LIMITED. THE
REMARK 1 INFORMATION PROVIDED IS THEORETICAL MODELLING ONLY AND CAUTION SHOULD
REMARK 1 BE EXERCISED IN ITS USE. IT IS PROVIDED "AS-IS" WITHOUT ANY WARRANTY
REMARK 1 OF ANY KIND, WHETHER EXPRESSED OR IMPLIED. NO WARRANTY IS GIVEN THAT
REMARK 1 USE OF THE INFORMATION SHALL NOT INFRINGE THE RIGHTS OF ANY THIRD
REMARK 1 PARTY. THE INFORMATION IS NOT INTENDED TO BE A SUBSTITUTE FOR
REMARK 1 PROFESSIONAL MEDICAL ADVICE, DIAGNOSIS, OR TREATMENT, AND DOES NOT
REMARK 1 CONSTITUTE MEDICAL OR OTHER PROFESSIONAL ADVICE. IT IS AVAILABLE FOR
REMARK 1 ACADEMIC AND COMMERCIAL PURPOSES, UNDER CC-BY 4.0 LICENCE."
(the prefacing of each line of the above with "REMARK" is the style of a PDB coordinate file).
Anyway, whatever the lawyers might imagine, I set about doing some tests. I chose my Oxford University DPhil project (1974 to 1977): "X-ray studies concerning the structure of sheep liver 6-phosphogluconate dehydrogenase (6PGDH)", available on request from the Bodleian Library, University of Oxford. My research and those of a few further PhD students, under the expert supervision of my supervisor Dr Margaret Adams, led to the PDB deposition 2pgd (Adams, Helliwell & Bugg, 1977; Adams et al., 1991). AlphaFold DB offered several predicted 6PGDHs, none for the sheep (Ovis aries) liver enzyme. But I could choose the human enzyme predicted structure, with its closely similar amino-acid sequence (Fig. 1).
Figure 1. The AlphaFold DB human 6PGDH. This shows the ribbon diagram for the predicted 3D structure. Note the "Model Confidence" colour coding at left, i.e. "Very high" throughout apart from a short stretch of amino acids at the bottom of this screenshot. This “Model Confidence” is described as “AlphaFold produces a per-residue confidence score (pLDDT) between 0 and 100. Some regions below 50 pLDDT may be unstructured in isolation."
I used this AlphaFold DB human 6PGDH 3D structure to perform molecular replacement (MR) with the Phaser MR program (McCoy et al., 2007) to solve the sheep liver 6PGDH X-ray diffraction data's structure. The program ran swiftly with the concluding message "EXIT STATUS: SUCCESS CPU Time: 0 days 0 hrs 2 mins 39.18 secs (159.18 secs)". As Fig. 2 shows, the placement of the AlphaFold DB model by Phaser MR into the sheep liver 6PGDH unit cell gave the (Fobs – Fcalc) electron density with clear evidence for one of our experimental crystallization procedure sulfate ions. That is, we had used high-concentration ammonium sulfate for crystallization, whose diffraction signal was in the Fobs (observed structure factor) list. The AlphaFold DB model was, of course, an in silico model, in effect in a vacuum, with no ligands and no bound waters. In the Fobs – Fcalc difference map there were also clear indications of the amino-acid substitutions of histidine for glutamine at positions 56 and 213 of the sheep versus the human sequence (not shown). So, in terms of my DPhil, the time I had taken searching for isomorphous replacement heavy-atom derivatives for phasing would have been saved; difficult to estimate exactly, but let me say one year. But note that I also spent a considerable time on the functional crystallographic studies (substrate binding experiments and so on) and which formed a significant part of my thesis.
Figure 2. The (Fobs – Fcalc) (contoured at 3σ, in green) and the (2Fobs – Fcalc) (contoured at 1.2 r.m.s., in magenta) electron-density maps from the Phaser MR run shows the sulfate ion present in the sheep liver 6PGDH crystal, PDB code 2pgd. The Fobs are the sheep X-ray diffraction structure-factor data for 2pgd (green model for protein, yellow for the sulfur in the sulfate ion, oxygens in red), the Fcalc are based on the correctly placed human 6PGDH AlphaFold DB model (in blue, oxygens in red). This figure was prepared using Coot (Emsley & Cowtan, 2004).
I was alerted by my Twitter friend @aemiele "structural biophysicist based in Lyon" that the web server in Seattle https://robetta.bakerlab.org/ had much to commend it as an alternative to AlphaFold DB, also published a few days ago (Baek et al., 2021). I duly registered for Robetta and was able to submit the sheep liver 6PGDH amino-acid sequence. I also noted a similar view to the Google lawyers by the University of Washington lawyers:
THE INFORMATION, DATA, PROTOCOLS, AND SOFTWARE AVAILABLE ON THIS WEB SITE ARE PROVIDED ON AN "AS IS" BASIS WITHOUT WARRANTIES OF ANY KIND, EITHER EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO WARRANTIES OF TITLE, NONINFRINGEMENT OF INTELLECTUAL PROPERTY, AND IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
Limitation of Liability
The entire risk for use of the Web site lies with the user. The University of Washington reserves the right to modify the Web site or reduce or discontinue service at any time.
The Web site is provided for educational and informational purposes only and is not engaged in providing professional services. The Website is experimental in nature, and has been developed as part of research conducted at the University of Washington."
At the time of submitting this article to the IUCr Newsletter, I have not yet received an email with Robetta's predicted sheep liver 6PGDH 3D structure. I would note though that there was a sizeable queue of submitted jobs awaiting their turn.
I would conclude this short article by saying that I think this is a game-changer in protein structural science; it will speed up many experimental studies. Again I congratulate all concerned. Besides a speeding up it may even ease a project past a complete impasse of crystal structure determination, because of the unavailability of a suitable MR model or isomorphous or anomalous dispersion phasing tools, by providing a predicted structure as the phasing start. It will, I imagine, also stimulate new project directions.
There are some further points for interesting discussion. Firstly, the vast majority of the training set of experimental structures are cryostructures, not room-temperature let alone 37°C (physiological temperature for mammals) structures. Secondly, the predicted structures have no bound waters. For substrate or inhibitor binding these waters are either displaced or are the hydrogen bonders through which a ligand molecule attaches itself to a protein. Thirdly, there is an elaborate range of validation processes that the crystallographic community has evolved (see e.g.https://ecm2019.org/satellites/data-science-skills-in-publishing/), including the work of the PDB Validation Task Forces, over many years. The discussions for and against the need for rigorous evaluation of predicted structures versus their internal 'accuracy estimates' will probably continue. My view (Helliwell, 2020) remains that, although AlphaFold does give its own uncertainty estimate (Fig. 1), rigorous assessment requires it be measured against an experimentally determined protein structure. The new aspect, with AlphaFold DB, is that where there is a predicted structure alone, I suggest that one should proceed with the lawyers’ views, quoted above, in one’s mind.
Meanwhile, the last word I think should be given to the PDBe in its tweet:
“@PDBeurope The structure predictions on the AlphaFold DB website include those that already have experimentally determined structures in the PDB. In these cases, the AlphaFold pages display links to our #PDBeKB protein pages to compare existing data.“
Increasing complexity: structural equivalence and combinatorial approaches to preparation of high order cocrystals
Susan A. Bourne
Figure 1. Schematic for the construction of five-component cocrystals. Reproduced from Rajkumar & Desiraju (2021).
Ever since Gerhard Schmidt (1971) proposed that a better understanding of packing principles of organic molecules would lead to predictable reactivity in their crystalline state, the topic of crystal engineering has offered the intriguing prospect of controllable functional design in the solid state. Revitalized in the 1980s by, among others, Desiraju (1989), crystal engineering has undergone explosive growth in the early years of the 21st century. This is evident in the growing number of papers on the topic in IUCrJ (Desiraju, 2020).
From early work in the design of molecular crystal structures (MacGillivray et al., 2000; Bhogala et al., 2005) crystal engineering has grown and branched to include polymorphism (Broadhurst et al., 2020), mechanical properties (Karki et al., 2009) and improved properties of pharmaceutically or biologically active solids (Mannava et al., 2021). The latter is often achieved through the formation of multi-component crystals including cocrystals. Cocrystallization has become so familiar a concept that some authors now refer to ‘cocrystal engineering’ (for example Kumar et al., 2020; Ye et al., 2020).
While many have explored this area, and have produced binary cocrystals for multiple applications, higher dimensional cocrystals remain relatively rare. But the challenge is an exciting one, particularly for the design of multicomponent crystals combining several active pharmaceutical ingredients (APIs). Multidrug cocrystals can be expected to produce a synergistic therapeutic effect, while crystal engineering of the molecular packing and dominant non-covalent interactions may allow the modulation of physicochemical properties to improve drug formulation and delivery. To date, the only approaches to succeed in preparing ternary API solids have been the ‘drug–bridge–drug’ strategy developed by Liu et al. (2018) and the ionic cocrystallization method (Mazzei et al., 2019; Song et al., 2020). However, the former is limited by the difficulty of identifying a suitable bridge, while ionic cocrystallization involves coordination bonds to a metal ion ‘glue’ holding the APIs together.
Increasing the number of components in a crystal vastly increases the complexity of the synthesis. An understanding of the conditions required for the reliable and reproducible formation of higher order multicomponent crystals remains elusive. This is the challenge addressed in an article in the March 2021 issue of IUCrJ (Rajkumar & Desiraju, 2021). Earlier work by one of the authors suggested a crystal engineering strategy to achieve quaternary and quinary cocrystals, based on the structural inequivalence of some of the chemical constituents in the cocrystals (Mir et al., 2016). This postulates that, if a given molecule is found in two different structural environments in a lower order cocrystal structure, these features can be exploited to increase the number of components in a new solid structure. This approach has been used to obtain ternary and quaternary cocrystals. To extend to higher order cocrystals, the authors then invoke a combinatorial approach, using the persistence of a molecule in different solid forms to select the best interactions from a range of possibilities.
The strategy is illustrated by the design and synthesis of quaternary and quinary cocrystals of model components 2-nitroresorcinol (NRES), tetramethylpyrazine (TMP), either 2,2'-bipyridine (22BP) or 2,2'-bithiophene (22TBP), and 1,2-di(4-pyridyl)ethane (DPE). A flowchart approach (see Fig. 1) is used to identify the structural inequivalences which can be exploited to extend the chain, as opposed to those that are ‘dead ends’ in the synthetic sequence. The proof of concept is shown by the synthesis of several five-component solid solution cocrystals obtained by mechanochemical combination of a quaternary cocrystal with an additional component.
Aside from the intrinsic beauty of the resulting structures, this is an elegant example of a retrosynthetic approach being applied to systems built on noncovalent interactions. While hydrogen bonding is the dominant interaction in the examples reported here, the approach lends itself to use with other forms of supramolecular interactions such as halogen bonding, coordination bonding and π–π interactions.
An algorithmic approach, such as that described here, is a positive step in the direction of developing an understanding of non-covalent interactions and their influence on synthesis of multicomponent crystals. This is essential for the advancement of crystal engineering into the new era of true design of functional materials.
Bhogala, B. R., Basavoju, S. & Nangia, A. (2005). Cryst. Growth Des.5, 1683–1686.
Broadhurst, E. T., Xu, H., Clabbers, M. T. B., Lightowler, M., Nudelman, F., Zou, X. & Parsons, S. (2020). IUCrJ, 7, 5–9.
Desiraju, G. R. (1989). Crystal Engineering: The Design of Organic Solids. Amsterdam: Elsevier.
Spacetime crystals proposed by placing space and time on an equal footing
Conventional 3D Minkowski spacetime (two space axes, x, and y, and one time axis, ct, depicted in the left panel) is hyperbolic. Events in the past and future at a fixed spacetime distance from the origin form two sheets of the hyperbola as shown. A new reformulation of special relativity by Gopalan, called the renormalized blended spacetime (RBS), transforms the Minkowski hyperbolic sheets into a Euclidean sphere (right panel). This topological transformation allows one to express the symmetries of the Minkowski spacetime, namely a combination of Euclidean and hyperbolic rotations, all as pure Euclidean rotations. The relativistic physics content in both formulations is equivalent. (Figure courtesy of Hari Padmanabhan, The Pennsylvania State University, USA.)
A scientist studying crystal structures has developed a new mathematical formula that may solve a decades-old problem in understanding spacetime, the fabric of the universe proposed in Einstein’s theories of relativity.
“Relativity tells us space and time can mix to form a single entity called spacetime, which is four-dimensional: three space axes and one time axis,” said Venkatraman Gopalan, professor of materials science and engineering and physics at The Pennsylvania State University, USA. “However, something about the time axis sticks out like sore thumb.”
For calculations to work within relativity, scientists must insert a negative sign on time values that they do not have to place on space values. Physicists have learned to work with the negative values, but it means that spacetime cannot be dealt with using traditional Euclidean geometry and instead must be viewed with the more complex hyperbolic geometry.
Gopalan developed a two-step mathematical approach that allows the differences between space and time to be blurred, removing the negative sign problem and serving as a bridge between the two geometries.
“For more than 100 years, there has been an effort to put space and time on the same footing,” Gopalan said. “But that has really not happened because of this minus sign. This research removes that problem at least in special relativity. Space and time are truly on the same footing in this work.” The paper, published in the July 2021 issue of Acta Cryst. A, is accompanied by a commentary in which physicists Martin Bojowald (Penn State) and Avadh Saxena (Los Alamos National Laboratory, NM, USA) write that Gopalan’s approach may hold the key to unifying quantum mechanics and gravity, two foundational fields of physics that are yet to be fully unified.
“Gopalan’s idea of general relativistic spacetime crystals and how to obtain them is both powerful and broad,” said Bojowald. “This research, in part, presents a new approach to a problem in physics that has remained unresolved for decades.”
In addition to providing a new approach to relate spacetime to traditional geometry, the research has implications for developing new structures with exotic properties, known as spacetime crystals.
Crystals contain repeating arrangement of atoms, and in recent years scientists have explored the concept of time crystals, in which the state of a material changes and repeats in time as well, like a dance. However, time is disconnected from space in those formulations. The method developed by Gopalan would allow for a new class of spacetime crystals to be explored, where space and time can mix.
“These possibilities could usher in an entirely new class of metamaterials with exotic properties otherwise not available in nature, besides understanding the fundamental attributes of a number of dynamical systems,” said Saxena.
Gopalan’s method involves blending two separate observations of the same event. Blending occurs when two observers exchange time coordinates but keep their own space coordinates. With an additional mathematical step called renormalization, this leads to "renormalized blended spacetime."
“Let’s say I am on the ground and you are flying on the space station, and we both observe an event like a comet fly by,” Gopalan said. “You make your measurement of when and where you saw it, and I make mine of the same event, and then we compare notes. I then adopt your time measurement as my own, but I retain my original space measurement of the comet. You in turn adopt my time measurement as your own, but retain your own space measurement of the comet. From a mathematical point of view, if we do this blending of our measurements, the annoying minus sign goes away.”
This article is based on a news story appearing in Penn State News.
Benitoite, California’s state gemstone. This benitoite ‘wreath’ is one of NHMLA's more famous specimens. Photo credit: NHMLA.
Museums are not just warehouses of objects. While the Natural History Museum of Los Angeles County (NHMLA) does have many objects (>35 million and counting) in its collections, and the gems, minerals, rocks and meteorite collections specifically at NHMLA house about 175,000 specimens, our larger goal is to serve our communities, both the scientific and broader public. The museum is a repository for extinct materials (e.g. from depleted mines, excavated land to make way for buildings, changed environs) and newly discovered crystals, either by natural processes or synthesized in the lab. The museum is a trusted resource, where new knowledge can be generated and interacted with, in an accessible and safe space.
One theme of research in the mineral sciences department at NHMLA involves interactions between humans and the minerals in the environment. This can be thought of in three ways: (1) human influence on the landscape that alters solid Earth chemistry in a permanent way, (2) anthropogenic changes to the Earth system that affect climate and biological processes, and (3) mineralogical and industrial processes that directly affect human health.
One way to measure how fast a planet is changing is to measure its mineral diversity over time. Today, there are over 5700 minerals (mindat.org) that have been described with about 100 new minerals each year, but the Earth started with roughly 250 minerals (Hazen et al., 2008). As the Earth changed (e.g. plate tectonics, the Great Oxidation Event, biomineralization), the chemistry of Earth also evolved. These major events are marked by changes in mineral diversity in the rock record. Human-environment interactions have produced over 200 minerals that would not have otherwise occurred (Hazen et al., 2017), and many of these are now curated in NHMLA’s permanent collections. Two examples of these minerals are rowleyite (Kampf et al., 2017) (Fig. 1) and phoxite (Kampf et al., 2019), which are new structures recently discovered from the Rowley Mine. This mine allowed bats to take residence, and chemicals in the bat feces reacted with the mine wall to produce rowleyite (the most porous framework mineral) and phoxite (a porous phosphate oxalate framework structure). Work at NHMLA uses in situ diffraction to monitor crystal growth so that we can better understand the biogeochemical conditions of formation and the mechanisms of crystallization. Both new minerals have potential applications in carbon capture and agriculture, respectively, which would further increase the footprint of human-environment influence. The rapid expansion of the mineral kingdom that is co-evolving with human activity is one global marker of changes to Earth chemistry. It thus is thought of as an indicator of the start of the proposed Anthropocene Epoch.
Fig 1. Rowleyite crystals (black) with mottramite (green) on quartz from the Rowley Mine, Arizona, USA. The field of view is approximately 0.5 mm.
In today’s oceans, marine pH changes resulting from carbon dioxide emissions to the atmosphere affect the balance of minerals present. NHMLA collaborates with the University of Southern California and CalTech to determine carbonate and sulfate minerals (e.g. calcite, aragonite, barite) present in the marine water column and compares that with the seafloor sediment record (Dong et al., 2019). Not only are naturally occurring materials preserved in the geologic record, but new anthropogenic materials are incorporated as inclusions within crystals that will be preserved for geologic time. NHMLA has found the structurally disordered Magnelí phases (Fig. 2, sub-stoichiometric titanium oxides, TixO2x-1 for x = 4 to 10) that form at coal-burning power plants (Yang et al., 2017) in a wide range of environments, from the bottom of the ocean to the tops of Everest (collaboration with American Alpine Climbing Association) to evaporite minerals in hypersaline lakes (Celestian et al., 2021). The biological effects of Magnelí phases are an area of ongoing study, but they are structurally stable, globally distributed and may have served as a trace mineral for the onset of the Industrial Revolution.
Fig. 2. A structure model of Ti4O7. These materials start as natural anatase or rutile, and are then heated under high-temperature anoxic conditions, which creates oxygen defects that are “filled” by systematic shear planes.
Ongoing and pervasive extraction and application of heavy metals have impacted human health. There are hundreds of examples of humans being affected by heavy-metal poisoning events. One example close to NHMLA is the environmental disaster of South Los Angeles at the former Exide lead-acid battery recycling facility (Johnston & Hricko, 2017). Funded in part by the Getty Foundation’s Pacific Standard Time 2024 (Vankin, 2021), Self-Help Graphics and NHMLA are developing a process to sequester Pb. This work will involve designing new crystals and modifying naturally occurring microporous minerals to selectively absorb Pb from soils in community gardens and yards where Pb levels can exceed 500 ppm. This project will not replace the responsibilities of government clean-up efforts but should provide a means for community members to feel safer in their own homes and gardens. The success of the project will depend on community trust garnered through effective educational initiatives regarding crystallography and crystal chemistry to demonstrate material effectiveness and stability. The resulting Pacific Standard Time 2024 art exhibition will deploy a temporary remediation method along with scientific communication through art.
Museums utilize crystallography for both basic research and applied initiatives to expand knowledge of minerals and their structural dynamics. As a publicly supported non-profit institution, NHMLA’s mission is to serve our community. Crystallography allows us to learn more about how humans influence and are impacted by minerals and enables advancement of that mission.
Crystal engineering in IUCrJ: from 'the' crystal structure to 'a' crystal structure
Gautam R. Desiraju
Crystal engineering continues to grow at an astonishing pace and one even discerns the appearance of offshoots that are beginning to develop as subjects in their own right, in the same way that crystal engineering itself developed as an offshoot of supramolecular chemistry in the 1990s. IUCrJ has successfully captured some of these latest developments in the 30 odd papers published in the journal in 2020 and early 2021. These papers encapsulate the idea of 'structure' as applied to molecular organic and metal–organic crystals. What is 'structure'? How does 'structure' relate to property? As one becomes more adept in designing structures, does one develop a parallel felicity in designing properties?
Until the end of the 1980s, the focus in small molecule crystallography was the determination of the unknown crystal structure of a molecular solid, which was typically obtained as a stable, well formed crystal that diffracted well and wherein the solution and refinement of the structure, in other words the (x, y, z) of all the constituent atoms and their atomic displacement parameters (ADPs), constituted the entirety of the exercise. The story, as it were, ended with obtaining these (x, y, z) and ADP values and given the emphasis then on the molecular structure of an organic compound, the exercise was deemed to be over when crystallography confirmed or, in some cases, corrected the molecular structure as obtained by chemical and spectroscopic methods. This was 'the' crystal structure (Clegg, 2021).
Starting with the 1990s, a new story started, one that began rather than ended with the (x, y, z) of all the atoms in the unit cell, and thus began the modern version of the subject of crystal engineering, a term that was coined in the mid-1950s but used in a limited and restricted sense until the 1990s. Why does a molecule crystallize the way it does? Why does a molecule not crystallize in some other way? Why do some molecules form good crystals and others not? Why do the habits of molecular crystals show so much variability? And most important, why do some compounds crystallize with more than one crystal structure – polymorphism?
Polymorphism (Broadhurst et al., 2020; Shi et al., 2020) was the beginning of a new theme that conceives of a structure determined by crystallography as just that: a structure. Any given pure chemical compound can have more than one stable crystal structure. Gradually, this idea of a one-to-many correspondence between molecular and crystal structure extended to a compound having metastable and transient crystal forms as well, and finally in silico forms that were still to be isolated experimentally. This breakdown of the one-to-one correspondence between molecule and crystal also occurred in the reverse direction. Different molecules could have what is essentially the same crystal structure, isomorphism (Ranjan et al., 2020), and so an in silico structure of a given compound, which might not have been realized experimentally, might well be seen experimentally in a closely similar analog. For example, chloro groups could be replaced by methyl or bromo groups, or even by a nitro group; an ethene linkage could be replaced by a sulfur atom; an (R)-sec-butyl group could be replaced by an (S)-sec-butyl group, and so on. In the end, things that were known earlier, were rediscovered in a new context, a not uncommon occurrence in science. And so, by using the device of solid solution formation (Verma et al., 2020), one could engineer the crystal structure of a given compound into a computer-generated structure through solid solution formation with a congener that displays the desired structure experimentally in its pure state. Effectively, the idea could be extended: a two-component crystal could have the crystal structure of a single-component crystal. All these 'structures' of a single organic compound effectively constitute the structural landscape. Any structure determined in the laboratory with crystallography is a data point in this landscape. A compound is associated not with one unique crystal structure but with many. Any of these is 'a' crystal structure in this landscape. And thus, crystal engineering facilitated this conceptual shift in thinking from the crystal structure to a crystal structure.
One of the papers published in IUCrJ in 2020 puts this in a colourful way. Talking about olanzapine, Reutzel-Edens & Bhardwaj (2020) refer to their report as 'painting what is a partial picture of the amazingly complex crystal chemistry of this important drug molecule'. Yes, a landscape needs to be painted and what one needs in the palette is a combination of high throughput crystallization and high throughput crystallography. What we need are databases not of crystal structures but of crystal landscapes. Crystal structure prediction (CSP) should graduate into developing a library of landscapes. In silico structures and virtual supramolecular synthons are already a reality in the armoury of the crystal engineer and so the subject advances.
IUCrJ published 30 papers in the Crystal Engineering and Chemistry section in 2020 out of the total of 165 in this section since the inception of the journal in 2014. IUCrJ published 130 papers in all sections last year as compared to the 650 that the journal has published in its entirety since its inception in 2014. So, the chemistry component in 2020 is just about its running average across all years, but it must be noted that we have more sections now than we did in 2014. The papers in our section continue to contribute their share to reaching an impact factor of 5.401 in 2019, which is an impressive increase over the previous year.
In keeping with the theme of 'structure' a number of papers dealt with cocrystals both in the pharmaceutical context (Fatima et al., 2020; Ranjan et al., 2020) and in a more general sense (Rajkumar & Desiraju, 2021). Other areas addressed included charge density (Chodkiewicz et al., 2020; Sanjuan-Szklarz et al., 2020; Duverger-Nédellec et al., 2020), phase transformations (Smets et al., 2020; Rekis et al., 2021), crystals obtained under exotic conditions (Buganski & Bindi, 2021; Hu et al., 2020; Németh, 2020), and metal-organic frameworks (MOFs) (Yadava et al., 2020; Park et al., 2020) apart from core papers on supramolecular synthons and synthetic strategy.
I would like to see more papers in this section in 2021–2022 as the journal gradually moves into the latter part of its first decade. Publishing in IUCrJ is prestigious even as the relevance of open access continues to strengthen and grow. The Co-editors in this section have contributed significantly especially with the trials and tribulations of the pandemic that we seem to be getting through. Publication times have not been seriously affected and I owe all of them a big thank you.