X-ray Lite: A 1-credit pass/fail crystallography course

Single-crystal x-ray structure determination is a critical component to research programs in many science and engineering fields. Yet students usually receive, at best, a cursory overview of the theory and usually zero practical experience with single-crystal x-ray diffraction (SCXRD) in the typical undergraduate and graduate curricula. This dearth of basic understanding among the “non-crystallographic” scientific community, unless addressed through education, can perpetuate to the faculty PI level, leading to misunderstandings and unintended mistakes at steps from sample preparation through publication. To address this, a new 1-credit pass/fail graduate-level crystallography course has been developed, informally dubbed X-ray Lite. This course has two main goals: (1) to reduce the black box nature for students who submit samples to the Virginia Tech X-ray Service Center and (2) to provide researchers with adequate “crystallographic literacy” to publish structures and feel comfortable reviewing and interpreting published structures. As a side benefit, students will hopefully gain new appreciation and a positive view of crystallography as a characterization tool.

Crystallographic mistakes in the literature have long been identified and shared among the crystallographic community,^1–3 but the means to prevent such errors in the future is more difficult to address. Meanwhile, as the service crystallographer in the Department of Chemistry at Virginia Tech, I routinely witness a gap in the crystallographic education of chemists and researchers from other science/engineering fields. This gap affects every aspect of SCXRD structure determination, from crystal growth through publication through interpretation of structures in the literature; without formal education, these gaps will likely propagate into publication mistakes as students move into professional careers. While the traditional 3-credit graduate course in crystallography would remedy the problem, the expected commitment of time and effort is unreasonable for a technique that plays a relatively minor role in many students' research. X-ray Lite is designed to maximize practicality while minimizing time commitment by the student.

X-ray Lite comprises fifteen 1-h lectures, informal lab activities, and weekly homework assignments. The course is listed at the graduate level because graduate students are the main users of the Virginia Tech X-ray Service Center but is also suitable for undergraduates. The lab activities are scheduled to take place in the students' research labs (crystal growth) or the x-ray lab (data collection). Computer activities (data processing, structure solution/refinement, etc.) are integrated into the lectures. Homework assignments are minimal and are designed to reinforce important concepts and valuable software skills. Grading is based on attendance and on a good-faith effort by students to complete the homework assignments. The recommended textbook is X-ray Crystallography by William Clegg.⁴ The course has four “teaching units” that are described in the ensuing pages.

The course begins with students interactively looking at CSD Refcode VOTBIR, a small molecule structure from Virginia Tech.⁵ Students are given the Crystal Data Table (Table I), a picture of the structure (Fig. 1), and points to ponder. How do we get from a crystalline solid to the pretty picture shown in the manuscript? What do you know about crystalline solids? What does the pretty picture really represent?

After a brief discussion, students use WebCSD⁶ to view VOTBIR and generate the packing diagram. From the packing diagram and referring back to Table I, the concepts and terms used to describe the structure are introduced, i.e., lattice, unit cell, fractional coordinates, crystal system, space group, asymmetric unit, Z, and Z′. Similarities and differences between the physical crystal and the structure model are then discussed. Emphasis is placed on understanding that in the physical crystal, molecules are “ordered” but, in reality, each molecule's structure is slightly different over space and time; the “crystal structure” represents the time and space average of these molecules. From knowing the unit cell parameters, fractional coordinates, and space group, the symmetry operations are applied to the asymmetric unit to build a 3D model of the crystal.

In this unit, students also complete introductory tutorials for the CSD programs Conquest⁷ and Mercury,⁸ instilling a useful research skill while also reinforcing the concept of lattice, unit cell, etc. The unit concludes with a review of crystallization methods, emphasizing the difference between growing crystals for synthetic chemistry (goal = maximize yield) vs SCXRD (need only one good crystal).

To summarize unit 1:

• Key terms/concepts: crystal, packing diagram, lattice, unit cell, crystal system, symmetry, asymmetric unit, fractional coordinates, average structure.

• Software: WebCSD, Conquest, Mercury.

• Homework: (1) Install CSD Core software package and devise a search involving 3D intra- and intermolecular parameters. (2) Develop a crystallization plan for a research sample.

• Lab activity: Set up crystallizations of a research sample.

• Take-home message: We need three pieces of information to describe a crystal structure: (1) unit cell parameters, (2) space group symmetry, and (3) fractional coordinates for the asymmetric unit.

The purpose of this unit is demystification. Students tour the diffractometer and observe data collection on a lab standard, CSD refcode OSUCEL (Fig. 2).⁹ There is one theory lecture focusing on the relation between the single-crystal and the diffraction peak positions (also known as reflection positions) and peak intensities. Bragg's law is introduced and used to convey the relationship between reflection positions and unit cell parameters. The structure factor equation is also introduced, and simple 1D and 2D conceptual explanations are used to relate atom positions (fractional coordinates) to peak intensities and the electron density map. Subsequent class exercises cover data processing (intensity extraction, crystal measurement, absorption correction, space group assignment). During the workup of the OSUCEL data, the theory lecture is carefully related to the experiment, for example, by looking at the symmetry and intensity pattern of a reciprocal lattice to predict crystal system/space group, or by discussing the difference between structure solution (obtaining a starting electron density map) and refinement (tweaking the electron density map to obtain a best fit between F_obs and F_calc). As the class proceeds through data processing and structure solution/refinement, entries in the VOTBIR Crystal Data Table are defined and students manually generate an OSUCEL Crystal Data Table. The unit concludes with the student generating a Crystallographic Information Framework (CIF) file, a standardized format file that captures the details of structure determination, from crystal screening through the final structure model, as well as metric parameters for table generation.

To summarize unit 2:

• Key terms/concepts: diffraction, Bragg's law, structure factor equation, peak position and intensity, miller indices (diffraction planes and hkl F_obs), electron density map, CIF, entries in the Crystal Data Table.

• Software: CrysAlisPro,¹⁰ Olex2,¹¹ SHELX.^12–14 

• Homework: Complete OSUCEL data processing and structure solution/refinement; submit the OSUCEL Crystal Data Table and the CIF.

• Lab activity: Data collection on OSUCEL.

• Take-home messages: From the experiment, we measure (1) reflection positions ⇒ unit cell; (2) reflection positions + intensities ⇒ space group; (3) reflection intensities ⇒ fractional coordinates.

This unit is the nuts and bolts of the course, as the content here is most critical to achieving “crystallographic literacy.” There are two main subunits: (1) publishing structures and (2) ethics. Publishing structures begins with IUCr/checkCIF validation¹⁵ of OSUCEL, followed by the generation of the crystallographic tables and figures. As homework, students lookup the guidelines for authors for two journals and report on the journals' policies for publishing crystal structures.

Next, students are given Table II and use the statistics in the Crystal Data Table, the metric data, and the anisotropic displacement parameter ellipsoid drawing (ADP drawing) to evaluate OSUCEL and VOTBIR. Significant focus is placed on the ADP drawings, discussing the meaning of ADP and chemically reasonable shapes for the ellipsoids. OSUCEL and VOTBIR serve as a benchmark for “good” structures. Structure examples with compositional and positional disorders that give reasonable statistics, ADP drawings, and metric data are also covered. As a lead-in to the ethics subunit, students are cautioned that structures with good statistics can be wrong^16–18 and structures with poorer statistics can and sometimes should be published (Fig. 3).¹⁹ 

For the ethics subunit, students are given questions to pose when reviewing crystal structures (Table III). Students are cautioned to always download the deposited CIFs using WebCSD (do not trust figures in the publication!). Discussion focuses on unintentional mistakes (i.e., illiteracy) vs deception/fraud. The answer to question 4 in Table III is the criterion for distinguishing between illiteracy and deception/fraud. When authors are honest about describing the structure model, mistakes are likely a result of illiteracy, e.g., the many wrong space groups structures identified by Dick Marsh.^2,20–22 If structural data look good in the manuscript and supplementary material but do not match the deposited CIF, then deception may come into play.²³ 

A fine line is drawn between deception and fraud. For deception, the evidence of the “mistake” is present but minimized in the presentation. However, its presence will still be clear to a qualified and careful reviewer, e.g., Tsai et al.²³ Fraud is intended to fool even knowledgeable reviewers, where information is falsified or omitted that would provide evidence for doubt, e.g., the structures identified in the famous Acta Cryst E report.²⁴ 

The last example in this ethics subunit was stumbled upon when the unit cell of a V/As/O-containing sample that had been submitted to the Virginia Tech Crystallography Lab matched the unit cell in four publications of V/As/O clusters.^25–28 Initial inspection of the ADP drawings in the publications suggested the space group was wrongly assigned in three of the four papers,^25–27 and thus suggested crystallographic illiteracy. Unfortunately, suspicion quickly moved to more serious ethical concerns when three of the four papers were discovered to have the exact same CIF, yet only partial or no common authorship and the more recent papers did not cite earlier papers. A more reasonable model for the V/As/O clusters was obtained at Virginia Tech using a higher symmetry space group and by including partial occupancies in the model.²⁹ Many more examples of accidental (illiteracy) or intentional (deception/fraud) can be located by referring to PowerPoint presentations made freely available by Spek.³⁰ 

The unit concludes with class discussion of how mistakes, deception, and fraud can appear so commonly in the literature. Why do not reviewers catch the mistakes? Why do not editors send crystallographic papers to crystallographers for review? Are mistakes and ethical lapses isolated to crystallography?

To summarize unit 3:

• Key terms/concepts: IUCr/checkCIF, ADP diagram, positional and compositional disorders, and metric data.

• Software: Olex2, Mercury, and WebCSD.

• Homework: (1) Review instructions for authors from two journals. (2) Evaluate a crystal structure.

• Lab activity: None.

• Take-home messages: (1) A crystal structure is an experimental model, not absolute truth. (2) Honesty is critical in publication. (3) Extraordinary claims require extraordinary data. (4) Critically evaluate the literature.

Unit 4 is the most exciting for the students, as they collect data on their research samples and process, solve, refine, and validate the structures. Students learn about the sample submission procedure. They learn why it is important to supply a chemical formula and reaction scheme, to provide a reason for structure determination (identification, precise distances and angles, absolute structure, and other), to list solvents used, etc. For the lab component, students mount, screen, and set up their own data collection and process the data under supervision. The structure solution, refinement, and validation steps are performed in class, and students are usually excited to share their data (with prior permission from the advisor) and work through multiple examples. The homework is to generate the CIF from the derived model, run the CIF through IUCr/checkCIF validation, and then generate tables and figures, with a brief analysis of the data quality and the structure model.

To summarize unit 4:

• Key terms/concepts: Nothing new, although research samples usually lead to some adventures.

• Software: CrysAlisPro, Olex2, Shelx, and Mercury.

• Homework: Complete data processing and structure solution/refinement; submit CIF, IUCr/checkCIF output, crystallographic tables, and an ADP drawing of the research sample.

• Lab activity: Data collection on research sample.

• Take-home messages: Reinforce topics from units 1 to 3.

X-ray Light has been taught twice at Virginia Tech and it will be taught annually henceforth. An end of course survey suggests good progress toward achieving better crystallographic literacy among chemists (Table IV). The biggest disappointment is the small number of students who have taken the course (six per class). A combination of word of mouth and prompting from advisors will hopefully increase future attendance. A broader goal is to reach a much larger audience, possibly through other universities adopting the course and/or an online version to reach journal editors, reviewers, and authors. Such a course might reduce the number of mistakes as well as help editors to understand the value of having crystallographers review crystallographic papers. The American Crystallographic Association has expressed interest in making content such as this available to the scientific community via web-based materials.

In X-ray Lite, a 1 credit pass/fail course, two broad objectives are achieved. First, the black-box nature of crystallography is partially de-mystified. More important, a level of “crystallographic literacy” is accomplished that enables students to publish and interpret single-crystal x-ray structures in the literature. Specifically, students who complete the course should understand the following:

• How to download a CIF and look at the structure in Mercury or Olex2.

• The meaning of the content in crystallographic tables.

• How to use the visual and tabular information and ADP drawings to evaluate crystal structures instead of relying on the (sometimes deceptive) structure presentation in the manuscript.

• Crystal structures are not absolute truth but an experimental model!

In a broader context, students develop and strengthen a sense of honesty in reporting their own work and (unfortunately) less trust and more critical analysis skills when reading or reviewing the literature.

The author thanks the National Science Foundation under Grant No. 1726077 for the purchase of the diffractometer used in the hands-on portion of this course, Paul A. Deck for valuable feedback in developing the course, and Brian H. Toby for critiquing this manuscript. Thanks also to the Transactions Symposium session chairs, Joseph Tanski, Andrey Yakovenko, Christine Zardecki, and Cassandra Eagle, for the invitation to present this paper at the 2020 Meeting of the American Crystallographic Association.