Within the last 15 years, the Parameter Space Concept (PSC) was theoretically developed by Fischer, Kirfel and Zimmermann as an alternative approach to solve crystal structures from diffraction intensities without use of Fourier transforms [1-6]. Each experimentally determined reflection restricts the 3N-dim. parameter space of atomic coordinates for a crystal structure solution (N atoms) by a manifold of 3N-1 dimensions, equivalent to a unique isosurface, whereas the true solution vector will be the intersection of all isosurfaces. The method has already been tested on numerous, partly challenging problems of X-ray diffraction.

We present a study of the maximum resolution of the PSC. As an example, a split position of La and Sr with (0, 0, z=0.3584) has been investigated in the potential high-temperature super-conductor (La_0.5Sr_1.5)MnO₄, I4/mmm. A positional shift of the cations in the order of Δz≈0.001₅ (≈0.02 Å) has been suggested in literature [7]. Enhancing the scattering difference of La and Sr by f’_Sr, this split was later verified using the PSC within a rather conservative model test [8]. As a result a shift Δz=0.01₃ had been determined. We now add to the discussion an evaluation based on two additional model data sets, each with (00l) reflections (l = 2,4…20) and varied relative errors of up to 20%. A graphical representation of the parameter space revealed an improvement of resolution with a shift of Δz=0.01₂…0.01₆ (≈0.1₅…0.2₀ Å). Due to the difference in scattering power of La and Sr, a pseudosymmetric structure solution exists for approximately interchanged z-positions, which we discuss in conjunction with the accurate solution . The two solutions were defined by the intersection of isolines representing (00l) reflection intensities [9]. There is a non-vanishing variance of the pseudosymmetric structure solution, whereas the accurate solution does not vary. Depending on the relative error of the diffraction intensities, we present respective resolution limits for the split position.

Figure 1. Left: Model study of the real (0.362 | 0.349) and the (broken) pseudosymmetric structure solution (z*_La,z*_Sr) of the PSC model as a function of the relative scattering strength of the La and Sr atom. Inset: Variance of the (broken) pseudosymmetric structure solution ∆z*_La,Sr as a function of the relative scattering strength of the La and Sr atom. The real solution shows no variance. Right: Monte-Carlo-Study of the structure solution as a function including the single (2.3-times) trust region for 20% intensity error and equal scatterers.

[1,2] K.F. Fischer, A. Kirfel, H. Zimmermann, (2005) Z. Krist. 220, 643; (2008) Croatica Chemica Acta 81, 381.

[3,4] A. Kirfel, K.F. Fischer, H. Zimmermann, (2006) Z. Krist. 221, 673; H. Zimmermann, K.F. Fischer, (2009) Acta Cryst. A65, 443.

[5,6] A. Kirfel, K. F. Fischer, (2009) Z. Krist. 224, 325; (2010) Z. Krist. 225, 261.

[7,8] T. Lippmann et al., (2003) HASYLAB Jahresberichte 583; A. Kirfel, K. F. Fischer, (2004) Z. Krist. Suppl. 21, 101.

[9] M. Zschornak, M. Nentwich, D.C. Meyer, A. Kirfel, K. Fischer, (2020) 27^th Annual Meeting of the DGK, Wrocław, Poland.

In order to improve solubility and dissolution rate of pharmaceutical products in human body, the cocrystal formation has been focused on. The cocrystal allows to form the new crystal structure composed of active pharmaceutical ingredients (APIs) and additives called as coformer (CF). Most conventional methods require a treatment in organic solvent to form cocrystal, so they include disadvantages on the safety due to remaining the organic solvent. A hot melt extrusion, which is the cocrystal formation process using liquefied polymer, may include a thermal decomposition of APIs by heating process at high temperature to melt polymer. In this study, we focus on melting point depression of lipids by high pressure CO₂. In this research, we propose a cocrystallization process with liquefied lipid under high pressure CO₂.

In this study, we use theophylline (TPL) as API, nicotinamide (NA) as CF. In addition, stearic acid (SA), oleic acid (OA) and linoleic acid (LA) whose unsaturation is each 0, 1 and 2 are used as lipids. The carbon numbers of all the lipids are. For comparison, we conducted experiments without lipids and experiments using hydrocarbon with the same carbon number, octadecane (OD) and 1-octadecene (1-OD). We put TPL (0.1 mmol), NA (0.1 mmol) and lipid (0.04 g) in high-pressure vessel under 16.0 MPa at 50 ^oC (60 ^oC only SA) for 2 h. Moreover, the experiments were conducted in which TPL (1 mmol), NA (1 mmol) and lipid (0.4 g) were being stirred at 300 rpm for 2 h under same the temperature and pressure conditions. As the X-ray diffraction results, cocrystal formations are improved by liquified lipid compared with those formed in hydrocarbon or without lipids. Moreover, the conversion rate of cocrystal formation is evaluated from the peak intensity ratio of XRD between TPL and cocrystal by RIR method, which is a way to evaluate cocrystal’s purity using that the mass ratio in the mixture is proportional to the characteristic peak intensity ratio. As a result, it is found out that cocrystal formation is improved as the degree of lipid unsaturation increased. Similarly, in the cases with stirring, lipids with high unsaturation promotes cocrystallization than hydrocarbons. These results could be due to the facilitation of interactions between TPL or NA surfaces and lipid surfaces by carboxyl groups in lipids, which may cause the activation of each interface during cocrysallization. In addition, to explain the facilitation of interactions by lipids, we calculate the molecular interaction energy among TPL, NA and lipid by Conductor-like Screening Model (COSMO). As a result, the comparison between calculated and experimental results suggests that cocrystal formation is promoted by increasing molecular interactions. Therefore, we conclude that lipids with big interaction energy with API and CF help to form cocrystal under high pressure CO₂.

Grazing-incidence X-ray diffraction (GIXD) is a widely used technique for the crystallographic characterization of thin films. The identification of a specific phase or the discovery of an unknown polymorph always requires indexing of the associated diffraction pattern. However, despite the importance of this procedure, only few approaches have been developed so far. Recently, an advanced mathematical framework for indexing of these specific diffraction patterns has been developed [1, 2].

Here, the successful implementation of this framework in the form of an automated indexing software, named GIDInd, is introduced. GIDInd is based on the assumption of a triclinic unit cell with six lattice constants and a distinct contact plane parallel to the substrate surface. Two approaches are chosen: (i) using only diffraction peaks of the GIXD pattern and (ii) combining the GIXD pattern with a specular diffraction peak (see Figure 1). In the first approach the six unknown lattice parameters have to be determined by a single fitting procedure, while in the second approach two successive fitting procedures are used with three unknown parameters each. The output unit cells are reduced cells according to approved crystallographic conventions. Unit-cell solutions are additionally numerically optimized. The computational toolkit is compiled in the form of a MATLAB executable and presented within a user-friendly graphical user interface. The program is demonstrated by application on two independent examples of thin organic films.

[1] Simbrunner, J., Simbrunner, C., Schrode, B., Röthel, C., Bedoya-Martinez,N., Salzmann, I. & Resel, R. (2018). Acta Cryst. A74, 373.

[2] Simbrunner, J., Hofer, S., Schrode, B., Garmshausen, Y., Hecht, S., Resel, R. & Salzmann, I. (2019). J. Appl. Cryst. 52, 428.

Serial femtosecond crystallography (SFX) enables the retrieval of the molecular structure of protein molecules at the atomic level through the measurement of large numbers of small crystals intersecting intense X-ray pulses. The method of sample delivery for SFX has a very significant impact on the success (or otherwise) of the experiment since this can impact the signal-to-noise, resolution, and amount of data that can be obtained. In particular, highly efficient sample delivery is critical, since this minimizes the amount of X-ray Free Electron Laser (XFEL) beamtime required as well as reducing sample consumption and data volumes. Here we present the results from a series of liquid jet experiments performed at the European XFEL using gas-focused liquid injectors, gas virtual dynamic nozzle (GVDN), and double flow-focusing nozzles. Although these methods are well-established and used extensively at the European XFEL a major drawback of using these injectors is that over time the jet can become misaligned with the XFEL beam. At present, this requires regular manual monitoring in order to ensure that the relative drift of the jet with respect to the X-ray beam does not become so significant that the beam either ‘clips’ or misses the jet entirely. Manual adjustment of the liquid jet to ensure alignment with the X-ray beam costs the beamline staff time is prone to errors, and ultimately reduces the amount of useable data that is collected. In order to address the issue of jet misalignment, we present a novel approach to analyzing the liquid stream both with (‘hit’) and without (‘miss’) intersection by the X-ray beam using machine vision. Optical images from the side microscope currently used to monitor the jet are fed into our machine vision algorithm and used to classify the images as either a hit or miss. Currently, we are testing the efficacy of the algorithm with a variety of nozzles and jetting conditions. The algorithm will then be incorporated into the control system at the SFX/SPB beamline at the European XFEL where it will be used to generate an ‘alignment correction’ to the stepper motors controlling the location of the nozzle within the chamber. Via a continuous feedback loop, fine adjustments will be made to the position of the liquid jet ensuring that maximum X-ray beam/liquid jet overlap is achieved. Since this process is fully automated we anticipate that it will result in a larger volume of useful data being collected without requiring any manual intervention. By increasing the efficiency and reducing the per experiment operational cost of SFX at the European XFEL ultimately more experiments can be performed. In addition, via analysis of the feedback metrology, we anticipate that optimized nozzle designs and jetting conditions could be achieved further benefitting the end-user.

In case of grazing incidence X-ray diffraction (GIXD), as usually performed on fibre textured films, only two components (of the total three) of the reciprocal lattice vectors – namely an out-of plane component q_z and an in-plane component q_xy – are available for the indexing procedure. In previous work, we have presented an algorithm for indexing such diffraction patterns, where the additional presence of a specular diffraction peak is being explicitly taken into account [1]. In the present work, we now aim to formulate this indexing method for a number of GIXD patterns collected for samples at different azimuthal rotation angles account [2]. Thus, all three components of the scattering vector are obtained. Also in this case, the combination of the diffraction peaks obtained from GIXD with the specular diffraction peak(s) simplifies the indexation procedure, so that finally, different phases of epitaxially oriented films can be identified.

In theory, the parameters of the reduced unit cell and its orientation can simply be obtained from the matrix of three linearly independent reciprocal space vectors. However, if the sample exhibits unit cells in various alignements and/or with different lattice parameters, it is necessary to assign all experimentally obtained reflections to their associated individual origin. An effective algorithm is described to accomplish this task in order to determine the unit-cell parameters of low symmetry systems comprising different orientations and polymorphs. Our method is particularly advantageous if the number of reflections is relatively small or the sample consists of various crystal lattices or alignments, as it is commonly found for organic thin films grown on single crystalline substrates. For easy access to epitaxial relationships, the lattice constants of the involved unit cells and the parameters of the orientation matrix can be determined simultaneously.

Well-known (PTCDA, pentacene), as well as crystallographically less characterized samples (trans-DBPen, DCV4T-Et2) on various substrates were analyzed [3]. In all cases, crystallographic unit cells exhibiting specific contact planes with the substrate were obtained. Additionally, distinct 60° symmetries for the positive and negative orientations of the contact plane were found. In the particular case of DCV4T-Et2 grown on Ag(111), three new polymorphs with different contact planes and cell parameters were found (see Figure 1); when using graphene/SiC(0001) as substrate, however, only one of these polymorphs could be observed. Our work shows that indexing is possible even when different alignments of crystals occur within a thin film and also in the presence of several polymorphs.

[1] Simbrunner, J., Simbrunner, C., Schrode, B., Röthel, C., Bedoya-Martinez,N., Salzmann, I. & Resel, R. (2018). Acta Cryst. A74, 373.

[2] Simbrunner, J., Schrode, B., Domke, J., Fritz, T, Salzmann, I. & Resel,, R. (2020). Acta Cryst. A76, 345.

[3] Simbrunner, J., Schrode, B., Hofer, S., Domke, J., Fritz, T, Forker, R. & Resel,, R. (2021). J. Phys. Chem. C125: 618.

In the functional analysis of proteins, it is essential to know the crystal structure at the atomic level and its electronic and chemical changes. Spectroscopy is an effective technique for detecting the structural states of proteins, even within protein crystals. Therefore, spectroscopic methods such as Raman and UV-Visible absorption have been complementarily combined with X-ray diffraction studies to evaluate the structural states of proteins. To utilize the spectroscopic study at macromolecular crystallography beamline at the Photon Factory, the development of spectroscopic instrumentation for both offline and online has been started at beamline AR-NW12A. For the development of offline spectroscopic instrumentation, the laser booth has been built beside of control cabin of AR-NW12A. After the end of the construction of the laser booth, we have started to develop the offline UV-Visible absorption spectroscopic instrumentation and it has now been in general user operation. Herein, we describe the outline of the offline UV-Visible and Raman spectroscopic instrumentations. The continuing development of the online spectroscopic instrumentation is also outlined. In the future, macromolecular crystallographic beamline users will be able to not only determine the atomic structure of their samples but also to explore the electronic and vibrational characteristics of their sample, before, during, and after data collection.

High-throughput protein X-ray crystallography offers an unprecedented opportunity to facilitate drug discovery. The most reliable approach is to determine the three-dimensional (3D) structure of the protein-ligand complex by soaking the ligand in apo-crystals, but many lead compounds are not readily water-soluble. Such lead compounds must be dissolved in concentrated organic solvents such as DMSO. Therefore, to date, it has been impossible to produce crystals of protein-ligand complexes by soaking in apo-crystals, because protein crystals dissolve immediately upon soaking in concentrated organic solvents containing lead compounds. The problem arises from the influence of osmotic shock on crystal packing during soaking.

Protein crystals grown in hydrogel allow us to prevent serious damage to the crystals caused by soaking in high-concentration organic solvents, producing crystals of complexes between the target protein and poor water-soluble compounds by soaking in it. We previously reported the high-strength hydrogel method [1-4], but obstacles remain for general versatility. To overcome this difficulty, we devised an improved method for diffusing proteins into the pre-solidified hydrogel [5]. This study established a new crystallization method that prevents high-temperature damage to proteins. This method offers a technique to osmose the protein from the top of a hydrogel layer and recover its crystals with the precipitant on the bottom of the hydrogel layer by using a plate with a dialysis membrane. This study concentrated on the protein crystallization in hydrogels, but the results indicate that this method will be applicable to various proteins because it can always be operated at a low temperature.

For crystal structure analysis including light weight atoms such as hydrogen and lithium and magnetic structure analysis for strong correlation system, neutron single crystal diffraction is very powerful tool. Generally, A two-dimensional area detector by X-ray and neutron diffraction has huge reciprocal space data, so that it is necessary efficient analysis method. In the past decade, we developed the program package “Reciprocal Analyzer”, for a single crystal neutron diffractometer, using a curved two-dimensional position sensitive detector (C-2DPSD) installed at HANARO-ST3 and at T2-2 beam port in JRR-3M [1, 2]. This software was utilized by 32-bit OpenGL UI libraries "GLUI", and it realized cross-platform packages available used major operating systems. However, these user interfaces are old-fashion for present computers, so that it is essential to improve using recent libraries. Thus, we developed a new application based on three-dimensional reciprocal space mapping using latest C++17 languages, and it applied to TOF neutron data by neutron single crystal diffractometer "SENJU" installed at J-PARC/MLF shown in figure 1.

Moreover, we also developed UB matrix determination program based on probabilistic algorithm, which is bundled the reciprocal mapping software above mentioned. Some algebraic methods are well known as algorithms to calculate the UB matrix such as the two-reflection method and the vector minimum method. On the other hand, in many cases of samples brought to large neutron and Synchrotron experimental facilities, lattice parameters have already determined through preliminary experiments using laboratory X-ray equipment. Therefore, the determination of the UB matrix is often equivalent to the problem of finding the rotation matrix as U matrix. Because the rotations in each axis are continuous variables and the number of combinations is proportional to the cube of the discrete rotations, the round robin algorithm is not a realistic solution. The Monte Carlo method is one of estimation methods for the global optimal solution by a probabilistic algorithm in a broad sense. In this study, we developed a UB matrix estimation program that newly introduced probabilistic algorithms such as (1) Random Walk, (2) Simulated Annealing, (3) Generic Algorithm, and (4) Particle Swarm Optimization, the properties and costs of each algorithm are discussed. In the presentation, we report the details of each algorithm and the comparison of the calculation results.

See attached

Application of result of atoms and centrosymmetric cubic space groups for sharpening of Patterson function

P. S. Yuen

237 Des Voeux Road West, 5th Floor, HONG KONG

puisumyuen@netvigator.com

|F_obs|² is used in the Patterson function. All phases equal 0. The value of the function is non-negative. The Patterson peaks are broad. The result of atoms and centrosymmetric cubic space groups is that an approximate structure of the crystal is contained in the peaks of the calculated electron densities [1]. We apply this property to the crystal of the Patterson function, to sharpen the Patterson peaks. We use a hydrogen atom with random coordinates in the general position of the space group of the crystal of the Patterson function. Combine the phases with all |F_obs|². Some of these phases have signs -1. Therefore, some electron densities are negative, and some Patterson peaks are sharpened. We apply this method to Ba₃Y₂B₆O₁₅ [2]. Space group of the Patterson function is Im-3. Some results are presented in Table 1 and Fig.1.

Table 1. Some peaks in the sharpened Patterson function.

Label

x

y

z

Peak height

Half-width

Origin

0.000

0.000

0.000

14076

0.0361^s

Ba1 - Y1

0.344

0.000

0.251

3545

0.0253^s

Ba1 - O1

0.322

0.000

-0.077

12074^h

0.0421^s

Y1 - O1

-0.049

0.000

-0.321

14940^h

0.0517

^h higher peak height. ^s smaller half-width (Compare with peaks in the Patterson function)

Figure 1.Sharpened Patterson peak Ba1-O1

[1] Yuen, P. S. Result of using atoms and centrosymmetric cubic space groups. (Unpublished).

[2] Zhao, S., Yao, J., Zhang, G., Fu, P. & Wu, Y. (2011). Acta Cryst. C67, i39.

Keywords: IUCr2020; abstracts; atom; centrosymmetric cubic space group; sharpening.;

An attempt to find the use of atomic scattering factors and centrosymmetric cubic space groups; two choices of random phases in direct methods

P. S. Yuen

237 Des Voeux Road West, 5th Floor, HONG KONG

puisumyuen@netvigator.com

In [1], we have used one hydrogen atom with random coordinates in a general position of centrosymmetric cubic space groups to calculate the phases. An approximate structure of the crystal is contained in the peaks of the calculated electron densities. As atomic numbers and atomic scattering factors are not included, the electron densities of the peaks of the approximate structure of calculated electron densities do not follow the pattern of the atomic species. Procedures for identifying this approximate structure are presented in [1]. A simple new method for crystal structure determination is presented in [2]. This involves a large number of combinations of the peaks. If we can distinguish the different types of atoms, the procedures in [1] will be more efficient. The number of combinations in [2] will be significantly reduced. This leads to two fundamental and important questions in X-ray crystallography: What is the result of using atomic numbers and centrosymmetric cubic space groups? What is the result of using atomic scattering factors and centrosymmetric cubic space groups? If we can obtain an answer to one of these questions, the peaks in the calculated electron densities may then be classified into species of atoms. This is very useful for identification of the atoms of the approximate structure. As an attempt to answer the second question, in this article, we use the lightest and heaviest atom of the crystal, with random coordinates in general positions of the space group. As in [1], the result of using phases from these atoms is that an approximate structure of the crystal is embedded in the peaks of the calculated electron densities. The electron densities of the peaks of approximate structure do not follow the trend of atomic numbers. More investigation is needed.

Random initial phases have been employed in direct methods. Phases from one atom with random coordinates in a general position, and phases from the lightest and heaviest atom may be used as random phases. They are random in the sense that they are
phases from one or two atoms with random coordinates. They have the property of an approximate structure of the crystal contained in the peaks of the calculated electron densities. This may be useful when these are employed as random phases in direct methods.

[1] Yuen, P. S. Result of using atoms and centrosymmetric cubic space groups. (Unpublished).

[2] Yuen, P. S. Determination of structure of CoS₂ by the means of a simple new method; a solution to the phase problem for centrosymmetric cubic crystals. (Unpublished).

Keywords: IUCr2020; abstracts; initial phases; random phases; approximate structure;