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Control of zeolite framework flexibility for ultra-selective carbon dioxide separation
research-article
Author(s):
Peng Du
1 ,
Yuting Zhang
1 ,
Xuerui Wang
1 ,
Stefano Canossa
2 ,
Zhou Hong
3 ,
Gwilherm Nénert
4 ,
Wanqin Jin
1 ,
Xuehong Gu
1
,
Publication date (Electronic):
17 March 2022
Journal:
Nature Communications
Publisher:
Nature Publishing Group UK
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There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.
Abstract
Molecular sieving membranes with uniform pore size are highly desired for carbon dioxide separation. All-silica zeolite membranes feature well-defined micropores, but the size-exclusion effect is significantly compromised by the non-selective macro-pores generated during detemplation. Here we propose a template modulated crystal transition (TMCT) approach to tune the flexibility of Decadodecasil 3 R (DD3R) zeolite to prepare ultra-selective membranes for CO 2/CH 4 separation. An instantaneous overheating is applied to synchronize the template decomposition with the structure relaxation. The organic template molecules are transitionally converted to tight carbon species by the one-minute overheating at 700 °C, which are facilely burnt out by a following moderate thermal treatment. The resulting membranes exhibit CO 2/CH 4 selectivity of 157~1,172 and CO 2 permeance of (890~1,540) × 10 −10 mol m −2 s −1 Pa −1. The CO 2 flux and CO 2/CH 4 mixture selectivity reach 3.6 Nm 3 m −2 h −1 and 43 even at feed pressure up to 31 bar. Such strategy could pave the way of all-silica zeolite membranes to practical applications.
Abstract
All-silica zeolite membranes are highly desired for natural gas upgrading but the size-exclusion effect is compromised by defects generated during high-temperature detemplation. Here, the authors develop a strategy to fabricate ultra-selective DD3R zeolite membranes via tuning the zeolite flexibility under rapid template decomposition.
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Most cited references52
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Crystal structure refinement with SHELXL
George M. Sheldrick (2015)
Introduction The first version of SHELX dates back to about 1970 and, after extensive testing, it was first released in 1976. Since then the program system has been developed continuously. The early history has been described by Sheldrick (2008 ▶). The present paper is intended to explain the philosophical and crystallographic background to developments between 2008 and 2015 in SHELXL, the program in the SHELX system responsible for crystal structure refinement. Although SHELXL may also be used for the refinement of macromolecular structures against high-resolution data, most of the new developments have concentrated on the refinement of chemical structures, such as those published in Section C of Acta Crystallographica. Readers not familiar with SHELX may find it useful to look at Sheldrick (2008 ▶) before reading this paper. A major change since 2008 is that the distribution is performed via the SHELX homepage (http://shelx.uni-ac.gwdg.de/SHELX/), which also provides a great deal of documentation, tutorials and other useful information. The programs are updated more frequently than in the past and the list of recent changes should be consulted regularly to see if it is necessary to download a new version. The homepage also contains a list of registered users (but not their email addresses); currently there are over 8000 spread over more than 80 countries. SHELX workshops are announced on the homepage, and many of the talks given at these workshops may be downloaded there. SHELXL is compiled with the Intel ifort FORTRAN compiler using the statically linked MKL library, and is available free to academics for the 32- or 64-bit Windows, 32- or 64-bit Linux and 64-bit Mac OS X operating systems. Multithreading is achieved using OpenMP along the lines suggested by Diederichs (2000 ▶), and the program is particularly suitable for multiple-core processors. SHELXL and CIF format The importance of depositing crystallographic data Although the IUCr journals have led the way in insisting that experimental crystallographic data should be deposited, several leading chemical journals still only require the deposition of a CIF (Hall et al., 1991 ▶) containing just the results of the crystal structure determination and not the X-ray or neutron reflection data used to determine the structure. In this respect, biological crystallographers are more advanced. The PDB (Protein Data Bank; Berman, 2008 ▶) has required the deposition of reflection data since February 2008 and virtually all journals that report biological crystal structures, including high-profile journals such as Nature and Science, require a PDB ID for the structure. This has already had a considerable impact. For example, it has led to the retraction of several structures in which the data do not support the claim that a particular ligand was bound to a protein. One very recent example of the use of such deposited data (Köpfer et al., 2014 ▶) can be mentioned here, since it involved the use of SHELXL to refine occupancies and obtain standard uncertainties for them. For over 50 years, the accepted model (Hodgkin & Keynes, 1955 ▶) for the potassium channel present in many living systems was that it involved the transport of both potassium ions and water molecules, based on the argument that adjacent binding sites could not be occupied by K+ cations because they would repel one another, and so the intermediate sites must be occupied by water molecules. Several protein crystal structures were refined at modest resolution with alternating potassium ions and water molecules in the channel and appeared to support this model. However, to the authors’ credit, they deposited their reflection data, including the Friedel pairs, although that was not then obligatory. When sophisticated molecular dynamics (MD) calculations showed that only a model with adjacent K+ cations could account, by a sort of knock-on effect, for the very high potassium permeability observed, it was necessary to reinvestigate the structure using the deposited X-ray reflection data. Both the occupancy refinements with SHELXL and the analysis of the anomalous data with SHELXD (Schneider & Sheldrick, 2002 ▶) and ANODE (Thorn & Sheldrick, 2011 ▶) showed conclusively that the four connected potassium sites are almost fully occupied, as predicted by the MD calculations. Archiving crystallographic data To make the deposition and archiving of reflection data as simple as possible, the CIF written by SHELXL now includes the .hkl reflection data file, embedded as CIF text: _shelx_hkl_file ; ... reflection data in SHELX HKLF 2, 3, 4 or 5 format ... ; _shelx_hkl_checksum 12345 The checksum provides a check that the data have not been corrupted accidentally. The .res results file from the refinement and the .fab file (see below), if used in the refinement, are embedded into the CIF in the same way. The SHELX program SHREDCIF may be used to extract these files from the CIF archive and rename the .res file to .ins, for example to perform further refinements with SHELXL. The intention is that such CIFs containing embedded data should become standard for deposition and archiving. It is particularly convenient that only one file is needed. CIF identifiers beginning with _shelx_ are reserved for use by the SHELX programs, but of course other program authors may use a similar construction for embedding the reflection data etc. Users who do not wish to preserve their carefully measured data for posterity in this way have criticized the embedding of the reflection data on the grounds that (a) the resulting CIF is too large for submission with a paper for publication and that (b) certain CIF-processing programs take a long time to read such a CIF and may even choke in the attempt. However, it should be noted that (a) the figures submitted with a paper often involve larger files and (b) SHREDCIF can usually read and dismember such a CIF in less than one second! To generate a CIF without intensity data for other purposes, e.g. for input to a molecular graphics program, the keyword NOHKL may be used in the SHELXL ACTA instruction. It is difficult to understand why several leading chemical journals still only require the deposition of the atom coordinates, etc., but not the reflection data, especially now that the Cambridge Structural Database (CSD; Allen, 2002 ▶) accepts the new CIFs and strongly encourages deposition of the reflection data. A simple solution would be for journals to require a confirmation that the full data have been deposited with the CSD (Bruno & Groom, 2014 ▶) or COD (Gražulis et al., 2012 ▶), analogous to the way in which the PDB requires deposition of the structural and reflection data before issuing a PDB ID. Including CIF items at the end of the .hkl file Since SHELX76, the reflection data have been read until a reflection with indices 0,0,0 or a blank line (or card) or the end of the file was encountered. The rest of the file was never read by the SHELX programs. This means that additional data specific to that data set, such as details of the data collection and processing, may conveniently be appended to the .hkl file, which is a much safer way of preserving them than putting them in a separate file. For example, the Bruker scaling program SADABS (Krause et al., 2015 ▶) now appends CIF format items such as those shown below to the .hkl file that it outputs: _exptl_absorpt_process_details ‘SADABS 2014/4’ _exptl_absorpt_correction_type multi-scan _exptl_absorpt_correction_T_max 0.7489 _exptl_absorpt_correction_T_min 0.7208 _exptl_special_details ; The following wavelength and cell were deduced by SADABS from the direction cosines etc. They are given here for emergency use only: CELL 0.71072 6.100 18.294 20.604 90.006 89.992 90.000 ; SHELXL uses the CIF items found at the end of the .hkl file to replace items to which it would otherwise have given the value ‘?’. It ignores all other items. So in this example, the first four CIF items find their way (left justified) into the output CIF, but although _exptl_special_details is legal for a CIF it is not included as a CIF item because this CIF identifier would not otherwise have been output. However, it is still included in the .cif file as part of the embedded .hkl file, so that the information is not lost. Unfortunately, because of a fundamental CIF design weakness (the same character ‘;’ is used for both the beginning and end of a text item; it would have been better to have used a different terminator such as ‘:’), SHELXL has to replace ‘;’ in this example by ‘)’ when embedding the .hkl file, and SHREDCIF repairs the damage by turning a leading ‘)’ in an otherwise blank line back to ‘;’. In this example, the cell following _exptl_special_details is not the same as in the CELL instruction used in the .ins file, because there is a reorientation matrix in the HKLF 4 instruction to transform the indices to the conventional P21212 setting for the space group. However, it is still useful to preserve it in case the .hkl file becomes orphaned. Refinement against neutron diffraction data and special facilities for H atoms The new features in SHELXL for refinement against neutron data have been discussed recently by Gruene et al. (2014 ▶). If a NEUT instruction is placed before SFAC, neutron scattering factors are employed, and the default bond lengths to H or D atoms are lengthened to correspond to internuclear distances rather than the distances appropriate for refinement against X-ray data. Whereas for X-rays H and D are treated specially, for neutrons they are treated as normal atoms. The HFIX and AFIX instructions may still be used to generate starting positions for H and D atoms, but it is recommended to use geometric restraints rather than a riding model for their refinement against neutron data. This is particularly important when anti-bumping restraints are applied; they work much better for a restrained than for a riding-model refinement of the H and D atoms against neutron data. Chiral volume restraints for refinement against neutron data The chiral volume restraint CHIV, which is often used for macromolecular refinement, is interpreted as follows if NEUT is set. If three atoms other than H or D are bonded to the atom in question, the H and D atoms are ignored and the CHIV restraint operates in the same way as for a refinement against X-ray data. If there are exactly three bonded atoms including H and D, the latter are used in the restraint. Thus, CHIV 0 N1 could be used to restrain a terminal –NH2 group to be planar, and CHIV with a nonzero target value could be used to make it nonplanar. Anisotropic refinement of H and D atoms against neutron data Since the neutron scattering factors for H, and especially for D, are of a similar order of magnitude to those for other atoms, H and D also need to be refined anisotropically for refinement against neutron data. Unfortunately, this results in about twice as many parameters as for a standard refinement against X-ray data, and the number of data available may well be less than for an X-ray refinement, so further restraints such as the new RIGU rigid-bond restraint (Thorn et al., 2012 ▶) may be required. The RIGU restraints require that the relative motion of bonded atoms is at right angles to the bond joining them. This sets up three restraints per atom pair, one of which is equivalent to the classical rigid-bond restraint DELU. RIGU is very generally applicable and it is almost always safe to add a RIGU instruction without further parameters to the .ins file. The resulting displacement ellipsoid plots tend to appear chemically more reasonable than those from an unrestrained refinement and there is usually little change in the final R factors. The following example, using data from Lübben et al. (2014 ▶), is a little different, because it involves the anisotropic refinement of all atoms, including H atoms, using SHELXL against neutron diffraction data collected at 9 K. The .ins file was the same as that used for refinement against X-ray data, except that: (i) a NEUT instruction was placed before SFAC, so that neutron scattering lengths were used instead of X-ray scattering factors; (ii) instead of using a riding model for the refinement of the H atoms, SADI (equal distance) restraints were applied to the O—H bonds in the water molecule, the C—H bonds in the CH2 and CH3 groups, and the H⋯H distances within the CH3 group; and (iii) a much larger value was obtained for the extinction parameter (EXTI). Close inspection of the atomic displacement ellipsoids in Fig. 1 ▶(a) shows that the assumption that the relative motion of the H atoms is at right angles to the bonds holds well, even for the unrestrained refinement. The refinement with tight RIGU restraints (RIGU 0.0001) for the bonded atoms (Fig. 1 ▶ b) looks very similar, but the H-atom displacement ellipsoids are aligned so that their smallest principal axes are even closer to the bond directions, as required when the motion is at right angles to the bonds. However, Fig. 1 ▶(b) also reveals a small weakness of the rigid-bond assumption: the H-atom displacement ellipsoids appear to be slightly squashed in the direction of the bond. This is probably because the amplitude of the zero-point motion along the bond is larger for the H atom than for the atom to which it is bonded, because of the smaller mass of the former, but the rigid-bond restraint tries to make them equal. As a result, the R 1 value is slightly higher for the RIGU-restrained refinement (0.0342 rather than 0.0304). This effect is only observable here because of the extremely low temperature (9 K) and the high-quality data; at higher temperatures, the RIGU restraints can be very useful to stabilize the anisotropic refinement of H and other atoms against neutron data. Fig. 1 ▶ also exhibits much larger atomic displacement ellipsoids for the H atoms than for the remaining atoms. At such low temperatures, the frequently made assumption that the isotropic displacement parameters of the atoms can be set to 1.2 or 1.5 times the equivalent isotropic U values of the atoms to which they are bonded is clearly not justified. However, at temperatures above about 100 K it has been shown that this assumption is less seriously flawed (Lübben et al., 2014 ▶). Capelli et al. (2014 ▶) recently showed that Hirshfeld atom refinement provides a much more accurate way of deriving anisotropic displacement parameters for H atoms from X-ray data. Other new facilities for H atoms and CF3 groups Except where the NEUT instruction is used, both H and D are now treated as special in the input syntax. This is useful when both are present, e.g. when the crystals came from an NMR tube containing a deuterated solvent. The AFIX instructions for CH3 groups may now also be used to set up CF3 groups, but it is better to refine these as rigid groups or with distance restraints (DFIX or SADI) than by applying a riding model, because the latter can be unstable. An HTAB instruction without any parameters instructs the program to find possible hydrogen bonds. These now include C—H⋯O interactions when the C atom is directly or indirectly attached to an electronegative atom (Taylor & Kennard, 1982 ▶). Such weak interactions involving H atoms attached to peptide Cα atoms are common in protein structures (Desiraju & Steiner, 1999 ▶). The resulting full HTAB and EQIV instructions are appended after the END instruction of the .res file and need to be (selectively) transferred to the beginning of the .ins file, so that they will be included in the CIF generated by the next refinement. This facilitates the generation of tables of hydrogen bonds, and helps to prevent hydrogen bonds involving symmetry-equivalent atoms from being overlooked. Absolute structure determination In the distant past, it was often assumed that it was necessary to include a heavy atom, e.g. by making a rubidium salt or bromobenzoate derivative, in order to obtain a reliable absolute structure, for instance to establish which enantiomer of a chiral molecule was correct. Since then, experimental and computational methods have made such progress that the absolute structure can often even be determined with Mo Kα radiation when the heaviest atom is oxygen (Escudero-Adán et al., 2014 ▶). When the 2008 SHELX paper was written, the method of choice to determine the absolute structure was to refine the Flack parameter (Flack, 1983 ▶) as one of the parameters in a full-matrix refinement. Since then it has become clear that this led to a substantial overestimation of the standard uncertainty of the Flack parameter, and that post-refinement methods using either a Bayesian approach (Hooft et al., 2008 ▶) or quotients or differences of the Friedel opposites as observations (Parsons et al., 2013 ▶) give more reasonable estimates of the Flack parameter, and especially its standard uncertainty. This led to the IUCr/checkCIF requirement that Friedel opposites should not be merged in the deposited data. For small-molecule refinements with SHELXL, the input .hkl file should contain the unmerged data. This enables the program to produce a more complete output CIF and to estimate the Flack parameter using the Parsons quotient method for all noncentrosymmetric structures. This approach works well even for twinned structures. For structure refinement, the reflections are, by default, merged according to the point group of the crystal structure (MERG 2 in SHELXL notation). In the relatively rare cases that result in an intermediate value of the Flack parameter with a small standard uncertainty, in order to obtain the most accurate calculated intensities and hence difference density, it is still necessary to refine the Flack parameter by the full-matrix method (TWIN/BASF). However, a Flack parameter of 0.5 with a small standard uncertainty is a warning sign that the true space group might be centrosymmetric! Estimates of standard uncertainties One side effect of the inclusion of Friedel opposites is that there will be nearly twice as many data for the refinement of a noncentrosymmetric structure, which, using the usual least-squares algebra, would lead to a reduction in the estimated standard uncertainties of all parameters by a factor of nearly 21/2. SHELXL now uses the number of unique reflections as defined by the Laue group, rather than the number of observations, in the formula used to estimate the standard uncertainties (Spek, 2012 ▶). It could be argued that all reflection intensities are independent measurements, and this was approximately true for unscaled data from point detectors before the introduction of focusing optics. However, it is now standard practice to scale the data so that equivalent reflections (usually including Friedel opposites) become more equal, in order to correct for absorption and differences in the effective crystal volume irradiated, and then the equivalent reflections can no longer be regarded as independent observations. In some cases, this change may result in a modest increase in the estimated standard uncertainties, but these were generally underestimated anyway (Taylor & Kennard, 1986 ▶). The new method of estimating standard uncertainties also applies to twinned structures, where some SHELXL97 users were required by referees to throw away some of their carefully measured data so that the number of observations would be equal to the number of unique reflections. Now all the experimental data may be used and the estimated standard uncertainties should be more realistic. With SHELXL97, it was necessary to use the third least-squares parameter to correct the estimated standard uncertainties; this is not required anymore (except for ‘SQUEEZEd’ structures). Input of partial structure factors The new ABIN instruction was primarily designed to facilitate the use of the SQUEEZE facility (Spek, 2015 ▶) in the program PLATON (Spek, 2009 ▶), but it can also be used to input a bulk solvent model for a macromolecule. PLATON calculates the partial structure factors corresponding to a blob of unmodelled difference density and writes them to the .fab file. The ABIN instruction causes h, k, l, A and B to be read from the .fab file, where A and B are the real and imaginary components, respectively, of a partial structure factor. These reflections are read in free format (one reflection per line) and may be in any order. Duplicates, systematic absences and reflections outside the resolution limits for refinement are ignored. Symmetry equivalents are generated automatically. At least one symmetry equivalent (according to the point group) of each reflection present in the .hkl file, including all reflections in all twin components if the structure is twinned, should be present in the .fab file. For twinned structures, it is necessary first to use the new LIST 8 instruction (see below) to generate detwinned data for input to PLATON. The A and B values refer to the untwinned structure, but in the case of a twinned structure, after applying the appropriate symmetry transformations, they are added to the calculated structure factors for all twin components. ABIN takes two free variable numbers (Sheldrick, 2008 ▶) n 1 and n 2 as parameters. The A and B values read from the .fab file are multiplied by kexp[−8π2 Usin2θ/λ2], where k is the value of free variable n 1 and U is the value of free variable n 2. These two optional parameters may be needed when the partial structure factors come from a bulk solvent model of a macromolecule, but are probably not needed for use with SQUEEZE. SQUEEZE should only be used where it is not possible to model the disordered solvent by normal methods, e.g. when there is a continuous ribbon of diffuse difference density along one of the unit-cell axes. Partial structure factors and ABIN should always be used in preference to the old procedure of modifying the input .hkl file, which made it impossible to remodel the disordered density should a better method become available. Extending the PART number concept The use of PART numbers, introduced in SHELXL93, has proved invaluable in the refinement of disordered structures. Two atoms are considered to be bonded if they have the same PART number or if one of them is in PART 0. The resulting connectivity table is used for the generation of H atoms (HFIX and AFIX), for setting up restraints such as DELU, SIMU, RIGU, CHIV, BUMP and SAME, and for generating tables of geometric parameters (BOND, CONF, HTAB). Usually, most of the atoms are in PART 0, but, for example, a molecule or side chain disordered over three positions could use PART 1, PART 2 and PART 3. If the PART number is negative, bonds are not generated to symmetry-equivalent atoms. It should be noted that positive PART numbers 1, 2, 3 etc. correspond to the alternative location indicators A, B, C etc. in PDB format. However, this notation is difficult to use when there is a disorder within a disorder. A BIND instruction that specifies two numbers may now be used to get around this problem. For example, BIND 2 4 means that, in addition to the usual PART rules, atoms in PART 2 may also bond to atoms in PART 4. Negative PART numbers are allowed in the BIND instruction. As an example, consider an n-butyl substituent coordinated through atom C1 that splits into two disorder components at C2. Atom C1 is then in PART 0, C2A, C3A and C4A in PART 1, and C2B, C3B and C4B in PART 2. Atom C1 is bonded to both C2A and C2B but, because these two atoms have different PART numbers, H atoms will be generated correctly using the HFIX instruction. However, if there is a further disorder starting at atom C3B, this cannot be handled easily by SHELX97. Atoms C3B and C4B can be split into C3B′ and C4B′ in PART 3 and into C3B′′ and C4B′′ in PART 4, but then atoms C3B′ and C3B′′ are not bonded to C2B because they have different nonzero PART numbers. Extra bonds could have been inserted into the connectivity table with: BIND C2B C3B’ BIND C2B C3B” but then HFIX or AFIX would still not generate the correct H atoms, because they need to refer to the PART numbers of the neighbouring atoms too. However, the alternative BIND 2 3 BIND 2 4 now enables the H atoms to be generated correctly. Since SHELXL allows atoms to have the same names if they have different PART numbers, atoms C3A, C3B′ and C3B′′ could all be labelled C3 in this example. This would simplify the naming of the H atoms, but might confuse non-SHELX programs that read the .res file. As with almost every disorder, the use of RIGU is strongly recommended here. Other new features in SHELXL One of the most common cases of instability in crystal structure refinements is when the atomic displacement parameters refine to appreciably negative values. The new XNPD instruction may be used to combat this. When an isotropic displacement parameter, or a principal component of an anisotropic displacement parameter, refines to a value less than (e.g. more negative) the value specified with the XNPD instruction, it is replaced by that value, and the displacement parameters U iso or U ij are recalculated. Thus, the default setting of XNPD -0.001 avoids the risk of the refinement becoming unstable, but still leads to nonpositive definite (NPD) atoms being recognized and reported. For problematic cases, it may be desirable to set XNPD to a small positive value. However, it should then first be checked that the negative value was not caused by an error in the input file, e.g. an incorrect element type or site-occupation factor. The new LIST 8 option writes h, k, l, F o 2, σ(F o 2), F c 2, ϕ (phase angle in degrees), d spacing in ångström (Å) and 1/(w 1/2) in CIF format to the .fcf file, where w is the weight derived from the weighting scheme and used in the refinement. For weak reflections, 1/(w 1/2) should be only a little larger than σ(F o 2). This list is on an absolute scale and is detwinned, merged (according to the point group of the crystal structure) and sorted, but without eliminating the anomalous contributions (except in the calculation of ϕ, so that the corresponding electron density is real). This option is essential for applying the SQUEEZE option in PLATON to twinned structures, but also has other uses. RTAB D2CG followed by atom names may be used to calculate the distance between the first named atom and the unweighted centroid of the remaining atoms, together with its standard uncertainty. This can be used to calculate distances to ring centroids, for example. As in SHELXL97, ‘+filename’ may be used to insert further instructions whilst reading the .ins file. These instructions are not echoed to the .res file. The new ‘++filename’ may be used to insert instructions that should be echoed to the .res file. The ‘+filename’ instruction itself is echoed to the .res file but ‘++filename’ is not. These instructions are useful for reading in long lists of restraints, etc. Although the SAME instruction for generating distance restraints is very convenient, especially when combined with the use of residues (RESI) so that the same atom names may be used when there are several chemically identical solvent molecules, it is less convenient when some of those solvent molecules are disordered, for example, tetrahydrofuran (THF), with one atom either above or below the plane of the other four. A SADI instruction with no parameters now causes SADI (similar distance) restraints to be generated from all the SAME instructions. These appear after the END instruction in the .res file. They can be moved to the start of the new .ins file, and edited and extended to give fine control over the refinement of such disorders. The TWIN instruction no longer requires integer matrix elements. The matrix is used to generate the indices of the reflections of the twin components, and if they differ by more than 0.1 from integers they are ignored. This enables the refinement of rhombohedral obverse/reverse twins, and is also useful for pseudomerohedral twins in which some of the reflections of a minor twin domain overlap nearly perfectly with reflections of the major domain and have to be taken into account, and other reflections of the minor domain do not overlap and can be ignored. If the twin components are more equal, the HKLF 5 format reflection data may be a better approach. Details of further changes since 2008 may be found on the SHELX homepage (http://shelx.uni-ac.gwdg.de/SHELX/). Conclusions This account of changes and extensions to SHELXL since 2008 is testimony to the continuous development of the structure refinement techniques that is still taking place. In that time, CIF has advanced to become the standard for the deposition and archiving of crystallographic data, and this is reflected in many of the changes in SHELXL. The .ins and .hkl files used for input to SHELXL have remained, with very minor exceptions for which there were good reasons, upwards compatible since SHELX76. Another reason why SHELX has remained popular over many generations of computer hardware is its strict ‘no dependencies’ philosophy: no external programs, libraries (such as DLLs) or environment variables are required to run any of the SHELX programs (except SHELXLE).
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OLEX2: a complete structure solution, refinement and analysis program
Oleg V. Dolomanov, Luc Bourhis, Richard Gildea … (2009)
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SHELXT – Integrated space-group and crystal-structure determination
George M. Sheldrick (2015)
1. Introduction Although crystal structure determination by means of X-ray diffraction has had a major scientific impact for the last 100 years, it still requires the solution of the crystallographic phase problem. This problem arises because although methods for measuring the intensities of the diffracted X-rays have made considerable progress during that time, the direct experimental measurement of their relative phases is still only rarely practicable. Small-molecule crystal structures are usually solved by the use of probability relationships involving the phases of the stronger reflections, the so-called direct methods (Sheldrick et al., 2001 ▶; Giacovazzo, 2014 ▶) or more recently by the iterative use of Fourier transforms, e.g. dual-space methods such as charge flipping (Oszlányi & Sütő, 2004 ▶; Palatinus, 2013 ▶), in which the phases are constrained by the observed reflection intensities in reciprocal space and by the properties of the electron density in real space. Before the phase problem can be solved, the usual procedure is to determine the space group of the crystal with the help of the Laue symmetry of the diffraction pattern, the presence or absence of certain reflections (the systematic absences) and statistical tests (e.g. to distinguish between centrosymmetric and non-centrosymmetric structures). This space-group determination may be upset by the presence of dominant heavy atoms or by pseudo-symmetry affecting the intensities of certain classes of reflections, and in some cases the space group is ambiguous. For example, the space groups I222 and I212121 have the same systematic absences, as do Pmmn and two different orientations of Pmn21. Many dual-space methods perform at least as well when the data are first expanded to the nominal space group P1 (Sheldrick & Gould, 1995 ▶). In this paper ‘P1’ will be used to cover the centred triclinic non-centrosymmetric space-group settings such as C1 as well; the data do not need to be re-indexed for the primitive cell. After solving the phase problem in P1, the space group can be determined using the P1 phases (Burla et al., 2000 ▶; Palatinus & van der Lee, 2008 ▶) and this turns out to be a very robust general approach. SHELXT also employs this strategy. The systematic absences are not then used for the space-group determination, but all the weak reflections are still useful for identifying the best solution. Fig. 1 ▶ summarizes the course of structure determination using SHELXT. The individual stages will now be discussed in detail. The current version of SHELXT is intended for single-crystal X-ray data and is not suitable for neutron diffraction data. 2. Solving the phase problem for data expanded to space group P1 SHELXT reads standard SHELX format and files. It extracts the unit cell, Laue group (but not space group) and the elements that are expected to be present (but not how many atoms of each). A number of options, e.g. that all trigonal and hexagonal Laue groups should be considered ( ), may be specified by command-line switches. A summary of the possible options is output when no filename is given on the SHELXT command line and further details are available on the SHELX home page. The data are first merged according to the specified Laue group and then expanded to P1. In theory, SHELXT could also have been programmed to determine the Laue group, e.g. by calculating the R values or correlation coefficients when the equivalent reflections are merged. However, the Laue group has to be known to scale the data, which is an essential step for the highly focused beams now common for synchrotrons and laboratory microsources, because the effective volume of the crystal irradiated is different for different reflections and needs to be corrected for. So in practice it is best to determine the Laue group first anyway. Even though programs such as XPREP (Bruker AXS, Madison, WI 53711, USA) are no longer required to determine the space group, it is still necessary to identify the correct unit cell and metric symmetry. 2.1. Dual-space iteration starting from a Patterson superposition The P1 dual-space recycling in SHELXT may start with random phases, but the default option of starting from a Patterson superposition minimum function (Buerger, 1959 ▶; Sheldrick, 1997 ▶) is usually more effective. Two copies of the sharpened Patterson function, displaced from each other by a strong Patterson vector, are superimposed and the minimum value of the two is calculated at each grid point. The resulting map is used as the initial electron density for the dual-space recycling. In an ideal case it is a double image of the structure consisting of 2N peaks, where N is the number of unique atoms, but the space-group symmetry has been lost. Since the dual-space recycling is being performed in P1 anyway, this is a good start and 2N is a significant reduction from the N 2 peaks in the original Patterson. The subsequent dual-space recycling is performed using the modified structure factors where E is the normalized structure factor, and a new density map is calculated by a hybrid difference Fourier synthesis with phases and coefficients where and G c are obtained by Fourier transformation of the current map. The default values for m and q are 3 and 0.5, respectively, but may be changed by the user. Based on experience with other structure-solution programs, q should probably be larger for large equal-atom structures and smaller for structures involving heavy atoms (to reduce Fourier ripples), but in practice it is rarely necessary to change the default values. SHELXT adds unmeasured data above and below the resolution limit of the data in the file similar to the free lunch method described by Caliandro et al. (2005 ▶). This enables structures to be solved at an earlier stage in the data collection and is particularly useful for data collected with diamond-anvil high-pressure cells, with which it is not always possible to collect complete data. It reduces the effects of series-termination errors in the Fourier syntheses, but tends to make the electron-density integration used to assign the element types less reliable. 2.2. The random omit procedure Omit maps are frequently used in macromolecular crystallography to reduce model bias. A small part of the structure is deleted and the rest is refined to reduce memory effects, then a new difference-density map is generated and interpreted. This concept plays an important role in SHELXT, but because no model is available at the P1 dual-space stage, it is implemented differently. The following density modification is performed unless otherwise specified by the user. A mask M(x) is constructed consisting of Gaussian-shaped peaks of unit volume at the positions of the maxima in the electron-density map. A small number of these Gaussian peaks are then deleted from the mask at random, usually every third dual-space cycle, and the new density is obtained by multiplying the original density ρ(x) with the mask: at each grid point x in the unit cell. This allows the random omit method to be implemented efficiently using fast Fourier transforms (FFTs) in both directions. Imposing a shape function in this way improves the atomicity of the map. Negative density is truncated to zero, a common theme in phase improvement by density modification (Shiono & Woolfson, 1992 ▶). Compared with charge flipping, the stronger imposition of atomicity probably allows the resolution requirements to be relaxed. On the other hand, charge flipping should be better for the solution of severely disordered or modulated structures, precisely because they are not atomistic! To decide which P1 solution is best, three criteria are considered: (a) The correlation coefficient CC between G o and G c, where G c are the amplitudes obtained by Fourier back-transformation of the modified electron density. (b) The structure factors G c are normalized to give E c and R weak is calculated as the average value of for the 10% of unique reflections (including systematic absences) with the smallest observed normalized structure factors E (Burla et al., 2013 ▶). In this way, the weak reflections can still play a decisive role in the structure solution even though they were not used directly to determine the space group. (c) The chemical figure of merit CHEM is calculated by performing a peak search and calculating all bond angles involving two distances in the range 1.1 to 1.8 Å. CHEM is the fraction of these angles that lie between 95 and 135° (Langs & Hauptman, 2011 ▶). The combined figure of merit CFOM is given by where X is 1.0 unless reset by the user. For organic or organometallic structures, especially for low resolution or incomplete data, the alternative, is sometimes better, but this is not the default option because it is not appropriate for inorganic and mineral structures. If CFOM is less than a preset threshold, the program refines further sets of starting phases, increasing the number of iterations each time this is done. 3. Using phases to find the origin shift and space group The idea of trying all possible space groups in a specified Laue group is also sometimes used in macromolecular crystal structure determination. For example, if the crystal is orthorhombic P, Laue group mmm, and only the Sohncke space groups need to be considered, a molecular-replacement program can be asked to test all eight possibilities. If only one of the eight gives a solution with good figures of merit, both the crystal structure and the space group have been determined! For chemical problems the situation is more interesting, because there are 30 possible orthorhombic P space groups and a total of 120 possibilities when different orientations of the axes are taken into account (as in SHELXT). The procedure used in SHELXT to find space groups and origin shifts that are consistent with the P1 phases is based closely on the methods proposed by Burla et al. (2000 ▶) and Palatinus & van der Lee (2008 ▶), so it only needs to be summarized here. For a reflection h with P1 phase ψ and its mth symmetry equivalent h m = hR m with P1 phase ψ m , where R m is a 3 × 3 rotation matrix and t m is the corresponding translation vector, we define For the correct space group and the correct origin shift Δx, η should be close to zero. To facilitate comparisons, the figure of merit α is defined as the F 2-weighted sum of η2 over all pairs of equivalents for all reflections, normalized so that it should be unity for random phases. α should be as small as possible for the correct combination of space group and origin shift. SHELXT first calculates α for the space group ; this value is referred to as α0. If α0 is less than about 0.3, the space group is probably centrosymmetric. For centrosymmetric space groups, the origin shift may be used to place a centre of symmetry on the origin; however, SHELXT has to take into account that the space group may possess more than one non-equivalent centre of symmetry. For , η is calculated with a FFT and for non-centrosymmetric, non-polar space groups a two-dimensional grid search followed by a one-dimensional search is performed to speed up the calculation. The space-group search is performed in parallel for all space groups that need to be tested. Although the solution with the lowest α value is often the correct one, only unlikely solutions with α greater than a specified value (default 0.3) are eliminated before going on to the next stage. 4. Assigning chemical elements to the electron-density peaks Each solution with a reasonable α value is first subject to ten cycles of density modification in the chosen space group after applying the origin shift. This density modification consists only of averaging the phases of equivalent reflections taking the space-group symmetry into account and resetting negative density to zero. A peak search is then performed, and the density inside a sphere (default radius 0.7 Å) about each peak is summed. It is better to use integrated densities rather than peak heights because the atoms may have different atomic displacement parameters. However, these integrated densities are not on an absolute scale, so the problem is how to set the scale so that they correspond to atomic numbers and the elements can be assigned. SHELXT attempts to set the scale as follows, going on to the next test only if the previous tests are negative: (a) If carbon is specified as one of the elements present, the program searches for peaks with similar integrated densities separated from each other by typical C—C distances (i.e. between 1.25 and 1.65 Å). If enough are found, the scale is set so that they will have average atomic numbers of 6. (b) If boron is expected, boron cages with distances between 1.65 and 1.8 Å are searched for. (c) A search is made for oxyanions. The oxygen atoms should have similar integrated densities to each other and similar distances to a central atom. (d) If the above tests are negative, it is assumed that the heaviest atom expected corresponds to the peak with the highest integrated density. This can run into trouble if, for example, there is an unexpected bromide or iodide ion in the structure and it has not been possible to fix the scale by one of the above methods. When the density scale has been found, it is used to assign elements to the remaining atoms. If it then appears that there are high-density peaks that cannot be assigned because only light atoms were expected, chlorine, bromine or iodine atoms are added. Some rudimentary checks are made to ensure that the element assignments are chemically reasonable. 5. Isotropic refinement and absolute structure determination After the atoms have been assigned, an isotropic refinement is performed using a conjugate-gradient solution of the least-squares normal equations. This is similar to the CGLS refinement in SHELXL (Sheldrick, 2008 ▶, 2015 ▶) and is performed in parallel. For non-centrosymmetric space groups this is followed by the determination of the Flack parameter (Flack, 1983 ▶) by the quotient method (Parsons et al., 2013 ▶) and inversion of the structure if the value of the Flack parameter is greater than 0.5. It is thus very likely that the structure determined by SHELXT will correspond to the correct absolute structure (so far no examples to the contrary have been reported). If α0 is below 0.3 and no atom heavier than scandium is expected, the program stops after finding a plausible centrosymmetric solution. The command-line switch may be used to force the program to test all space groups in the assumed Laue group. 6. Building the structure The following algorithm used to assemble the structure is diabolically simple but almost always builds and clusters the molecules in a way that is instantly recognizable. No covalent radii etc. are used, so the algorithm is independent of the element assignments. (a) Generate the SDM (shortest-distance matrix). This is a triangular matrix of the shortest distances between unique atoms, taking symmetry into account. (b) Set a flag to for each unique atom, then change it to for one atom (it does not matter which). (c) Search the SDM for the shortest distance for which the product of the two flags is . If none, exit. (d) Symmetry transform the atom with flag corresponding to this distance so that it is as near as possible to the atom with flag , then set its flag to . (e) Go to (c). The next stage is to centre the cluster of molecules optimally in the unit cell. This is complicated, but makes extensive use of the tables of alternative origins for the different space groups given in Chapter 3 of Giacovazzo (2014 ▶). For example, for space group there are four alternative origins (0, 0, 0; 0, 0, ½; ½, 0, ¼; ½, 0, ¾1), but for there are only two (0, 0, 0; 0, 0, ½). These are combined with the lattice centring (in this case 0, 0, 0; ½, ½, ½). For polar space groups the optimal position along the polar direction(s) (e.g. along the body diagonal of the unit cell for space group R3 indexed on a primitive rhombohedral lattice) that minimizes the maximum distance of any atom from the centre of the unit cell is determined. 7. Examples The first example is an organoselenium compound (Clegg et al., 1980 ▶) for which an extract from the listing file from SHELXT is shown in Fig. 2 ▶. Four different Patterson superposition vectors were used by default to start four dual-space structure solution attempts in parallel. This was a good choice because the computer had an Intel i7 processor with four cores. On the evidence of the combined figure of merit CFOM, one of the four (try 1) is a good P1 solution. The correlation coefficient CC and the chemical figure of merit CHEM clearly indicate the correct solution, but R weak is less clear. N is the number of peaks used in the density modification, Sig(min) is the height of peak N divided by the r.m.s. (root-mean-square) Fourier map density and Vol/N is the volume per peak in Å3. The best phase set was then used to search for the space group and three space groups are reported (Fig. 3 ▶); the other 11 space groups tested were rejected because one or more figures of merit were too high. The space group P21 is clearly indicated by the values of R1, R weak, α and the Flack parameter, so there can be little doubt that it is correct, and in fact all the atoms are assigned to the correct elements. Note that although α0 is less than 0.3, the non-centrosymmetric space groups were searched as well because an atom (Se) heavier than scandium was specified on the instruction. The second example (Müller et al., 2006 ▶) involves a reorientation of the unit cell. Since two orientations of Pmn21 have the same systematic absences, both (and possibly also the centrosymmetric Pmmn) would have had to be tried for a conventional structure solution. SHELXT finds only one solution and all atoms are correct (Fig. 4 ▶). The Flack parameter is still rather approximate but is sufficient to indicate the correct absolute structure; it improves on anisotropic refinement including the hydrogen atoms. The third example (Walker et al., 1999 ▶) contains a bromine atom and so the non-centrosymmetric space group P1 is also tested, despite the good R1 and α values for the centrosymmetric solution (Fig. 5 ▶). In fact, this structure is pseudo-centrosymmetric and contains a mixture of diastereoisomers that imitates a centre of symmetry. The P1 solution is completely correct. Both solutions have similar figures of merit because the main difference is the position of one carbon atom that appears to be disordered in but not P1, but the Flack parameter strongly indicates P1. The last example shows what can go wrong. This structure was published by Barkley et al. (2011 ▶) in the non-centrosymmetric space group , but there are two warning signs: checkCIF (Spek, 2009 ▶) detects an inversion centre (a B alert) and the Flack parameter is dubious: the current SHELXL (Sheldrick, 2015 ▶) gives a value of 0.46 (11). Often a value close to 0.5 indicates a centrosymmetric structure. At first glance, SHELXT appears to indicate because of a significantly lower R1 value. Unfortunately, the Flack parameter cannot be determined by SHELXT for this space group because the deposited data had been merged in a different non-centrosymmetric point group (hence ‘ ’ in Fig. 6 ▶). However, neither nor are correct! Basically all the solutions are the same structure and the correct space group is the centrosymmetric P63/mmc of which all the other space groups are subgroups. The cause of the debacle is that only for were the elements assigned completely correctly and hence this space group has a lower R1 value. For the correct space group P63/mmc the manganese atom has been incorrectly assigned as calcium. With the correct element assignments all the figures of merit would have been very similar for all the space groups. In such cases the highest-symmetry (centrosymmetric) space group is almost always correct. 8. Program development and distribution SHELXT is compiled with the Intel ifort Fortran compiler using the statically linked MKL library and is particularly suitable for multi-CPU computers. It is available free to academics for the 32- or 64-bit Windows, 32- or 64-bit Linux and 64-bit Mac OS X operating systems. The program may be downloaded as part of the SHELX system via the SHELX home page (http://shelx.uni-ac.gwdg.de/SHELX/), which also provides documentation and other useful information. Users are recommended to view the ‘recent changes’ section on the home page from time to time. The initial development of SHELXT was based on a test databank of about 650 structures, mostly determined in Göttingen, covering a wide range of problems. It has also been tested by more than 200 beta-testers for up to three years, in the course of which several thousand structures were solved (and a few not solved). It is difficult to generalize, but the correct space group was identified in about 97% of cases, and for about half of the structures every atom was located and assigned to the correct element. Most of the remaining structures were basically correct, the most common errors being carbon assigned as nitrogen or vice versa. Poor solutions were sometimes obtained when the heavy atoms corresponded to a centrosymmetric substructure but the full structure possessed a lower symmetry. It is always essential to check the element assignments, especially if the program has added extra elements, and also to check for the presence of disordered solvent molecules that may have been missed. The biggest danger is that inexperienced users may assume that the program is always right!
Author and article information
Contributors
Xuehong Gu:
ORCID: http://orcid.org/0000-0001-9953-0076
xhgu@njtech.edu.cn
Journal
Journal ID (nlm-ta): Nat Commun
Journal ID (iso-abbrev): Nat Commun
Title:
Nature Communications
Publisher:
Nature Publishing Group UK
(London
)
ISSN
(Electronic):
2041-1723
Publication date
(Electronic):
17
March
2022
Publication date PMC-release: 17
March
2022
Publication date Collection: 2022
Volume: 13
Electronic Location Identifier: 1427
Affiliations
[1
]GRID grid.412022.7, ISNI 0000 0000 9389 5210, State Key Laboratory of Materials-Oriented Chemical Engineering, College of Chemical
Engineering, , Nanjing Tech University, ; Nanjing, 211816 P. R. China
[2
]GRID grid.5284.b, ISNI 0000 0001 0790 3681, EMAT, University of Antwerp, ; 2020 Antwerp, Belgium
Author information
Yuting Zhang
http://orcid.org/0000-0002-2171-2096
Wanqin Jin
http://orcid.org/0000-0001-8103-4883
Xuehong Gu
http://orcid.org/0000-0001-9953-0076
Article
Publisher ID: 29126DOI: 10.1038/s41467-022-29126-6
PMC ID: 8930971
PubMed ID: 35301325
SO-VID: 0494ed19-94aa-4ea9-8c9b-86adfdf0b5f3
Copyright © © The Author(s) 2022
License:
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
History
Date
received
: 22
June
2021
Date
accepted
: 28
February
2022
Funding
Funded by: Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX21_1168)
Funded by: FundRef https://doi.org/10.13039/501100001809, National Natural Science Foundation of China (National Science Foundation of China);
Award ID: 22008111
Award ID: 21908097
Award ID: 22035002
Award Recipient
:
Yuting Zhang
Xuerui Wang
Xuehong Gu
Funded by: State Key Laboratory of Materials Oriented Chemical Engineering (ZK202002) Jiangsu
Specially-Appointed Professors Program
Funded by: National Key R&D Program of China (2021YFC2101200)
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