DSR: enhanced modelling and refinement of disordered structures with SHELXL

One of the remaining challenges in single-crystal structure refinement is the proper description of disorder in crystal structures. This paper describes a computer program that performs semi-automatic modelling of disordered moieties in SHELXL [Sheldrick (2015). Acta Cryst. C71, 3–8.]. The new program contains a database that includes molecular fragments and their corresponding stereochemical restraints, and a placement procedure to place these fragments on the desired position in the unit cell. The program is also suitable for speeding up model building of well ordered crystal structures.

1. Introduction

One of the remaining challenges in applied crystallography is the proper modelling of disorder in crystal structures. We refer here to the term `disorder' as the randomly differing position of some atoms in different unit cells (Müller et al., 2006; Müller, 2009). Crystal structures of small molecules and supramolecular systems tend to have disordered solvent molecules or disordered moieties, as illustrated by the summary statistics of the Cambridge Structural Database (CSD; Groom & Allen, 2014), which include roughly 23% of disordered structures. Although routines and methods to model disorder already exist in SHELXL (Sheldrick, 2008, 2015), we felt the need to make this procedure more intuitive, faster and more robust, even for large entities and complex cases. Therefore, we developed a new program called DSR (disordered structure refinement).

2. Technical description and functionality

DSR is written in Python and is executed via the system command line. Its main purpose is the transfer of molecular fragments to a user-defined location in the target structure. Writing a special DSR command into the SHELXL .res file of the target structure instructs DSR on where to place and how to orient a molecular fragment from the fragment database in the unit cell (Fig. 1). In addition, it is possible to define the occupancy, residue or part number of the inserted fragment. The fragment can be inverted, e.g. to fit the second conformer of twisted tetrahydrofuran. If desired, automatically calculated distance restraints for all bonds in the molecular fragment can replace the restraints obtained from the database. Additional options in the system command line allow the import and export of molecular fragments to and from the database, and listing of and searching for database content.

Figure 1 The general work flow of the DSR program.

2.1. Database

Since there are a number of molecules and functional groups that are regularly involved in disorder, we compiled a database for DSR with common molecular fragments similar to Guzei's `Idealized Molecular Geometry Library' (Guzei, 2014). Database entries contain the ideal starting geometry of a fragment, together with a corresponding stereochemical restraint dictionary (Evans, 2007; Konnert & Hendrickson, 1980), which typically consists of restraints for 1,2-distances (bonds) and 1,3-distances (equivalent to bond angles) for use in SHELXL. They are defined either by means of chemical equivalence (SADI) or as specific target values (DFIX, DANG). If applicable, information on planar groups of atoms is also included (FLAT). For now, the standard uncertainties (s.u.s) of the restraints come from the database and they are simply SIMU/RIGU [first atom] > [last atom]. In future versions, it might be possible to calculate suitable s.u.s during fragment transfer or to analyse the results of the SHELXL refinement to adapt the s.u.s to the respective structural environment.

The database is in ASCII text format and has been intentionally kept simple to be human-readable and -writable, which allows manual editing and extension of the database. The database entries provided with DSR include no hydrogen atoms (except for water), as the authors consider SHELXL constraints (AFIX) to be more robust and reliable for H-atom treatment in disordered moieties. Since every restraint command valid for SHELXL (including HFIX) is supported in the DSR database, appropriate riding H atoms can easily be included in a database entry by placing its respective HFIX command in the respective database entry (see Table 1). Such modifications should not be made in the main database provided with DSR (dsr_db.txt) but rather in the user database (dsr_usr_db.txt). This will never be overwritten during a program update and should therefore be used by users to store additional entries.

Table 1
Syntax of the DSR database dsr_db.txt and dsr_usr_db.txt

The complete syntax is explained in the supporting information.

<name>	Start tag
RESI class	Required; defines the residue name of the database entry
restraints	Any restraints and comments, following the SHELXL syntax
FRAG 17 a b c α β γ	FRAG card with AFIX number and cell parameters
Atom number x y z	One isotropic atom per line, following the SHELXL syntax, except that a negative SFAC number means the atom type as atomic number
</name>	End tag; the same as the start tag but with a slash

The database contains over 70 entries of commonly dis­ordered solvent molecules and molecular fragments, such as tetrahydrofuran, toluene, dichloromethane, tert-butyl groups, hexane and the tosylate anion, and also less common mol­ecules like supramolecular ligands (Pascu et al., 2014; Ronson et al., 2013; Ramadhar et al., 2015) and molecules that have been soaked into porous metal–organic framework complexes (Inokuma et al., 2013). The complete list at the time of writing is available in the supporting information (the pictures therein were drawn using Jmol; https://www.jmol.org/).

2.2. Import/export

New fragments from quantum mechanical calculations, experimentally determined crystal structures or structural databases like the CSD can be incorporated into the DSR database by manual addition of a new database entry. DSR accepts both Cartesian and fractional atomic coordinates. Another possibility for input is the fully automated import of fragments from the GRADE Web Server of Global Phasing Ltd (Smart & Womack, 2014). GRADE is a ligand restraint generator included in BUSTER (Bricogne et al., 2011), and its main source of restraint information is the CSD queried using the MOGUL program (Bruno et al., 2004) developed by the Cambridge Crystallographic Data Centre. Whenever small-molecule information is not available, GRADE uses quantum chemical procedures to obtain the restraint values.

Fragments from the database can be exported to a SHELXL .res file and a portable net graphics (.png) file to inspect the atoms of a fragment and their labelling scheme [utilizing PLATON (Spek, 2009) and ImageMagick (https://www.imagemagick.org) if installed]. A fragment can also be copied to the computer clipboard to be used in the Olex2 `fit mode' (Dolomanov et al., 2009; Guzei, 2014).

2.3. Transfer and refinement

DSR leaves the definition of disorder to the user and automates the time-consuming transfer and tedious restraining part. The main concept of DSR is similar to what is nowadays commonly applied in macromolecular crystallography, where a complete molecular fragment (see e.g. Figs. 2 or 5 below) is modelled instead of single atoms. The fitted fragment should contain at least three atoms.

Before going into more detail about how DSR works, we summarize briefly the manual steps typically performed when modelling a second conformer in SHELXL without DSR.

(1) Find and label all Q peaks corresponding to the secondary position of atoms in the difference Fourier map. Sometimes this requires several intermediate refinement steps.

(2) Assign a free variable to the site occupancy for both disordered components.

(3) Define restraints for bond lengths, bond angles and possibly anisotropic displacement parameters.

Using DSR, the above steps require one command line to be written into the SHELXL .res file. In practice, the user defines a minimum of three non-collinear target positions (occupied by atoms or Q peaks in the structure) and the corresponding atoms from the database fragment (source atoms) intended to be placed on the target positions. DSR then automatically generates the required input for the fitting procedure in SHELXL (FRAG/FEND) that is needed to place the requested fragment on the desired position in the unit cell. Afterwards, the SHELXL input file is prepared for a full refinement employing automatically adapted restraints from the DSR database.

The stereochemical restraints applied by DSR are capable of stabilizing poor starting models and thereby enhancing the least-squares minimization to move towards the global minimum. They are also capable of stabilizing moieties with low occupancy factors. Nevertheless, it is advisable for the user to check whether the restraints are physically sensible (Biadene, 2006; Müller, 2009). The applied restraints can also be manually softened or removed in a subsequent refinement step, if necessary, after considering the refinement stability. Detailed descriptions of practical examples of disorder modelling and refinement strategies in SHELXL can be found in the excellent Crystallographer's Guide to SHELXL (Müller et al., 2006).

Although DSR has been primarily defined as an aid in disorder modelling, it can also be employed for rigid-body refinements and to enhance model building of large and complex supramolecular structures sharing typical characteristics with macromolecular structures, i.e. a high degree of structural flexibility paired with a limited resolution of the experimental data. DSR has already been successfully employed in that context (Schouwey et al., 2014; Wise et al., 2015; Wood et al., 2015).

2.4. Two worked examples

Modelling of a perfluorinated tert-butyl group (Fig. 2) serves as a typical example where DSR greatly facilitates structure refinement of a 14-atom entity. The disorder of this group is frequently observed in the [Al(OR^F)₄]⁻ type of weakly coordinating counter-ion (Krossing, 2001; Bihlmeier et al., 2004; Köchner et al., 2012).

Figure 2 The numbering of the central atoms of the OC(CF3)3 fragment from the DSR fragment database. The molecular diagrams here and in subsequent figures were created using ShelXle (Hübschle et al., 2011).

The second position of the OC(CF₃)₃ moiety in Fig. 3 (left) (Lichtenthaler et al., 2013) is located near the positions of atoms O1 and C1 and the maxima in the difference Fourier density map (Q peak positions) of Q4, Q7 and Q6. These three Q peaks correspond to atoms C2, C3 and C4 in the database fragment (Fig. 2). Fortunately, the F atoms do not have to be placed explicitly, as the subsequent refinement with restraints allows the rotation of the CF₃ groups to the correct geometry.

Figure 3 (Left) A stick representation of [Al(OR^F)4]^−. The disordered perfluorinated tert-butyl OC(CF3)3 moiety is highlighted in green. Its second position is indicated by maxima in the difference Fourier density map (Q peaks), which are shown as coloured icosahedra. (Right) The second position of the disordered OC(CF3)3 moiety (blue), successfully placed using DSR.

DSR currently provides two options for placing fragments. The command PUT places the fragment on a desired position, leaving all target atoms unaffected. Alternatively, REPLACE replaces all target atoms. After PUT or REPLACE, the user gives the fragment name. To model and refine the second position of the OC(CF₃)₃ fragment requires the following DSR command line anywhere in the SHELXL .res file:

REM DSR PUT OC(CF3)3 WITH O1 C1 C2 C3 ON O1_1 C1_1 Q4 Q7 Q6 PART 2 OCC -21 RESI

Note that the REM at the beginning of the line prevents SHELXL from accidently interpreting the DSR command. The .res file can now be processed by DSR to insert the fragment by executing the following on the command line:

dsr -r filename.res

After successful fragment placement with DSR, the resulting structure includes all atoms of the second position of the disordered OC(CF₃)₃ moiety (Fig. 3, right). Atom names, site-occupancy factors and the free variable are automatically assigned. The second disordered part (PART 2), the instructions for residue class and number (RESI 4 CCF3), and the restraints for bond distances and displacement parameters to stabilize the subsequent refinement are also established. Furthermore, DSR introduces similarity restraints for the OC(CF₃)₃ moiety. Note the fairly large standard deviation of the 1,3-distance restraints for the CF₃ groups which allow a small tilt:

SADI_CCF3 0.02 C1 C2 C1 C3 C1 C4

SADI_CCF3 0.02 F1 C2 F2 C2 F3 C2 F4 C3 F5 C3 F6 C3 F7 C4 F8 C4 F9 C4

SADI_CCF3 0.04 C2 C3 C3 C4 C2 C4

SADI_CCF3 0.04 O1 C2 O1 C3 O1 C4

SADI_CCF3 0.04 F1 F2 F2 F3 F3 F1 F4 F5 F5 F6 F6 F4 F7 F8 F8 F9 F9 F7

SADI_CCF3 0.1 F1 C1 F2 C1 F3 C1 F4 C1 F5 C1 F6 C1 F7 C1 F8 C1 F9 C1

All other changes made to the .res file can be found in the supporting information. Fig. 4 illustrates a successful fragment placement and a robust disorder model with an occupancy of 0.44, which significantly improves the residual density.

Figure 4 The residual density maps around the disordered OC(CF3)3 group (left) before and (right) after treatment with DSR. The residual electron density is shown as a green (positive) or red (negative) mesh, with isolevels at ±0.70 e Å^−3 (left) and ±0.30 e Å^−3 (right).

Modelling of a disordered three-dimensional supramol­ecular coordination network is a second example to demonstrate the advantages of using DSR in a complex structure refinement. The structure consists of supramolecular clathrochelate ligands with a zinc ion in the centre, connected via cadmium ions to form a network (Pascu et al., 2014). In this case, 64% of the main-residue disorder is triggered by the disorder of the Cd ions over a special position (inversion centre) to which the clathrochelate ligands are coordinated. The stereochemical restraints for the organic part of the clathrochelate ligands were generated using GRADE and imported into the DSR database (Fig. 5).

Figure 5 The numbering of the B and N atoms of the clathrochelate ligand fragment (numbered pm41) from the DSR fragment database.

After setting the site-occupancy factor of the first modelled part (PART 1) of the clathrochelate to 0.50, the remaining Q peaks clearly show the second clathrochelate position (Fig. 6, left). The central Zn²⁺ cations of the clathrochelate PART 2 were added manually.

Figure 6 (Left) A stick representation of the coordination network of the example metal–organic framework compound. The clathrochelate moiety is highlighted in green. Its second position is indicated by maxima in the difference Fourier density map (Q peaks), which are shown as coloured icosahedra. (Right) The second position of the disordered clathrochelate moiety (blue), successfully placed using DSR.

The DSR placement of the second part of the clathrochelate entity works best if four (or more) reference points (Q peaks) are defined, to ensure a good starting position and orientation for the initial refinement. With the following DSR command, all 56 non-H atoms of the second clathrochelate part are introduced at the same time for subsequent refinement by SHELXL:

REM DSR PUT PM41 WITH N4 B7 N31 B20 ON Q7 Q133 Q44 Q171 PART 2 OCC 10.5 = RESI PM4

After this modelling step, R₁ dropped by 0.05 to about 0.25, which is also reflected in the decrease in residual density in the modelled region.

3. Concluding remarks

DSR is a powerful program to model disorder of medium-sized molecular fragments. It only requires a basic crystallographic background and spares its users most of the tedious work. It is flexible enough to be used with all existing refinement graphical user interfaces (GUIs). Although its main application will probably remain the modelling of disorder, DSR will also be beneficial for cases of chemical crystallography belonging to the macromolecular domain, for which a large number of repeating structural motifs need to be modelled and refined against data of limited resolution. Its application has been very promising, especially in the context of supramolecular chemistry. The fitting of ligands to previously identified binding sites of biological macromolecules and the modelling of structures measured at high pressure are possible fields for future applications.

4. Program availability

DSR runs on every platform that can run Python (versions 2 and 3), such as Windows, Linux and Mac OS X. It can run as a standalone command line program or can be integrated as a Python module within a GUI. The software is distributed under a free BSD-like license (Kratzert, 2015). The Windows installation file is created with the Inno Script Studio installer compiler (Kymoto, 2014). The Linux packages are regular .rpm and .deb files for Redhat- or Debian-based Linux distributions, respectively. The NetworkX software library (Hagberg et al., 2013) is supplied with the Windows installer and Linux program packages. DSR can be used together with any GUI like ShelXle (Hübschle et al., 2011) or WinGX (Farrugia, 2012).

The program executables and source files and a detailed user manual can be downloaded from the program's web page at https://www.xs3.uni-freiburg.de/research/dsr. The development platform is located at https://github.com/dkratzert/DSR.