computer programs
CrystalExplorer: a program for Hirshfeld surface analysis, visualization and quantitative analysis of molecular crystals
aSchool of Molecular and Life Sciences, Curtin University, PO Box U1987, Perth, WA 6845, Australia, and bSchool of Molecular Sciences, University of Western Australia, 35 Stirling Highway, Perth, WA 6009, Australia
*Correspondence e-mail: peter.spackman@curtin.edu.au
CrystalExplorer is a native cross-platform program supported on Windows, MacOS and Linux with the primary function of visualization and investigation of molecular crystal structures, especially through the decorated Hirshfeld surface and its corresponding two-dimensional fingerprint, and through the visualization of void spaces in the crystal via isosurfaces of the promolecule electron density. Over the past decade, significant changes and enhancements have been incorporated into the program, such as the capacity to accurately and quickly calculate and visualize quantitative intermolecular interactions and, perhaps most importantly, the ability to interface with the Gaussian and NWChem programs to calculate quantum-mechanical properties of molecules. The current version, CrystalExplorer21, incorporates these and other changes, and the software can be downloaded and used free of charge for academic research.
Keywords: intermolecular interactions; Hirshfeld surfaces; fingerprints; visualization; quantum-mechanical properties; computer programs; CrystalExplorer.
1. Introduction and background
Rational design of functional materials depends on our capacity to understand the driving forces of binding in the material, along with the mechanism which dictates the desired properties of the material. In the context of molecular crystals, this problem effectively reduces to understanding the strength and origin of intermolecular interactions and their relationship with crystal packing.
Hirshfeld surface (HS) analysis was initiated with the serendipitous discovery of the HS (Spackman & Byrom, 1997; McKinnon et al., 1998) as a novel means of partitioning space in molecular crystals into smooth non-overlapping molecular entities. Subsequent developments led to the invention of HS fingerprint plots (Spackman & McKinnon, 2002; McKinnon et al., 2004), or `fingerprints' for short. These are a convenient means of summarizing the intermolecular contacts present in crystals via a two-dimensional plot, with the decomposition of this fingerprint plot into features in order to identify particular interactions (McKinnon, Jayatilaka & Spackman, 2007). The mapping of scalar properties via a colour scale onto the HS (McKinnon, Fabbiani & Spackman, 2007), known as decoration, has also proven to be a powerful approach to quickly and easily gain insight into molecular environments in the crystalline state.
1.1. Prior versions of CrystalExplorer
The CrystalExplorer software was initially developed to facilitate HS analysis (Spackman & Jayatilaka, 2009), and that is still a primary purpose of the program which is currently widely used. However, the ability to perform quantum-chemical calculations, and subsequently generate isosurfaces and surface properties of quantum-mechanically derived quantities (Spackman et al., 2008), as well as the capacity to identify and visualize void spaces (Turner et al., 2011) in crystals, has contributed to the popularity of the tool over the past 15 years. These capabilities, made possible through an intuitive graphical user interface available on most desktop computers, have made CrystalExplorer into a valuable toolbox for advancing our comprehension and understanding of the structure and properties of molecular crystals.
1.2. Changes in CrystalExplorer21
Besides several important bug fixes, the latest version of CrystalExplorer now supports use of the open-source NWChem (Aprà et al., 2020) package as a quantum-mechanical back end (through the use of a Molden input file), in addition to the existing support for the Gaussian (Frisch et al., 2016) quantum-chemistry and Tonto (Jayatilaka & Grimwood, 2003) quantum-crystallography packages. Further improvements have been made in finer control over precise views down desired crystal directions, precision in energy tables and more.
2. Capabilities
The aim of this article is to provide a short overview of the capabilities of CrystalExplorer; the reader is referred to documentation available online at https://wiki.crystalexplorer.net for further details. CrystalExplorer reads a (Hall et al., 1991) and displays the molecules as ball-and-stick, van der Waals sphere or wireframe models that can be rotated or zoomed into using the mouse wheel.
2.1. Crystallographic tools and visualization
CrystalExplorer offers a number of options for building clusters of molecules, allowing the user to see as much or as little of the as desired. These include (i) generating molecules close to those on the screen by clicking on nearest-neighbour `ghost' atoms, (ii) generating the remaining atoms of incomplete molecules, (iii) generating all the atoms within a radius of a selection and (iv) generating `slabs' of complete unit cells. The program further includes a selection of tools that are typically found in crystallographic packages, allowing, for example, the calculation of geometric parameters (distances, angles etc.), and identification and graphical depiction of short contacts and hydrogen bonds.
2.2. Hirshfeld and other surfaces
HSs, along with what has come to be called HS analysis, have been described in detail in several publications (Spackman & Jayatilaka, 2009; McKinnon et al., 1998, 2004; Spackman, 2013; Spackman & Byrom, 1997). They arose from an exploration of possible methods to define a region of the crystal as surrounding a specific molecule, for the purpose of integrating the electron density `belonging' to that molecule.
In CrystalExplorer, the electron densities used to compute the HS surfaces come from tabulations of atomic wavefunctions expanded using exponential-type basis functions (Clementi & Roetti, 1974; Koga et al., 1993, 2000). Inspired by Fred Hirshfeld's `stockholder' partitioning of atoms in molecules (Hirshfeld, 1977), the resulting (spherical) atomic electron densities are used to construct the promolecule electron density and the procrystal electron density , which are then used to define the weight function,
This continuous scalar function has in all space, and the 0.5 isosurface of this function is the HS.
Surfaces of interest can be calculated in CrystalExplorer by selecting the molecule in question with the mouse and clicking on the HS icon. The user is subsequently prompted to choose the desired surface (and an optional property to decorate the surface) along with a desired surface resolution before the surface is calculated and presented in the three-dimensional graphical display. Fig. 1 shows the available molecular surfaces using as an example acetic acid [Cambridge Structural Database (CSD) refcode ACETAC01; Nahringbauer, 1970].
Molecular surfaces alone provide significant visual information when trying to understand crystal packing, but the addition of scalar `surface properties' mapped to colours decorating the surface further aids in intuitive understanding. Fig. 2 shows an example of an HS for saccharin, decorated with a variety of properties available in CrystalExplorer. The properties themselves are explained in Table 1. Only the properties on the last row of Fig. 2 require molecular quantum-mechanical wavefunctions for their evaluation; the other surfaces just make use of geometric distances to the HS, which itself is obtained using only the aforementioned tabulated atomic wavefunctions. Note how qualitatively similar the atom-generated promolecule-density isosurface is to the `molecular' quantum-mechanical electron-density isosurface (Mitchell & Spackman, 2000).
|
2.3. Fingerprint plots
CrystalExplorer can interactively generate fingerprint plots for all HSs calculated at a sufficiently high resolution. CrystalExplorer `links' the display of the fingerprint to its HS in that a mouse click on the fingerprint plot highlights the corresponding points on the HS (with red cones). Fingerprint plots can be exported in the PNG and PostScript formats, the latter being preferred for inclusion in some publications as it is an editable vector format unlike a rasterized PNG.
CrystalExplorer also provides options for decomposing a fingerprint plot into contributions from particular kinds of interactions. At present the user is limited to highlighting interactions on the basis of atom type (C, N, O etc.). Interactions are selected by choosing the atom type for the atoms inside the HS and for those outside it. The interactions with the inside and outside atoms switched can also be included by selecting the `include reciprocal contacts' option.
An example of fingerprint decomposition for urea (CSD refcode UREAXX01; Sklar, Senko & Post, 1961) can be seen in Fig. 3. The contacts between oxygen atoms inside the HS and hydrogen atoms (i.e. O⋯H contacts) outside of it have been selected, including reciprocal contacts (i.e. H⋯O contacts). The parts of the fingerprint that correspond to these interactions remain coloured while the rest of the plot is greyed out, and simultaneously the displayed HS colouring is greyed out with the exception of the regions involving the interaction. The total area of these regions relative to the total surface area of the HS is used to report a percentage contribution of the interaction. We can see from the figure that O⋯H and H⋯O interactions make up 36.6% of the surface area of the HS. There are two fragment patches corresponding to these kinds of interactions and both of them are highlighted by the red-coloured dnorm property.
2.4. CrystalExplorer model energies
CrystalExplorer computes pairwise intermolecular interaction energies using an approach inspired by the PIXEL (Gavezzotti, 2005) method, but the approach used in CrystalExplorer differs in several important points. Full details of the CrystalExplorer models are available in the literature (Turner et al., 2014; Mackenzie et al., 2017) and only a brief outline is provided here. The basic expression follows that used by Gavezzotti and others, whereby the intermolecular interaction energy is decomposed into four physically motivated terms (explained below) but with the exception that each term is multiplied by its own scale factor:
Here Eele is the classical electrostatic interaction energy between unperturbed quantum-mechanical charge distributions of the monomers, Epol is the polarization energy calculated as a sum over isotropic atomic polarizabilities multiplied by the square of the local electric field caused by the other monomer, Edis is Grimme's D2 dispersion correction (Grimme, 2006), and Erep is the exchange-repulsion energy calculated between unperturbed quantum-mechanical charge distributions of the monomers according to the formula for the sum of the exchange and repulsion terms reported by Su & Li (2009) and earlier by Hayes & Stone (1984). The four scale factors in this expression have been optimized for two wavefunction sources: CE-HF (using HF/3-21G monomer wavefunctions) and CE-B3LYP [using B3LYP/6-31G(d,p) monomer wavefunctions]. These scale factors were optimized against reference intermolecular interaction energies: counterpoise-corrected B3LYP-D2/6-31G(d,p) interaction energies for 1794 molecule/ion pairs extracted from 171 experimental crystal structures. The resulting models have a mean absolute deviation of 4.7 kJ mol−1 for CE-HF and 2.5 kJ mol−1 for CE-B3LYP relative to the reference data across an energy range spanning 3.75 MJ mol−1 (Mackenzie et al., 2017).
CrystalExplorer uses to determine which interaction pairs are unique. Those that are identical by symmetry are coloured in the same way so that the user may easily see the symmetry-related pairs and their corresponding interactions, along with the operation relating the two molecules. Fig. 4 shows an example interaction-energy output along with the corresponding graphical view for an acetic acid (CSD refcode ACETAC01) crystal.
The interaction energies described above provide quantitative insight into the binding (and non-binding) pairwise intermolecular interactions in the crystal but can be difficult to translate into the context of the actual CrystalExplorer alleviates this problem by providing a visualization technique to simplify the information, which we call `energy frameworks' (Turner et al., 2015). Energy frameworks permit us to examine `cooperative effects' in these intermolecular interactions, across the crystal. Specifically, energy frameworks allowing separate views for the electrostatic (red), dispersion (green) and total energy (blue for binding, gold for non-binding) terms between pairs are available. Fig. 5 shows an energy-framework visualization for adamantane tetracarboxylic acid (CSD refcode GEJVEW; Ermer, 1988), a molecular crystal comprising interpenetrated networks of hydrogen bonds.
Furthermore, these intermolecular interaction energies may be directly summed over a number of pairs to give a reasonable estimate of the lattice energy of a crystal (Thomas et al., 2018; Spackman, 2018); the CE-B3LYP model energies in particular yield results comparable in accuracy to dispersion-corrected periodic density-functional-theory calculations.
3. Availability and installation
CrystalExplorer installers can be downloaded at https://crystalexplorer.net and used free of charge for academic purposes. Commercial licences are also available. CrystalExplorer is supported on Windows 10, MacOS and several GNU/Linux variants.
Acknowledgements
The authors thank the many CrystalExplorer users who have provided valuable feedback facilitating development and improvements in the program.
References
Aprà, E., Bylaska, E. J., de Jong, W. A., Govind, N., Kowalski, K., Straatsma, T. P., Valiev, M., van Dam, H. J. J., Alexeev, Y., Anchell, J., Anisimov, V., Aquino, F. W., Atta-Fynn, R., Autschbach, J., Bauman, N. P., Becca, J. C., Bernholdt, D. E., Bhaskaran-Nair, K., Bogatko, S., Borowski, P., Boschen, J., Brabec, J., Bruner, A., Cauët, E., Chen, Y., Chuev, G. N., Cramer, C. J., Daily, J., Deegan, M. J. O., Dunning, T. H. Jr, Dupuis, M., Dyall, K. G., Fann, G. I., Fischer, S. A., Fonari, A., Früchtl, H., Gagliardi, L., Garza, J., Gawande, N., Ghosh, S., Glaesemann, K., Götz, A. W., Hammond, J., Helms, V., Hermes, E. D., Hirao, K., Hirata, S., Jacquelin, M., Jensen, L., Johnson, B. G., Jónsson, H., Kendall, R. A., Klemm, M., Kobayashi, R., Konkov, V., Krishnamoorthy, S., Krishnan, M., Lin, Z., Lins, R. D., Littlefield, R. J., Logsdail, A. J., Lopata, K., Ma, W., Marenich, A. V., Martin del Campo, J., Mejia-Rodriguez, D., Moore, J. E., Mullin, J. M., Nakajima, T., Nascimento, D. R., Nichols, J. A., Nichols, P. J., Nieplocha, J., Otero-de-la-Roza, A., Palmer, B., Panyala, A., Pirojsirikul, T., Peng, B., Peverati, R., Pittner, J., Pollack, L., Richard, R. M., Sadayappan, P., Schatz, G. C., Shelton, W. A., Silverstein, D. W., Smith, D. M. A., Soares, T. A., Song, D., Swart, M., Taylor, H. L., Thomas, G. S., Tipparaju, V., Truhlar, D. G., Tsemekhman, K., Van Voorhis, T., Vázquez-Mayagoitia, Á, Verma, P., Villa, O., Vishnu, A., Vogiatzis, K. D., Wang, D., Weare, J. H., Williamson, M. J., Windus, T. L., Woliński, K., Wong, A. T., Wu, Q., Yang, C., Yu, Q., Zacharias, M., Zhang, Z., Zhao, Y. & Harrison, R. J. (2020). J. Chem. Phys. 152, 184102. Google Scholar
Clementi, E. & Roetti, C. (1974). At. Data Nucl. Data Tables, 14, 177–478. CrossRef CAS Google Scholar
Ermer, O. (1988). J. Am. Chem. Soc. 110, 3747–3754. CSD CrossRef CAS Web of Science Google Scholar
Frisch, M. J., Trucks, G. W., Schlegel, H. B., Scuseria, G. E., Robb, M. A., Cheeseman, J. R., Scalmani, G., Barone, V., Petersson, G. A., Nakatsuji, H., Li, X., Caricato, M., Marenich, A. V., Bloino, J., Janesko, B. G., Gomperts, R., Mennucci, B., Hratchian, H. P., Ortiz, J. V., Izmaylov, A. F., Sonnenberg, J. L., Williams-Young, D., Ding, F., Lipparini, F., Egidi, F., Goings, J., Peng, B., Petrone, A., Henderson, T., Ranasinghe, D., Zakrzewski, V. G., Gao, J., Rega, N., Zheng, G., Liang, W., Hada, M., Ehara, M., Toyota, K., Fukuda, R., Hasegawa, J., Ishida, M., Nakajima, T., Honda, Y., Kitao, O., Nakai, H., Vreven, T., Throssell, K., Montgomery, J. A. Jr, Peralta, J. E., Ogliaro, F., Bearpark, M. J., Heyd, J. J., Brothers, E. N., Kudin, K. N., Staroverov, V. N., Keith, T. A., Kobayashi, R., Normand, J., Raghavachari, K., Rendell, A. P., Burant, J. C., Iyengar, S. S., Tomasi, J., Cossi, M., Millam, J. M., Klene, M., Adamo, C., Cammi, R., Ochterski, J. W., Martin, R. L., Morokuma, K., Farkas, O., Foresman, J. B. & Fox, D. J. (2016). Gaussian 16. Revision C.01. Gaussian Inc., Wallingford, Connecticut, USA. Google Scholar
Gavezzotti, A. (2005). Z. Kristallogr. Cryst. Mater. 220, 499–510. Web of Science CrossRef CAS Google Scholar
Grimme, S. (2006). J. Comput. Chem. 27, 1787–1799. Web of Science CrossRef PubMed CAS Google Scholar
Hall, S. R., Allen, F. H. & Brown, I. D. (1991). Acta Cryst. A47, 655–685. CrossRef CAS Web of Science IUCr Journals Google Scholar
Hayes, I. & Stone, A. (1984). Mol. Phys. 53, 83–105. CrossRef CAS Web of Science Google Scholar
Hirshfeld, F. L. (1977). Theor. Chim. Acta, 44, 129–138. CrossRef CAS Web of Science Google Scholar
Jayatilaka, D. & Grimwood, D. J. (2003). Computational Science – ICCS 2003, Lecture Notes in Computer Science, Vol. 2660, edited by P. M. A. Sloot, D. Abramson, A. V. Bogdanov, Y. E. Gorbachev, J. J. Dongarra & A. Y. Zomaya, pp. 142–151. Springer-Verlag Berlin Heidelberg. Google Scholar
Koenderink, J. J. (1990). Solid Shape. Cambridge: MIT Press Google Scholar
Koenderink, J. J. & van Doorn, A. J. (1992). Image Vis. Comput. 10, 557–564. CrossRef Web of Science Google Scholar
Koga, T., Kanayama, K., Watanabe, T., Imai, T. & Thakkar, A. J. (2000). Theor. Chem. Acc. 104, 411–413. Web of Science CrossRef CAS Google Scholar
Koga, T., Tatewaki, H. & Thakkar, A. J. (1993). Phys. Rev. A, 47, 4510–4512. CrossRef CAS PubMed Web of Science Google Scholar
Mackenzie, C. F., Spackman, P. R., Jayatilaka, D. & Spackman, M. A. (2017). IUCrJ, 4, 575–587. Web of Science CrossRef CAS PubMed IUCr Journals Google Scholar
McKinnon, J. J., Fabbiani, F. P. A. & Spackman, M. A. (2007). Cryst. Growth Des. 7, 755–769. Web of Science CrossRef CAS Google Scholar
McKinnon, J. J., Jayatilaka, D. & Spackman, M. A. (2007). Chem. Commun. pp. 3814. Google Scholar
McKinnon, J. J., Mitchell, A. S. & Spackman, M. A. (1998). Chem. Eur. J. 4, 2136–2141. CrossRef CAS Google Scholar
McKinnon, J. J., Spackman, M. A. & Mitchell, A. S. (2004). Acta Cryst. B60, 627–668. Web of Science CrossRef CAS IUCr Journals Google Scholar
Mitchell, A. S. & Spackman, M. (2000). J. Comput. Chem. 21, 933–942. Web of Science CrossRef CAS Google Scholar
Nahringbauer, I. (1970). Acta Chem. Scand. 24, 453–462. CSD CrossRef CAS Web of Science Google Scholar
Sklar, N., Senko, M. E. & Post, B. (1961). Acta Cryst. 14, 716–720. CSD CrossRef CAS IUCr Journals Web of Science Google Scholar
Spackman, M. A. (2013). Phys. Scr. 87, 048103. Web of Science CrossRef Google Scholar
Spackman, M. A. (2018). CrystEngComm, 20, 5340–5347. Web of Science CrossRef CAS Google Scholar
Spackman, M. A. & Byrom, P. G. (1997). Chem. Phys. Lett. 267, 215–220. CrossRef CAS Web of Science Google Scholar
Spackman, M. A. & Jayatilaka, D. (2009). CrystEngComm, 11, 19–32. Web of Science CrossRef CAS Google Scholar
Spackman, M. A. & McKinnon, J. J. (2002). CrystEngComm, 4, 378–392. Web of Science CrossRef CAS Google Scholar
Spackman, M. A., McKinnon, J. J. & Jayatilaka, D. (2008). CrystEngComm, 10, 377–388. CAS Google Scholar
Su, P. & Li, H. (2009). J. Chem. Phys. 131, 014102. Web of Science CrossRef PubMed Google Scholar
Thomas, S. P., Spackman, P. R., Jayatilaka, D. & Spackman, M. A. (2018). J. Chem. Theory Comput. 14, 1614–1623. Web of Science CrossRef CAS PubMed Google Scholar
Turner, M. J., Grabowsky, S., Jayatilaka, D. & Spackman, M. A. (2014). J. Phys. Chem. Lett. 5, 4249–4255. Web of Science CrossRef CAS PubMed Google Scholar
Turner, M. J., McKinnon, J. J., Jayatilaka, D. & Spackman, M. A. (2011). CrystEngComm, 13, 1804–1813. Web of Science CrossRef CAS Google Scholar
Turner, M. J., Thomas, S. P., Shi, M. W., Jayatilaka, D. & Spackman, M. A. (2015). Chem. Commun. 51, 3735–3738. Web of Science CrossRef CAS Google Scholar
Wardell, J. L., Low, J. N. & Glidewell, C. (2005). Acta Cryst. E61, o1944–o1946. Web of Science CSD CrossRef IUCr Journals Google Scholar
This is an open-access article distributed under the terms of the Creative Commons Attribution (CC-BY) Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited.