CRYSTAL GROWTH & DESIGN 2003 VOL. 3, NO. 1 3-8
Perspective Molecular Graphics: From Science to Art Jerry L. Atwood* and Leonard J. Barbour* Department of Chemistry, University of Missouri-Columbia, Columbia, Missouri 65211 Received November 8, 2002
ABSTRACT: The evolution of molecular graphics is briefly discussed. The utility of simplified representations of complex molecular assemblies is illustrated with several examples from the authors’ previously published works. To paraphrase Jules Henri Poincare´ (with some license taken), we do not study nature just because it is useful; we study it because we delight in it, and we delight in it because it is beautiful. This sentiment is perhaps no more acutely embraced than by those scientists concerned with studying the molecular world. While science explores the nature of the world around us, art explores our perception of that world. This apparent dichotomy between art and science can, in part, be reconciled by molecular graphics. In our efforts to understand the composition and, consequently, the behavior of matter, we use techniques such as X-ray diffraction to determine precise atomic positional parameters. This information allows us to extrapolate, using symmetry and translation, the arrangement of molecules in three-dimensional space. Once we have identified interesting features of either the molecular or extended structure, the challenge that remains is to effectively communicate our findings to others. To this end, we employ molecular graphics as a powerful visual aid because, as the well-known cliche´ goes, a picture can indeed be worth a thousand words. This is particularly true when the picture is carefully constructed to simultaneously simplify and clarify the concept that it illustrates. While it is useful to briefly describe the gradual evolution of molecular graphics, it is not our objective to provide a comprehensive review of the subject. In the early days of X-ray crystallography, the painstaking process of structure determination far overshadowed the task of producing accurately scaled molecular models. Before the popularization of supramolecular chemistry, the primary objective of diffraction studies was usually to elucidate molecular structure. After obtaining accurate atomic coordinates, metaphoric molecular models could be built to scale and then photographed to * To whom correspondence should be addressed. E-mail: atwoodj@ missouri.edu,
[email protected]. Jerry L. Atwood, Department of Chemistry, University of Missouri - Columbia, Columbia, MO 65211. Tel: (573) 882-8374. Fax: (573) 882-2754. Leonard J. Barbour, Department of Chemistry, University of Missouri - Columbia, Columbia, MO 65211. Tel: (573) 882-1811. Fax: (573) 882-2754.
Figure 1. ORTEP projections of Sm(C9H7)3 (a) as published in 1973 (reprinted from ref 3 with permission. Copyright 1973 American Chemical Society) and (b) reproduced as a ray-traced image.
illustrate manuscripts or presentations. The types of models that were employed depended on whether the
10.1021/cg020063o CCC: $25.00 © 2003 American Chemical Society Published on Web 12/07/2002
4
Crystal Growth & Design, Vol. 3, No. 1, 2003
Figure 2. A large hydrogen bonded capsule consisting of six C-isobutylpyrogallol[4]arenes. The green shape represents (idealistically) the guest-accessible space within the capsule. The capsule is held together by 48 intermolecular and 24 intramolecular hydrogen bonds (shown in yellow). (Reprinted with permission from ref 8. Copyright 2001 The Royal Society of Chemistry.)
emphasis was on representing bonds or atoms. The former were represented as either wireframe or balland-stick models constructed using wire and wooden, metal, or plastic spheres. When the emphasis was on molecular shape, space-filling models could be constructed using the popular Corey-Pauling-Koltun (CPK) models consisting of plastic spheres connected to one another by means of snap fasteners. Each sphere represents an individual atom colored according to element type (e.g., black for carbon, white for hydrogen, red for oxygen, blue for nitrogen) and its radius, usually 0.5 in./Å, is proportional to the van der Waals radius of the atom that it represents. Inorganic structures can be further simplified by representing the coordination sphere about metal centers as polyhedra. In the mid 1960s, crystallography was revolutionized by the availability of digital computers that could now be employed to perform the exhaustive calculations. Early efforts to model molecules were made by Project MAC at MIT when the first computer-generated wire-
Perspective
Figure 4. Projection perpendicular to the crystallographic c axis showing five calix[4]arene trimers in the hexagonal closepacked arrangement (Colors: gray, carbon; white, hydrogen; red, oxygen; yellow, bromine; blue, fluorine).
frame models were displayed on a cathode ray tube.1 At about the same time (1965), the Oak Ridge thermal ellipsoid plot (ORTEP) program was distributed by Carroll Johnson.2 ORTEP uses a series of line segments to illustrate molecules in the ball-and-stick metaphor with bonds represented by lines joining atoms, which, in turn, are represented as small spheres or even ellipsoids that model thermal motion probability. An example of the latter, dating from 1973,3 is reproduced in Figure 1a. Thermal ellipsoid plots rapidly became the standard for presenting models based on crystal structure analyses and, indeed, are still widely used today. Early versions of ORTEP did not perform hidden-line removal for intersecting spheres and were thus not suitable for simulating CPK models. However, in 1978 Motherwell and Clegg released the program PLUTO,4 which was designed to produce plots of wireframe, balland-stick, and spacefilled CPK-like models. These pioneering contributions to the illustration of molecular structure were all based upon vector graphics. One of the primary advantages of vector graphics is that figures are easily scaled without loss of resolution. The main disadvantages are that the images cannot incorporate continuous tone, and the number of available colors is limited. With the recent rapid advances in
Figure 3. Various views depicting the trimeric arrangement of calix[4]arene in (a) capped-stick representation viewed along the 3-fold axis, (b) spacefilling representation, also along the 3-fold axis, and (c) spacefilling representation perpendicular to the 3-fold axis. The superimposed semitransparent green spheres of radius 7.3 Å emphasize the minor deviations of the trimer from ideal spherical geometry. (Reprinted with permission from Science (http://www.aaas.org), ref 9. Copyright 2002 American Association for Advancement of Science.)
Perspective
Crystal Growth & Design, Vol. 3, No. 1, 2003 5
Figure 7. Ray-traced thermal ellipsoid plot showing a (H2O)10 cluster positioned between two tricyclic coordination complexes. Hydrogen bonds between water molecules are shown as fragmented cylinders. (Reprinted with permission from ref 12b. Copyright 2000 The Royal Society of Chemistry.) Figure 5. Spacefilled projection of an ellipsoidal capsule consisting of six molecules hydrogen bonded to one another. Twelve molecules of diethyl ether (blue and orange) are encapsulated and ordered by means of hydrogen bonds to the host assembly. The host molecules are positioned relative to one another such that their centroids describe the vertices of a trigonal antiprism (shown as semitransparent green panels).
Figure 6. Combined spacefilled and capped-stick representation showing the translation of two adjacent layers of p-tertbutylcalix[4]arene with respect to one another during uptake of vinyl bromide. The blue capped-stick molecules are common to both structures. The red molecule represents one molecule from an adjacent layer of the original structure. The yellow molecule shows the new position, after a 6 Å lateral shift (arrow), of this molecule after incorporation of vinyl bromide into the lattice. (Reprinted with permission from Science (http://www.aaas.org), ref 11a. Copyright 2002 American Association for Advancement of Science.)
affordable computer technology, the trend in computer graphics has begun to shift from vector-based to rasterbased graphics. The latter are well-suited to continuous tone images and can reproduce as many colors as needed. Ray tracing is a global illumination-based rendering method for the production of near-photorealistic images. The procedure involves calculating the paths taken by rays of light intersecting objects in a hypothetical scene. Starting at the viewer’s eye or
“camera”, each ray of light is traced through a pixel in the image plane, and into the scene. The pixel is then assigned the color value returned by the ray. Thus, pixel by pixel, an image is constructed by incorporating reflections and shadows to give a highly aesthetic, threedimensional appearance suitable for reproduction on a two-dimensional medium (e.g., Figure 1b). While vectorbased graphics are still widely used today, advances in computing power, electronic file transfer, manuscript preparation, and publication practices have popularized the use of ray-traced images in journal articles, books, web pages, and seminars. In particular, younger audiences tend to embrace such advances more readily and are far more demanding with regard to image-quality and ease of production. Undoubtedly, the aesthetics of our idealized molecular metaphors reflect, to some extent, our perception of a largely invisible world. The beauty of this world stems from its intrinsic symmetry and form, as well as its many mysteries. Since visual art is most often inspired by these very same properties in the macroscopic world, it can be maintained that molecular graphics represents a bridge between science and art, leaving the integrity of both intact. Critics are often heard to argue that devoting time to producing “pretty pictures” is a frivolous pursuit intended to embellish mediocre results. We prefer to take a positive viewpoint, believing that the simplistic beauty of good science is best explained with the aid of simple, yet informative illustrations that are easily comprehended by a diverse audience. Molecular biologists have long understood this concept, making use of cartoon ribbon diagrams to simplify the visualization of fantastically complicated molecular structures. While ensuring that scientific illustrations are also aesthetically pleasing may not necessarily improve the science, attention to image quality certainly makes the science itself more likely to be noticed.5 One of us (J.L.A.) has been research-active since the dawn of computer-based crystallography, while the other (L.J.B.) has authored the X-Seed6 software system for the modeling, analysis, and illustration of crystal structures. In what remains of this article, we will draw on our own experiences with regard to the use of molecular graphics to illustrate complex supramolecular
6
Crystal Growth & Design, Vol. 3, No. 1, 2003
Perspective
Figure 8. Representations of a supramolecular sphere consisting of 12 p-sulfonatocalix[4]arene molecules in (a) vector graphics wireframe mode and (b) ray-traced spacefilling mode.
assemblies. While we are well aware that the molecular scientist of today has access to a wide variety of other excellent software packages for much the same purpose, Figures 1b to 10a were produced using the POV-Ray7 interface of X-Seed. Our current research interests are primarily focused on the encapsulation of small molecular entities by relatively large supramolecular assemblies. We have shown that a spherical capsule, consisting of six C-isobutylpyrogallol[4]arene molecules assembled via 48 intermolecular hydrogen bonds, is stable in polar media.8 To adequately describe the capsule, with particular emphasis on the shape of its rather cavernous 1500 Å3 interior volume, we prepared the illustration shown in Figure 2. The projection shows that the pyrogallolarene molecules are arranged with their cavities directed toward the interior of the capsule. Furthermore, these molecular cavities significantly enhance the size of the guest-accessible interior volume of the capsule, which is represented by a large green sphere with six smaller hemispherical protrusions. In a separate study,9 we used semitransparent spheres to illustrate the shape of the exterior surface of a molecular assembly. In its pure crystalline form, calix[4]arene assembles to form trimers that are approximately spherical in shape (Figure 3). In the extended structure, the molecules form a hexagonal close-packed arrangement of these nearly spherical entities. The semitransparent spheres shown in Figure 3b,c reveal small indentations and protrusions that result in the formation of large voids in the hexagonal close-packed lattice. Further investigation showed that it is possible to entrap highly volatile gases such as methane and Freon in these interstitial voids under relatively extreme conditions of temperature and pressure. The combined usage of spacefilling and capped-stick metaphors in Figure 4 shows the arrangement of five calix[4]arene trimers. The capped-stick trimer in the foreground allows visualization of a single molecule of CF3Br in the interstitial void. Depicting the four remaining trimers in the spacefilling metaphor imparts a sense of scale and morphology.
Figure 9. Cartoon illustrations depicting bowl-shaped calixarene molecules as truncated cones. In most cases, the molecules pack in an up-down arrangement to form bilayers (a). However, when the molecules pack in an up-up fashion, curvature of the resulting arrangement yields (b) spheres or (c) tubules. The placement and scale of the truncated cones are derived from the crystallographic data.
Yet a further use of semitransparent geometrical objects to simplify the description of complex assemblies is exemplified by our report10 of a hexameric assembly closely related to that of pyrogallol[4]arene described above. In this instance, an ellipsoidal capsule is formed
Perspective
Crystal Growth & Design, Vol. 3, No. 1, 2003 7
Figure 10. (a) Twelve truncated cones represent the calixarene molecules of a supramolecular sphere; (b) abstract rendering of (a) titled “Molecular Mosaic” by America’s premier watercolorist, Paul Jackson.
by six host molecules positioned at the vertices of a trigonal antiprism (Figure 5). For decades, it has been common practice to describe inorganic complexes in geometrical terms (e.g., octahedral, trigonal bipyramidal, trigonal antiprismatic, etc.). As we note in our report, it is similarly instructive to understand the rather complicated structures of large supramolecular assemblies in terms of their solid geometric shapes. Very recently, we determined the solid-state structure of a polymorphic form of p-tertbutylcalix[4]arene obtained by sublimation of the compound.11 The structure consists of a bilayer type arrangement of the molecules. Owing to poor packing efficiency, the lattice contains large voids with an estimated free volume of about 235 Å3. Despite the lack of channels linking these voids to one another, it was possible to infuse vinyl bromide into a single crystal of the compound without destroying its crystallinity. Using the same crystal, we determined the structures both before and after exposure to vinyl bromide. We found that adjacent bilayers had shifted by about 6 Å with respect to one another during the phase transition. This net transformation of the lattice structure is illustrated in Figure 6. It would be remiss of us not to provide typical examples of a ray-traced thermal ellipsoid plots in the style of ORTEP, as shown in Figures 1b and 7.12 Although such figures are no longer considered mandatory by most journals for reports of crystal structures,
they still command a significant level of aesthetic appeal in addition to fulfilling their intended purpose. It was not purely by chance that our initial interest in enhanced molecular graphics coincided with our interest in supramolecular capsules. This work began with the discovery that p-sulfonatocalix[4]arene, a truncated cone-shaped molecule, can be induced to pack in the solid state to form bilayers, spheres, or tubules.13 Owing to the complexity of the structures, using vector graphics to illustrate the spherical (Figure 8a) or tubular assemblies in a meaningful way is not feasible since the overlap of molecules is highly confusing. However, a spacefilling ray-traced image (Figure 8b) with the molecules colored individually is both aesthetic and informative. To further simplify the various packing arrangements of the calixarenes, the molecules can be substituted by truncated cone-shaped objects (Figure 9). The positions and dimensions of the cones are accurately based upon the crystallographically determined coordinates of the molecules. Figure 10a shows an interpretation of the sphere similar to that in Figure 9b. Indeed, the intrinsic beauty and simplicity of this metaphor for the supramolecular sphere have inspired the painting shown in Figure 10b. The artist Paul Jackson viewed Figure 10a through the eye of a skilled watercolorist, and the result is a painting of significant aesthetic appeal. The painting serves to emphasize how the beauty of even the unseen molecular world can capture
8
Crystal Growth & Design, Vol. 3, No. 1, 2003
the imagination of the artist and scientist alike. Collaborative endeavors such as this have the added benefit of bringing the molecular world to the attention of nonscientists.
Perspective
(6)
Acknowledgment. We thank Paul Jackson for kind permission to reproduce his painting titled “Molecular Mosaic”.
(7) (8)
References
(10)
(1) Levinthal, C. Sci. Am. 1966, 214, 42-52. (2) Johnson, C. K. ORTEP - A FORTRAN thermal ellipsoid plot program for crystal structure illustrations. Report ORNL-3794, Revised, Oak Ridge National Laboratory, Oak Ridge, TN, 1965; p 70. (3) Atwood, J. L.; Burns, J. H.; Laubereau, P. G. J. Am. Chem. Soc. 1973, 95, 1830. (4) Motherwell, W. D. S.; Clegg, W. PLUTO: Program for Plotting Molecular and Crystal Structures; Cambridge University Press: Cambridge, England, 1978. (5) (a) Frankel, F. Envisioning Science: The Design and Craft
(9)
(11)
(12) (13)
of the Science Image; MIT Press: Cambridge, MA, 2002. (b) Frankel, F.; Whitesides, G. M. On the Surface of Things: Images of the Extraordinary in Science; Chronicle Books LLC, San Francisco, 1997. (a) http://x-seed.net. (b) Barbour, L. J. J. Supramol. Chem. 2001, 1, 189. http://www.povray.org. Atwood, J. L.; Barbour, L. J.; Jerga, A. Chem. Commun. 2001, 2376. Atwood, J. L.; Barbour, L. J.; Jerga, A. Science 2002, 296, 2367. Atwood, J. L.; Barbour, L. J.; Jerga, A. Proc. Natl Acad. Sci. U.S.A. 2002, 99, 4837. (a) Atwood, J. L.; Barbour, L. J.; Jerga, A.; Schottel, B. L. Science 2002, 298, 1000. (b) Steed, J. W. Science 2002, 298, 976. (c) Atwood, J. L.; Barbour, L. J.; Jerga, A. Chem. Commun. 2002, 2952. (a) Barbour, L. J.; Orr, G. W.; Atwood, J. L. Nature 1998, 393, 671. (b) Barbour, L. J.; Orr, G. W.; Atwood, J. L. Chem. Commun. 2000, 859. Orr, G. W.; Barbour, L. J.; Atwood, J. L. Science 1999, 285, 1049.
CG020063O
