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Custom-Printed 3D Models for Teaching Molecular Symmetry Brian K. Niece* Department of Biological and Physical Sciences, Assumption College, Worcester, Massachusetts 01609, United States
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S Supporting Information *
ABSTRACT: Models were prepared by 3D printing that can be used to demonstrate the operations required for the study of molecular symmetry. The models were designed to emphasize the order and locations of rotation axes and to clearly illustrate the more abstract reflection and improper rotation axes. The models were well-received by students in a course on molecular structure, who generally felt that their understanding of the topic was enhanced by using the models.
KEYWORDS: Upper-Division Undergraduate, Inorganic Chemistry, Physical Chemistry, Hands-On Learning/Manipulatives, Group Theory/Symmetry, Molecular Properties/Structure
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symmetry bisect a model rather than reflect an entire object. Some students expect mirrors to duplicate an object, whereas in molecular symmetry, a reflection plane completes a half model. Many students learn to identify mirror planes in a molecule, but have difficulty determining the final locations of atoms that move from outside to “inside” the mirror image when applying projection operators. Even more difficult is visualizing the result of an improper rotation, which is a two-step operation. In some cases, after applying the first step (for example, the rotation), a physical model no longer corresponds to any part of the original or final orientation. Instead, at this point, the result of the reflection exists only in the mirror image. Traditional physical models are not capable of addressing these concerns, because they cannot be bisected along a mirror plane to demonstrate how the model is completed by the symmetry operation. In the past few years, 3D printing of plastic objects has become commonplace. Printers available for a few thousand dollars can produce custom models of anything a chemist might imagine. As a result, customized molecular models are now readily available.10,11 Several reports in this journal have described methods for converting molecular modeling computer files into 3D printer files.12−16 Others report using 3D printed models to demonstrate potential energy surfaces,17−20 atomic orbitals,21−23 molecular orbitals,24,25 hybrid orbitals,26 VSEPR theory,27,28 peptide structure,29 and polymer structure.30 Rodenbough31 describes 3D printed
olecular symmetry is an important topic with applications in many areas of chemistry.1 This topic is typically taught in inorganic or physical chemistry classes. A thorough understanding of symmetry is important to the study of molecular bonding2 as well as electronic and vibrational spectroscopy.3 Symmetry can even be used to predict optical activity,4 a topic generally covered in organic chemistry courses. Developing an intuitive understanding of molecular symmetry requires students to visualize potentially unfamiliar motions in three dimensions. Although the goal is to develop sufficient facility with the concepts of symmetry so that they can identify symmetry elements and point groups from 2D drawings, many students need assistance acquiring this skill. Plastic or wooden molecular models can be very helpful, because they can be held, inspected from multiple angles, and rotated.5 Recently, the use of molecular modeling software has made it easier to produce “3D” models for display and manipulation on a computer screen. Computer-based tutorials and practice examples of molecular symmetry are available on the Internet.6 Several authors have described activities using games7,8 and everyday objects9 to help students learn symmetry concepts. The methods described above are very effective in helping students learn to picture molecular rotations, which can be performed with the various types of models. Some students, however, continue to struggle with reflection operations, and many have trouble picturing improper rotations. I believe this difficulty arises from the fact that these operations are different from anything they have prior experience with. Unlike mirrors they have used themselves or those used to demonstrate chirality in organic chemistry, reflection planes in molecular © XXXX American Chemical Society and Division of Chemical Education, Inc.
Received: January 18, 2019 Revised: July 15, 2019
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DOI: 10.1021/acs.jchemed.9b00053 J. Chem. Educ. XXXX, XXX, XXX−XXX
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models of unit cells for teaching crystal structure, and Casas32 describes models designed specifically to teach space symmetry. Scalfani33 presents models for teaching point symmetry and point groups, but these models do not address the difficulties noted above. In this report, I describe models designed to explicitly demonstrate all of the operations of point symmetry, including reflections and improper rotations, as Casas’s models do for space symmetry. In a recent report in this journal, Schiltz and Oliver-Hoyo describe physical models designed to help students visualize symmetry concepts.34 These authors present a clever model in which a transparent reflective surface demonstrates how a particular plane may complete the model of a water molecule, but fails to do so for an ammonia molecule, thus proving that the plane depicted is a symmetry element for one of the molecules but not the other. The permanent nature of this model makes it useful only for the two molecules (and point groups) it is built with. The models presented in this work can be separated along their mirror planes and mounted on a mirror to demonstrate each class of reflection in any of the modeled point groups. Schiltz and Oliver-Hoyo also describe a frame that mounts a molecular model on its principal rotation axis. Rotations about the principal axis can be measured, allowing students to investigate the rotation in a tactile way. Additional axes can be marked on the model, but the corresponding rotations cannot be performed while the model is mounted in the frame. The 3D printed models described here are free to rotate independently around any axis, which makes them more convenient for use in lecture demonstrations. Schiltz and Oliver-Hoyo’s models are designed to be durable but require a variety of materials and access to a machine shop to produce. The models presented here can be made with just a 3D printer and some paint.
Figure 2. 3D printed models of ammonia showing (a) 3-fold rotation and (b) vertical mirror symmetry operations.
shaped to represent the principle order of the axis (i.e., a C3 axis has a triangular cross-section). Holding the axis between the thumb and forefinger allows easy rotation of the molecule through the appropriate angle around each axis. Additional pieces allow the model to be divided in half along mirror planes. The halves are held together with hook-and-loop fasteners that can also be used to mount the model on a double-sided mirror to demonstrate how the mirror plane completes the original model (Figure 2b). Many improper rotation axes are coincident with mirror planes, such as the Sn axes of the Dnh groups. In these cases, the appropriate model will have holes to hold the improper rotation axis. A few point groups (Td and Oh in particular) contain improper rotation axes that are not coincident with other mirror planes. In these cases, separate pieces of the model are included for the improper rotation. The complete model of the molecule can be used as a reference while demonstrating the operation. After noting the orientation of the reference model, the model that splits along the reflection of the improper axis is held in the same position. The model is rotated according to the order of the axis, divided, and stuck to the mirror. At this point, the reflection in the mirror will match half of the reference, even though the physical model does not. Rotating the mirror and the reference 180° will reveal that the reflection in the other side of the mirror matches the other half of the reference. A video of this demonstration is included in the Supporting Information. Additional holes in the atoms of the models allow the mounting of “hats” that can be printed using various colors of plastic. These hats can be used to mark the atoms for demonstration of various additional features of the symmetry. For example, a terminal hydrogen atom can be changed to another element to reduce the symmetry of the molecule. The models can then be used to demonstrate how the symmetry operations of the original group either persist or are destroyed by the reduction in symmetry. An atom can be marked with a hat to aid students in keeping track of its final location after the application of a projection operator (Figure 3a). Some students struggle identifying the fate of the relative phases of p orbitals in projection operators, which can be demonstrated by marking an atom with two hats, as shown in Figure 3b. In many cases, the phases of molecular orbitals can even be modeled by the appropriate use of the hats, as shown in Figure 4.
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MODELS The models described here (Figure 1) represent molecules in seven common point groups, which include all of the possible
Figure 1. Molecular models of the seven point groups included in the set.
types of symmetry operation (Cn, σh, σv, and odd- and evenorder Sn). Each model is composed of a set containing multiple pieces. One piece of each set is a model of the entire molecule, with holes for the insertion of sticks representing each rotation axis in the point group (Figure 2a). The holes and sticks are B
DOI: 10.1021/acs.jchemed.9b00053 J. Chem. Educ. XXXX, XXX, XXX−XXX
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generally well-received by the students. One student noted that the models were “very helpful for visualizing the different operations and axes.” Another believed that “the tools that only allowed you to spin each molecule so far were extremely helpful.” Quantitative evaluation of the effectiveness of the models is difficult because of the small number of students taking the class (about six every other year), but one comment noted that a student “LOVED the symmetry models!!” Such enthusiasm indicates high engagement with a topic that many students find dry or frustrating and is a clear benefit of this technique. One student did note that the models were “more distracting because now I was trying to play with it and pass it.” This student concluded that “it was better when you just showed us yourself, unless one of us asked to see one model specifically.” This is a valid concern, and instructors should consider allowing more time or perhaps taking the models to lab where the students can investigate them at their leisure. From the instructor’s perspective, these models provide a convenient set of visual aids for teaching symmetry. Use of the mirror for demonstrating reflections and improper rotations helps reduce the students’ reliance on their imagination while learning those operations. The hats are particularly useful for helping the students to see where atoms move during symmetry operations, allowing the teacher to focus more on the mathematical implementation of projection operators and spend less time labeling diagrams of the molecules.
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CONCLUSION 3D printing makes it possible to prepare customized models for teaching the concepts of molecular symmetry. The models presented here can be printed with commonly available printers and allow the demonstration of rotation, reflection, and improper rotation operations in a variety of point groups. Students found the models helpful, noting that they made this topic easier to understand, “especially for the more complex symmetry operations.”
Figure 3. 3D printed models of benzene showing hats used to mark (a) an atom and (b) the phases of a p orbital for reference during application of projection operators.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.9b00053. Instructor notes describing how to prepare and use the set of models (PDF, DOC) STL and Makerbot Print files of all of the models and OpenSCAD source files for producing the models (ZIP) Video demonstration of the S4 improper rotation axis (MP4)
Figure 4. 3D printed model of a hydrogen molecule with hats denoting the phases of a σ antibonding molecular orbital.
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HAZARDS Care should be exercised when using a 3D printer to avoid contact with the heated extruder nozzle and hot plastic. In addition, some concerns have been raised about the air quality in the vicinity of a 3D printer.35 Finishing the models generates fine particles of plastic. Safety glasses should be worn, and the work should be completed in a fume hood or with a mask. Assembly of the mirror requires epoxy adhesive. Gloves and safety glasses should be worn during this procedure.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Brian K. Niece: 0000-0002-5963-998X Notes
The author declares no competing financial interest.
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ACKNOWLEDGMENTS This work was performed with the support of an Assumption College Course Load Reduction grant. Liz Hamblett is
RESPONSE TO THE MODELS These models have been used in an upper-level class on molecular structure for chemistry majors, where they were C
DOI: 10.1021/acs.jchemed.9b00053 J. Chem. Educ. XXXX, XXX, XXX−XXX
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(20) Teplukhin, A.; Babikov, D. Visualization of Potential Energy Function Using an Isoenergy Approach and 3D Prototyping. J. Chem. Educ. 2015, 92 (2), 305−309. (21) Griffith, K. M.; Cataldo, R. d.; Fogarty, K. H. Do-It-Yourself: 3D Models of Hydrogenic Orbitals through 3D Printing. J. Chem. Educ. 2016, 93 (9), 1586−1590. (22) Robertson, M. J.; Jorgensen, W. L. Illustrating Concepts in Physical Organic Chemistry with 3D Printed Orbitals. J. Chem. Educ. 2015, 92 (12), 2113−2116. (23) Smiar, K.; Mendez, J. D. Creating and Using Interactive, 3DPrinted Models to Improve Student Comprehension of the Bohr Model of the Atom, Bond Polarity, and Hybridization. J. Chem. Educ. 2016, 93 (9), 1591−1594. (24) Carroll, F. A.; Blauch, D. N. 3D Printing of Molecular Models with Calculated Geometries and p Orbital Isosurfaces. J. Chem. Educ. 2017, 94 (7), 886−891. (25) Carroll, F. A.; Blauch, D. N. Using the Force: ThreeDimensional Printing a π-Bonding Model with Embedded Magnets. J. Chem. Educ. 2018, 95 (9), 1607−1611. (26) de Cataldo, R.; Griffith, K. M.; Fogarty, K. H. Hands-On Hybridization: 3D-Printed Models of Hybrid Orbitals. J. Chem. Educ. 2018, 95 (9), 1601−1606. (27) Dean, N. L.; Ewan, C.; McIndoe, J. S. Applying Hand-Held 3D Printing Technology to the Teaching of VSEPR Theory. J. Chem. Educ. 2016, 93 (9), 1660−1662. (28) Dean, N. L.; Ewan, C.; Braden, D.; McIndoe, J. S. Open-Source Laser-Cut-Model Kits for the Teaching of Molecular Geometry. J. Chem. Educ. 2019, 96 (3), 495−499. (29) Meyer, S. C. 3D Printing of Protein Models in an Undergraduate Laboratory: Leucine Zippers. J. Chem. Educ. 2015, 92 (12), 2120−2125. (30) Scalfani, V. F.; Turner, C. H.; Rupar, P. A.; Jenkins, A. H.; Bara, J. E. 3D Printed Block Copolymer Nanostructures. J. Chem. Educ. 2015, 92 (11), 1866−1870. (31) Rodenbough, P. P.; Vanti, W. B.; Chan, S.-W. 3D-Printing Crystallographic Unit Cells for Learning Materials Science and Engineering. J. Chem. Educ. 2015, 92 (11), 1960−1962. (32) Casas, L.; Estop, E. Virtual and Printed 3D Models for Teaching Crystal Symmetry and Point Groups. J. Chem. Educ. 2015, 92 (8), 1338−1343. (33) Scalfani, V. F.; Vaid, T. P. 3D Printed Molecules and Extended Solid Models for Teaching Symmetry and Point Groups. J. Chem. Educ. 2014, 91 (8), 1174−1180. (34) Schiltz, H. K.; Oliver-Hoyo, M. T. Physical Models That Provide Guidance in Visualization Deconstruction in an Inorganic Context. J. Chem. Educ. 2012, 89 (7), 873−877. (35) Bharti, N.; Singh, S. Three-Dimensional (3D) Printers in Libraries: Perspective and Preliminary Safety Analysis. J. Chem. Educ. 2017, 94 (7), 879−885.
gratefully acknowledged for her assistance in learning how to successfully print 3D models. Tom Burke and Laurie Palumbo of Assumption College Media Services were invaluable in improving the quality of the demonstration video.
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DOI: 10.1021/acs.jchemed.9b00053 J. Chem. Educ. XXXX, XXX, XXX−XXX
