Article Cite This: J. Chem. Educ. XXXX, XXX, XXX−XXX
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3D-Printing Electron Density Isosurface Models and High-Resolution Molecular Models Based on van der Waals Radii Anna S. Grumman and Felix A. Carroll* Department of Chemistry, Davidson College, Davidson, North Carolina 28035, United States
J. Chem. Educ. Downloaded from pubs.acs.org by UNIV OF LOUISIANA AT LAFAYETTE on 05/07/19. For personal use only.
S Supporting Information *
ABSTRACT: 3D printing was used to prepare space-filling models of electron density isosurfaces and high-resolution molecular models on the basis of the van der Waals radii of atoms. Both model types provide students with kinesthetic simulations of steric effects in bimolecular substitution and elimination reactions. The models can be printed in small sizes for individual student use or large sizes for classroom demonstrations. These space-filling models can also enable visually impaired students to experience tangible representations of theoretical surfaces.
KEYWORDS: Hands-On Learning/Manipulatives, Molecular Modeling, Organic Chemistry, Second-Year Undergraduate, Computational Chemistry, Mechanisms of Reactions, Nucleophilic Substitution, Elimination Reactions, Noncovalent Interactions
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INTRODUCTION
SPACE-FILLING MODELS OF ELECTRON DENSITY PROBABILITY ISOSURFACES Internuclear distances and angles indicate spatial relationships of nuclei, but the size and shape of a molecule are determined by the region of molecular electron density that can exclude another chemical entity. In theoretical chemistry, this volume of space is often represented with a three-dimensional isodensity surface (isosurface) composed of points having identical values of local electron density probability (usually stated just as electron density).26 The local electron density represented by a point on an isosurface depends on the total molecular electron density enclosed by the isosurface. An isosurface enveloping a larger percentage of molecular electron density occupies a larger volume of space than does an isosurface enclosing a smaller percentage of electron density. As a result, a point on a smaller isosurface represents greater local electron density than does a point on a larger isosurface for the same structure. These relationships are illustrated for ethyl bromide in Figure 1. The calculated isosurface in which points have electron-density values of 0.01 au (center) encloses 97.2% of the molecular electron density.27 The 0.002 au isosurface of ethyl bromide (right) encloses 99.3% of the total electron density. Although all electron density isosurfaces can be informative, the larger isosurface in Figure 1 has greater relevance for bimolecular processes.28 Isosurface values of 0.002 au and 0.0033 au have been suggested to represent the
The molecular model sets typically used by introductory organic chemistry students represent bonds with thin plastic rods and atoms with small plastic polygons or spheres. These models are helpful when students are learning about molecular geometry, stereochemistry, and conformational analysis. However, the thin rods representing bonds may suggest to students that the electron density of a molecule is localized in small cylinders between nuclei. In addition, the uniform rods imply that covalent bonds involving atoms other than hydrogen are all the same length. The small atom pieces can give students the impression that atoms other than hydrogen are all the same size and that molecular volume is confined to the space occupied by the plastic pieces. Therefore, standard models do not adequately represent a number of important concepts related to intermolecular interactions. In recent years, 3D printing has enabled chemistry instructors to create new kinds of physical models. 3D-printed models can provide unique insights into pressure−volume− temperature relationships,1 potential energy changes associated with conformations or reactions,2−6 orbitals and bonding interactions,7−11 polymer chemistry,12 symmetry,13,14 crystal structures,15 and instrumentation.16−20 3D Printing has also been used to prepare models to illustrate molecular structure.21−25 The next step in model development is 3Dprinting models to teach steric effects in intermolecular interactions. This paper describes two types of space-filling models created for this purpose. © XXXX American Chemical Society and Division of Chemical Education, Inc.
Received: July 24, 2018 Revised: March 26, 2019
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DOI: 10.1021/acs.jchemed.8b00597 J. Chem. Educ. XXXX, XXX, XXX−XXX
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Figure 1. Computer-generated ball-and-spoke model of the minimum energy geometry of ethyl bromide (left) along with its calculated 0.01 au (center) and 0.002 au (right) electron-density isosurfaces.
Figure 2. Photograph of 3D-printed models of the 0.002 au electron density isosurfaces of (clockwise from top left) methyl bromide, ethyl bromide, isopropyl bromide, and tert-butyl bromide.
provided in the Supporting Information. A photograph (Figure 2) of the 3D-printed models of methyl bromide, ethyl bromide, isopropyl bromide, and tert-butyl bromide confirms that the models faithfully replicate the computed isosurfaces.
space occupied by molecules in condensed phases, whereas a 0.001 au isosurface is said to approximate the size of a molecule in the gas phase.26,29,30 To prepare 3D-printed models of electron-density isosurfaces, it was necessary to develop a method to generate STL files from molecular orbital calculations. DFT calculations with Spartan '16 were used to compute the minimum energy geometry of each structure and to generate a data set containing the x, y, and z values of points on the 0.002 au isosurface for the structure.31 MeshLab was then used to generate a stereolithography (STL) file from the data set.32,33 Any defects in an STL file were corrected with netfabb Basic or Meshmixer, which were also used to scale the models for size consistency.34,35 The final STL file was sliced with MakerBot software, and the model was printed with polylactic acid (PLA) filament on a MakerBot Replicator 2 3D printer.36 Details of model preparation as well as the STL files for these models are
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HIGH-RESOLUTION SPACE-FILLING MODELS BASED ON VAN DER WAALS RADII The 3D electron density isosurface models give students a unique perspective on the space-filling properties of molecules. However, these models are monochromatic. To make it easier for students to transition from standard model kits to spacefilling molecular models, it is beneficial to incorporate color into models associating molecular electron density with different nuclei. Kits for assembling space-filling models with colored atom pieces have long been used in biochemistry. In the 1940s, Hirschfelder developed a model set that was later improved by Taylor and then sold by Fisher Scientific. In these B
DOI: 10.1021/acs.jchemed.8b00597 J. Chem. Educ. XXXX, XXX, XXX−XXX
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Figure 3. Models of ethyl bromide assembled from FHT (left) and CPK (center) components with a 3D-printed van der Waals radii model of ethyl bromide (right).
data. Using 3D-printed models based on van der Waals radii for intermolecular processes in the liquid phase requires validation that the space-filling properties of van der Waals radii models match the electron-density isosurface appropriate for that phase. By displaying the van der Waals radii model of ethyl bromide (solid) and its 0.002 au electron density isosurface (dots) together, Figure 4 shows that there is a close
models, atoms were represented by colored wooden pieces that were spherical except for flattened surfaces where they could be connected to other wooden pieces with metal connectors. The flattened surfaces were oriented so that the models could represent common bond angles, such as 109° 28′ for tetravalent carbon.37 An example of a Fisher−Hirschfelder− Taylor (FHT) model of ethyl bromide is shown on the left in Figure 3. In 1953, Corey and Pauling reported the design of spacefilling models for use in protein research.38 Relative atom sizes in the Corey−Pauling models were based on element-specific dimensions, termed van der Waals radii by Pauling, which were determined from crystal structures.39 These Corey−Pauling models were designed to have the scale 1 in. = 1 Å. Later, Koltun patented a set of plastic atoms and connectors with similar design but smaller scale (0.5 in./Å).37,40 These models became known as Corey−Pauling−Koltun (CPK) models and have been widely used in biochemistry.41−43 A model of ethyl bromide constructed with CPK components is shown in the center of Figure 3.44 There are a number of reasons why students in introductory organic chemistry classes do not use such space-filling model kits, but complexity and cost are major factors. Several different components are required to construct models showing even common bonding patterns of a given atom.45−47 In addition, model-design choices may require parts representing some atoms (such as bromine in Figure 3) to have nonspherical contours. These shapes do not bother experts in the field, but such components could confuse beginning organic chemistry students. 3D printing can overcome these disadvantages of commercial space-filling model kits. 3D-printed models are not assembled from complex or expensive components. In addition, they can depict calculated geometries of even highly strained structures in ways that model components designed for just the most common geometries cannot.11 However, a requirement for printing space-filling models for educational use is a demonstration that the models adequately represent the steric effects they are intended to teach. For representing intermolecular steric interactions in solution, therefore, such space-filling models must correspond closely to 0.002 au electron-density isosurfaces.29,30 Virtual representations based on van der Waals radii are options in some computational programs, but it is important to note that Pauling based van der Waals radii on crystal-structure
Figure 4. Comparison of a van der Waals radii model of ethyl bromide (solid) with its 0.002 au electron-density isosurface (dots).
match between the two surfaces. Nevertheless, there are differences between the two model types.48,49 The concept of a van der Waals radius implies that the electron density around a nucleus is spherical. Both experimental data and calculations indicate that electron density around a bonded atom is elliptical, however, with the major axis perpendicular to the bond line between two atoms and the minor axis along the bond line.50,51 This anisotropic distribution of electron density is most evident near the bromine atom of ethyl bromide in Figure 4. Fortunately, differences between the surfaces are smaller near the carbon and hydrogen atoms. It can be concluded, therefore, that 3D-printed van der Waals radii models can adequately represent intermolecular steric effects of alkyl groups for introductory organic chemistry students. C
DOI: 10.1021/acs.jchemed.8b00597 J. Chem. Educ. XXXX, XXX, XXX−XXX
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Figure 5. Computer rendering of the STL files for van der Waals radii models of alkyl bromides as viewed from the backside of the Cα−Br bond. From left to right, the compounds are methyl bromide, ethyl bromide, isopropyl bromide, and tert-butyl bromide. The α carbons were given a distinctive color to highlight their surfaces. Note the small portion of the α carbon surface that is clearly visible in the model of tert-butyl bromide.
Figure 6. Painted van der Waals models of (clockwise from top left) methoxide ion, methyl bromide, ethyl bromide, isopropyl bromide, tert-butyl bromide, and tert-butoxide ion. The alkoxide ions differ from their alkyl bromide counterparts in heteroatom color (red for oxygen and dark red for bromine) and van der Waals radius.
STL files for van der Waals radii models were prepared in several steps, beginning with the minimum-energy geometries calculated as before. The atomic coordinates of a structure were saved in a Protein Data Bank format (PDB) file. The PDB file was imported into VMD, where the structure representation was changed to van der Waals, and the sphere resolution was set to 47.52,53 The STL files rendered with VMD were checked, repaired, and scaled as before. Then, the models were printed with PLA filament on a MakerBot Replicator 2 or Ultimaker 3 Extended 3D printer.36,54 The models printed in this way were very high resolution, as shown by the model of ethyl bromide in Figure 3. Students could readily identify the bromine, carbon, and hydrogen atoms solely on the basis of the radii of those atoms. It is especially important that students could easily distinguish the backsides of the α carbons of the alkyl halides, particularly in tert-butyl bromide (Figure 5). Recognition of the surface of the α carbon
is essential if students are to understand the role of steric hindrance in substitution and elimination reactions.55 In order to provide students hands-on experience with a set of space-filling models for studying bimolecular substitution and elimination reactions, van der Waals radii models of methyl bromide, ethyl bromide, isopropyl bromide, tert-butyl bromide, methoxide ion, and tert-butoxide ion were printed (Figure 6). Details of model preparation as well as STL files for these models are provided in the Supporting Information. These models were then painted in CPK colors so that students could relate them more directly to the models constructed with their own molecular model sets.56
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RESULTS AND DISCUSSION Both electron density isosurface and van der Waals radii models have been used to teach SN2 and E2 reactions in firstsemester introductory organic chemistry classes. Groups of D
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four students at a time met with an instructor during a short segment of their laboratory period.57 The instructor first discussed the concept of an electron density isosurface and described the preparation of the models. Students then compared a ball-and-stick model of ethyl bromide to its electron density isosurface model and noted the volume of electron density shown by the isosurface model. The instructor next introduced the van der Waals radii models and compared them to the electron density isosurface models. Then students were asked to use models of methoxide ion and ethyl bromide to demonstrate an SN2 reaction. Observing how students manipulated the models gave the instructor a quick indication of their understanding of the reaction pathway. Almost all of the students initially brought the methoxide ion to the backside of the ethyl bromide α carbon atom so that the methoxide carbon, the oxygen atom, and the methyl bromide α carbon were oriented in a straight line. This allowed the instructor to point out that the transition state geometry requires a developing C−O···C bond angle nearer 109°, as shown in Figure 7.58
Figure 8. Steric hindrance to contact of methoxide oxygen with the α carbon of tert-butyl bromide and collision of oxygen with an anticoplanar hydrogen atom instead.
concepts that can take much longer to grasp from textbook figures or ball-and-stick models.62 Two additional uses of these space-filling models may be noted. First, the electron density isosurface and van der Waals radii models can provide concrete representations of computer-generated images for students who are blind or visually impaired.63 Second, the scale of the 3D-printed models is limited only by the print-volume capacities of 3D printers. Therefore, instructors can prepare very large models for classroom demonstrations. As an example, Figure 9 shows
Figure 7. Contact of methoxide oxygen with the backside of the α carbon of ethyl bromide.
Students then used the van der Waals radii models to explore steric effects in SN2 and E2 reactions involving alkyl halides and alkoxides (Figures 7 and 8).59 Through this simulation, they not only saw but also felt the differences in steric hindrance for reaction of a nucleophile with methyl and 1°, 2°, and 3° alkyl halides. The reactivity trend had been discussed in class, but students found that the physical sensation of trying to bring the methoxide oxygen into contact with the backsides of the α carbons of different alkyl bromides made the concepts more real to them. Students also experienced the greater steric barrier to the SN2 reaction and thus the greater chance for an E2 reaction when tert-butoxide ion was the nucleophile−base.58,60 After students had experienced the space-filling models, they were asked to indicate whether the models helped them understand important concepts of bimolecular substitution and elimination reactions.61 Sixty of the 61 students responded affirmatively (see the Supporting Information), with comments such as, “I finally see why steric hindrance matters in SN2.” These comments indicate that the kinesthetic experience of studying substitution and elimination reactions with the electron density isosurface and van der Waals radii models may help students understand in just a few minutes important
Figure 9. Larger 3D-printed models for classroom use.
much larger models of tert-butyl bromide and methoxide ion. The model of methoxide was printed as a single model, whereas the tert-butyl bromide model was printed as two sections that were glued together before painting. Another educational benefit of these space-filling models is that they can contribute substantially to the development of students as scientists. Robinson noted that “models are ways of thinking about, representing, and manipulating ideas” and that “the ability to accept and use different theories and models for the same system generally develops slowly, if at all, in E
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students.”64 If students always use the same kind of molecular model set, they may always think about chemistry in terms of those small plastic pieces. By experiencing the space-filling models reported here, however, students in introductory organic chemistry classes will learn more quickly that balland-stick models give incomplete representations of intermolecular interactions. As they develop an understanding that all models have limitations, they will become more open to consideration of new conceptual as well as physical models of chemistry in the future.65
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(8) Robertson, M. J.; Jorgensen, W. L. Illustrating Concepts in Physical Organic Chemistry with 3D Printed Orbitals. J. Chem. Educ. 2015, 92 (12), 2113−2116. (9) 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. (10) 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. (11) 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. (12) 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. (13) 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. (14) Casas, L.; Estop, E. Virtual and Printed 3D Models for Teaching Crystal Symmetry and Point Groups. J. Chem. Educ. 2015, 92 (8), 1338−1343. (15) 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. (16) Porter, L. A., Jr.; Washer, B. M.; Hakim, M. H.; Dallinger, L. F. User-Friendly 3D Printed Colorimeter Models for Student Exploration of Instrument Design and Performance. J. Chem. Educ. 2016, 93 (7), 1305−1309. (17) Giannini, J.; Stewart, C. Inexpensive, Open Source Epifluorescence Microscopes. J. Chem. Educ. 2016, 93 (7), 1310−1315. (18) Porter, L. A., Jr.; Chapman, C. A.; Alaniz, J. A. Simple and Inexpensive 3D Printed Filter Fluorometer Designs: User-Friendly Instrument Models for Laboratory Learning and Outreach Activities. J. Chem. Educ. 2017, 94 (1), 105−111. (19) Piunno, P. A. E. Teaching the Operating Principles of a Diffraction Grating Using a 3D-Printable Demonstration Kit. J. Chem. Educ. 2017, 94 (5), 615−620. (20) Higman, C. S.; Situ, H.; Blacklin, P.; Hein, J. E. Hands-On Data Analysis: Using 3D Printing to Visualize Reaction Progress Surfaces. J. Chem. Educ. 2017, 94 (9), 1367−1371. (21) Penny, M. R.; Cao, Z. J.; Patel, B.; Sil dos Santos, B.; Asquith, C. R. M.; Szulc, B. R.; Rao, Z. X.; Muwaffak, Z.; Malkinson, J. P.; Hilton, S. T. Three-Dimensional Printing of a Scalable Molecular Model and Orbital Kit for Organic Chemistry Teaching and Learning. J. Chem. Educ. 2017, 94 (9), 1265−1271. (22) Jones, O. A. H.; Spencer, M. J. S. A Simplified Method for the 3D Printing of Molecular Models for Chemical Education. J. Chem. Educ. 2018, 95 (1), 88−96. (23) Paukstelis, P. J. MolPrint3D: Enhanced 3D Printing of Balland-Stick Molecular Models. J. Chem. Educ. 2018, 95 (1), 169−172. (24) Van Wieren, K.; Tailor, H. N.; Scalfani, V. F.; Merbouh, N. Rapid Access to Multicolor Three-Dimensional Printed Chemistry and Biochemistry Models Using Visualization and Three-Dimensional Printing Software Programs. J. Chem. Educ. 2017, 94 (7), 964−969. (25) Meyer, S. C. 3D Printing of Protein Models in an Undergraduate Laboratory: Leucine Zippers. J. Chem. Educ. 2015, 92 (12), 2120−2125. (26) Matta, C. F.; Gillespie, R. J. Understanding and Interpreting Molecular Electron Density Distributions. J. Chem. Educ. 2002, 79 (9), 1141−1152. (27) Electron density is given in atomic units (au). The value of 1 au of electron density is one electron per bohr.3 One bohr is 5.29177 × 10−11 m. The percentages of electron density enclosed by the isosurfaces were obtained with Spartan '16. (28) Shusterman, G. P.; Shusterman, A. J. Teaching Chemistry with Electron Density Models. J. Chem. Educ. 1997, 74, 7, 771−776 noted that isosurfaces representing higher electron density are useful for depicting bonding within a structure.
ASSOCIATED CONTENT
* Supporting Information S
The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.8b00597. Detailed procedures for preparing STL files of electron density isosurface models and van der Waals radii models (PDF) Compressed folder containing STL files for printing 0.002 au electron density isosurface models of methyl bromide, ethyl bromide, isopropyl bromide, tert-butyl bromide, methoxide ion, and tert-butoxide ion and STL files for printing van der Waals radii models of methyl bromide, ethyl bromide, isopropyl bromide, tert-butyl bromide, methoxide ion, and tert-butoxide ion (ZIP)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Felix A. Carroll: 0000-0002-1831-5997 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS Davidson College supported this project, and Michael Bovino assisted with the model evaluations. Sean Ohlinger of Wavefunction, Inc. provided guidance for the electron density isosurface calculations.
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REFERENCES
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(29) Bader, R. F. W.; Carroll, M. T.; Cheeseman, J. R.; Chang, C. Properties of Atoms in Molecules: Atomic Volumes. J. Am. Chem. Soc. 1987, 109, 26, 7968−7979 and references therein. (30) Bentley, J. Electron Density as a Descriptor of Thermal Molecular Size. J. Phys. Chem. A 2000, 104 (42), 9630−9635. (31) Spartan '16 is a product of Wavefunction, Inc. The DFT calculations used the default settings for an equilibrium geometry calculation (ωB97X-D functional and the 6-31G* basis set). (32) (a) MeshLab. http://www.meshlab.net/ (accessed March 2019). (b) Cignoni, P.; Callieri, M.; Corsini, M.; Dellepiane, M.; Ganovelli, F.; Ranzuglia, G. MeshLab: an Open-Source Mesh Processing Tool. Proceedings of the 2008 Eurographics Italian Chapter Conference, Salerno, Italy, 2008; The Eurographics Association, 2008; pp 129−136, DOI: 10.2312/LocalChapterEvents/ItalChap/ItalianChapConf2008/129-136. (33) Fagan, T. J. How to Create an STL file from a XYZ file in MeshLab, 2014. Fab Academy. http://fabacademy.org/archives/ 2014/tutorials/pointcloudToSTL.html (accessed March 2019). (34) Sather, B. Netfabb Basic is now just Netfabb, 2016. Netfabb Additive Manufacturing Blog. https://blogs.autodesk.com/netfabb/ 2016/10/18/netfabb-basic-is-now-just-netfabb/ (accessed March 2019). (35) Autodesk Meshmixer. http://www.meshmixer.com/ (accessed March 2019). (36) MakerBot Learning Tips: What is MakerBot Desktop?, 2016. MakerBot. https://www.makerbot.com/media-center/2016/07/22/ makerbot-learning-tips-makerbot-desktop (accessed March 2019). (37) (a) Francoeur, E. The Forgotten Tool: The Design and Use of Molecular Models. Soc. Stud. Sci. 1997, 27 (1), 7−40. (b) Francoeur, E. Molecular Models and the Articulation of Structural Constraints in Chemistry. In Tools and Modes of Representation in the Laboratory Sciences; Klein, U., Ed.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2001; pp 95−115. (38) Corey, R. B.; Pauling, L. Molecular Models of Amino Acids, Peptides, and Proteins. Rev. Sci. Instrum. 1953, 24 (8), 621−627. (39) Pauling, L. The nature of the chemical bond and the structure of molecules and crystals: An introduction to modern structural chemistry, 3rd ed.; Cornell University Press: Ithaca, NY, 1960. (40) Koltun, W. L. Space Filling Atomic Units and Connectors for Molecular Models. U.S. Patent 3,170,246, 1965. (41) Gurd, F. R. N. The Use of Corey-Pauling-Koltun Space-Filling Models in Teaching. Biochem. Educ. 1974, 2 (2), 27−29. (42) Clarke, F. H. New Skeletal-Space-Filling Models: A model of an enzyme active site. J. Chem. Educ. 1977, 54, 4, 230−235 described an alternative model set. (43) For some examples of instructor-constructed space-filling models in organic chemistry, see (a) Lambert, F. L. Molecular Models for Lecture Demonstrations in Organic Chemistry. J. Chem. Educ. 1953, 30 (10), 503−507. (b) Kenney, M. E. Lecture-Size Molecular Models with Magnetic Couplings. J. Chem. Educ. 1962, 39 (3), 129. (c) Kellett, J. C., Jr.; Martin, A. N. Inexpensive Space-Filling Display Models. J. Chem. Educ. 1966, 43 (7), 374−375. (44) CPK Atomic Models, Research and Teaching Sets. Harvard Apparatus. http://www.harvardapparatus.com/cpkr-atomic-modelsresearch-and-teaching-sets.html (accessed March 2019). (45) The eight components of the CPK model of ethyl bromide in Figure 3 were purchased for $41.54, which is more than the cost of a student molecular model set. (46) For example, eleven atom pieces are available for carbon. https://www.harvardapparatus.com/catalogsearch/result/index/?p= 1&q=cpk+atomic+models+carbon+atom (accessed March 2019). (47) Even so, the necessary atom components may not be available for unusual or strained structures: Boyd, D. R. Space-Filling Molecular Models of Four-Membered Rings. J. Chem. Educ. 1976, 53 (8), 483− 488. (48) Dean, P. A. W. Facets of van der Waals Radii That Are Not Commonly Included in Undergraduate Textbooks. J. Chem. Educ. 2014, 91 (1), 154−157.
(49) For discussions of the variation of van der Waals radii values from one source to another, see (a) Badenhoop, J. K.; Weinhold, F. Natural steric analysis: Ab initio van der Waals radii of atoms and ions. J. Chem. Phys. 1997, 107 (14), 5422−5432. (b) Hu, S.-Z.; Zhou, Z.-H.; Xie, Z.-X.; Robertson, B. E. A comparative study of crystallographic van der Waals radii. Z. Kristallogr. - Cryst. Mater. 2014, 229 (7), 517−523. (50) (a) Nyburg, S. C.; Faerman, C. H. A revision of van der Waals atomic radii for molecular crystals: nitrogen, oxygen, fluorine, sulfur, chlorine, selenium, bromine and iodine bonded to carbon. Acta Crystallogr., Sect. B: Struct. Sci. 1985, B41 (4), 274−279. (b) Nyburg, S. C.; Faerman, C. H.; Prasad, L. A revision of van der Waals atomic radii for molecular crystals. II. Hydrogen bonded to carbon. Acta Crystallogr., Sect. B: Struct. Sci. 1987, B43 (1), 106−110. (51) Eramian, H.; Tian, Y.-H.; Fox, Z.; Beneberu, H. Z.; Kertesz, M. On the Anisotropy of van der Waals Atomic Radii of O, S, Se, F, Cl, Br, and I. J. Phys. Chem. A 2013, 117 (51), 14184−14190. (52) VMD was developed by the Theoretical and Computational Biophysics Group in the Beckman Institute for Advanced Science and Technology at the University of Illinois at Urbana-Champaign Humphrey, W.; Dalke, A.; Schulten, K. VMD-Visual Molecular Dynamics. J. Mol. Graphics 1996, 14 (1), 33−38. (53) VMD can also render STL files of CPK representations, but the default CPK atom sizes in VMD are much smaller than the default van der Waals radii spheres. Therefore, CPK atom sizes must be enlarged by an arbitrary amount to produce models that resemble electron-density surfaces. See Grayson, P.; Gullingsrud, J.; Isralewitz, B.; Norris, D.; Stone, J. CPK. In VMD User’s Guide, Version 1.7.1; Theoretical Biophysics Group, University of Illinois and Beckman Institute, 2001. http://www.ks.uiuc.edu/Research/vmd/vmd-1.7.1/ ug/node56.html (accessed March 2019). (54) Ultimaker Cura software. https://ultimaker.com/en/products/ cura-software (accessed March 2019). (55) Diaz-Allen, C.; Sibbald, P. A. Using 3D Printing to Model Steric Interactions. Chem. Educ. 2016, 21, 10−12 reported preparation of space-filling models that were lower-resolution than those described here. (56) Although FHT models and some CPK models used brown to indicate bromine, the contemporary CPK color scheme was used here, with red for oxygen and dark red for bromine: CPK Coloring. Wikipedia. https://en.wikipedia.org/wiki/CPK_coloring (accessed March 2019). (57) No hazards are anticipated in the use of the models. Instructors should be aware of air quality concerns associated with 3D printing, but students need not be involved in model preparation. See Bharti, N.; Singh, S. Three-Dimensional (3D) Printers in Libraries: Perspective and Preliminary Safety Analysis. J. Chem. Educ. 2017, 94 (7), 879−885. (58) Transition state geometries were calculated with Spartan '16. Hartree−Fock calculations (using the 6-31G* basis set) for methoxide and methyl bromide found the angle of the developing C−O−C bond to be 109.2° in a solvent with a dielectric constant of 37.2. With tert-butoxide as the nucleophile, the angle of the developing bond was 129.8° in the same solvent. Bringing the space-filling models together in the correct orientation is important for demonstrating steric effects, especially when tert-butoxide is the nucleophile. (59) This exercise could reinforce the concepts of a computational laboratory experience on bimolecular substitution and elimination reactions. For example, see Csizmar, C. M.; Daniels, J. P.; Davis, L. E.; Hoovis, T. P.; Hammond, K. A.; McDougal, O. M.; Warner, D. L. Modeling SN2 and E2 Reaction Pathways and Other Computational Exercises in the Undergraduate Organic Chemistry Laboratory. J. Chem. Educ. 2013, 90 (9), 1235−1238. (60) Students also observed that increasing methyl substitution on the α carbon of an alkyl halide increases the number of β protons that can be abstracted in an E2 reaction. The instructor was careful to emphasize, however, that the primary effect of increasing the number of methyl substituents is to decrease the ΔG‡ for the E2 reaction by G
DOI: 10.1021/acs.jchemed.8b00597 J. Chem. Educ. XXXX, XXX, XXX−XXX
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about 4 kcal/mol with each α-methylation: Rablen, P. R.; McLarney, B. D.; Karlow, B. J.; Schneider, J. E. How Alkyl Halide Structure Affects E2 and SN2 Reaction Barriers: E2 Reactions Are as Sensitive as SN2 Reactions. J. Org. Chem. 2014, 79 (3), 867−879. (61) The instructor conducting the exercise was neither the laboratory instructor nor the lecture professor for these students. The students were told that neither of the other two instructors would see their comments and that their comments would not affect course grades. (62) For discussions of kinesthetic experiences and related topics, see (a) Shams, L.; Seitz, A. R. Benefits of multisensory learning. Trends Cognit. Sci. 2008, 12 (11), 411−417. (b) Bivall, P.; Ainsworth, S.; Tibell, L. A. E. Do Haptic Representations Help Complex Molecular Learning? Sci. Educ. 2011, 95 (4), 700−719. (c) Wu, H.-K.; Shah, P. Exploring Visuospatial Thinking in Chemistry Learning. Sci. Educ. 2004, 88 (3), 465−492. (d) Cook, M.; Wiebe, E. N.; Carter, G. The Influence of Prior Knowledge on Viewing and Interpreting Graphics with Macroscopic and Molecular Representations. Sci. Educ. 2008, 92, 5, 848−867 and references therein. (e) Mohamed-Salah, B.; Alain, D. To what degree does handling concrete molecular models promote the ability to translate and coordinate between 2D and 3D molecular structure representations? A case study with Algerian students. Chem. Educ. Res. Pract. 2016, 17 (4), 862−877. (f) Saveć, V. F.; Vrtacnik, M.; Gilbert, J. K. Evaluating the Educational Value of Molecular Structure Representations. In Visualization in Science Education; Gilbert, J. K., Ed.; Springer: Dordrecht, The Netherlands, 2005; pp 269−300. (g) Sivilotti, P. A. G.; Pike, S. M. The Suitability of Kinesthetic Learning Activities for Teaching Distributed Algorithms. In SIGCSE '07, Proceedings of the 38th SIGCSE technical symposium on Computer science education, Covington, KY, March 7−10, 2007; AMC Publications, 2007. https://dl.acm.org/citation. cfm?id=1227438#references (accessed March 2019). (h) Lujan, H. L.; DiCarlo, S. E. Too much teaching, not enough learning: what is the solution? Adv. Physiol. Educ. 2006, 30 (1), 17−22. (i) Kontra, C.; Lyons, D. J.; Fischer, S. M.; Beilock, S. L. Physical Experience Enhances Science Learning. Psychol. Sci. 2015, 26 (6), 737−749. (j) Freeman, S.; Eddy, S. L.; McDonough, M.; Smith, M. K.; Okoroafor, N.; Jordt, H.; Wenderoth, M. P. Active learning increases student performance in science, engineering, and mathematics. Proc. Natl. Acad. Sci. U. S. A. 2014, 111 (23), 8410−8415. (63) For papers on teaching chemistry to visually impaired students, see (a) Poon, T.; Ovadia, R. Using Tactile Learning Aids for Students with Visual Impairments in a First-Semester Organic Chemistry Course. J. Chem. Educ. 2008, 85 (2), 240−242. (b) Boyd-Kimball, D. Adaptive Instructional Aids for Teaching a Blind Student in a Nonmajors College Chemistry Course. J. Chem. Educ. 2012, 89 (11), 1395−1399. (c) Wedler, H. B.; Cohen, S. R.; Davis, R. L.; Harrison, J. G.; Siebert, M. R.; Willenbring, D.; Hamann, C. S.; Shaw, J. T.; Tantillo, D. J. Applied Computational Chemistry for the Blind and Visually Impaired. J. Chem. Educ. 2012, 89 (11), 1400−1404. (d) Supalo, C. A.; Isaacson, M. D.; Lombardi, M. V. Making Hands-On Science Learning Accessible for Students Who Are Blind or Have Low Vision. J. Chem. Educ. 2014, 91 (2), 195−199. (e) Melaku, S.; Schreck, J. O.; Griffin, K.; Dabke, R. B. Interlocking Toy Building Blocks as Hands-On Learning Modules for Blind and Visually Impaired Chemistry Students. J. Chem. Educ. 2016, 93 (6), 1049−1055. (f) Supalo, C. A. ConfChem Conference on Interactive Visualizations for Chemistry Teaching and Learning: Concerns Regarding Accessible Interfaces for Students who are Blind or Have Low Vision. J. Chem. Educ. 2016, 93 (6), 1156−1159. (64) Robinson, W. R. Learning about Atoms, Molecules, and Chemical Bonds: A Case Study of Multiple-Model Use. J. Chem. Educ. 2000, 77 (9), 1110−1111. (65) For a discussion of the role of models in organic chemistry, see Carroll, F. A. Perspectives on Structure and Mechanism in Organic Chemistry, 2nd ed.; Wiley: Hoboken, 2010.
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DOI: 10.1021/acs.jchemed.8b00597 J. Chem. Educ. XXXX, XXX, XXX−XXX
