3D Printing of Molecular Models with Calculated Geometries and p

Article pubs.acs.org/jchemeduc

3D Printing of Molecular Models with Calculated Geometries and p Orbital Isosurfaces Felix A. Carroll* and David N. Blauch Department of Chemistry, Davidson College, Davidson, North Carolina 28035, United States S Supporting Information *

ABSTRACT: 3D printing was used to prepare models of the calculated geometries of unsaturated organic structures. Incorporation of p orbital isosurfaces into the models enables students in introductory organic chemistry courses to have handson experience with the concept of orbital alignment in strained and unstrained π systems. KEYWORDS: Molecular Modeling, Organic Chemistry, Computational Chemistry, Aromatic Compounds, Conformational Analysis, Second-Year Undergraduate, Hands-On Learning/Manipulatives, Alkenes

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INTRODUCTION Molecular models are indispensable learning aids in organic chemistry. They give students hands-on experience with aspects of molecular geometry, conformation, and stereochemistry that drawings or computer-generated images cannot provide. An important limitation of widely used student molecular model sets, however, is that they do not represent π bonding with p orbital isosurfaces. Student model sets often use a pair of curved bond connectors to represent a double bond (Figure 1,

they are designed for the construction of structures having typical bonding parameters, such as bond angles of 109.5° for tetravalent carbon. Some highly strained structures cannot be constructed with student model sets. Other structures can be built, but the molecular strain must be accommodated by distortion of plastic bond pieces and not by variations in bond angles. Therefore, these model sets can give students an incomplete view of the origins of molecular strain. 3D printing is now being used to create entirely new physical models for chemical education. We introduced 3D models of potential energy surfaces to teach conformational analysis and the energetics of competitive reaction pathways as well as 3D models of P−Vm−T relationships to teach fundamental thermodynamic concepts.2−4 Now we have used 3D printing to develop a series of molecular models in which p orbital isosurfaces are incorporated into models of the calculated geometries of stable and highly strained olefins and conjugated π systems. These models enable students to examine unsaturated structures from a variety of perspectives in order to discover the roles that geometry and orbital alignment play in their energies.

Figure 1. Model of ethene assembled with a molecular model set (left) and the σ, π representation of π bonding (right).

left), and triple bonds are made using three curved bond connectors. Such models represent the planar geometry of alkenes and the linear geometry of alkynes quite well.1 However, these models are not consistent with textbook and class discussions of double bonds in terms of σ bonds formed by overlap of sp2 hybrid orbitals and π bonds resulting from the overlap of parallel p orbitals (Figure 1, right). Another important limitation of the molecular model sets commonly used by beginning organic chemistry students is that © XXXX American Chemical Society and Division of Chemical Education, Inc.

Received: November 30, 2016 Revised: May 5, 2017

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DOI: 10.1021/acs.jchemed.6b00933 J. Chem. Educ. XXXX, XXX, XXX−XXX

Journal of Chemical Education

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MODEL PREPARATION Density functional theory (DFT) calculations in Spartan ’16 were carried out to determine the minimum-energy geometry of each structure described here.5 The resulting atomic coordinates were saved in Protein Data Bank (PDB) file format. Virtual Molecular Dynamics (VMD)6 was used to produce a stereolithography (STL) file for each structure.7 Each STL file was checked for defects, and any needed repairs were made with netfabb Basic.8 Then each STL file was scaled in 123D Design9 so that the printed 3D models would have consistent dimensions. In order to incorporate 3D representations of p orbitals into the models, an isosurface was defined using the value of ψ2 that enclosed 90% of the electron density of the hydrogen 2pz wave function.10 Points lying on the isosurface were organized into triangular elements, which were stored in a virtual reality modeling language (VRML) file. The VRML file was converted to an STL file with Blender,11,12 and then 123D Design was used to align the p orbital isosurface with its carbon atom. STL files for the molecular skeleton and the p orbital isosurfaces were then exported with 123D Design. Initially, the STL files were printed in one or two colors with acrylonitrile−butadiene−styrene terpolymer (ABS) filament on a FlashForge Creator Pro 3D printer. The resulting 3D models could be used as produced or could be hand-painted to make the atoms, bonds, and isosurfaces more evident for students. Because 3D printing can be technically challenging and detailed painting of molecular models can be time-consuming, we found it worthwhile to have many of the models printed commercially. In these cases, Meshmixer13 was used to color the atoms, bonds, and isosurfaces, and the resulting VRML files were uploaded to a commercial 3D printing service. The discussion below includes photographs of the commercially prepared full-color models, and the Supporting Information provides STL files for the models included here.

Figure 4. 3D model of the allyl system with p orbital isosurfaces.

Figure 5. Line formulas for (a) s-trans-1,3-pentadiene and (b) 1,4pentadiene.

many models locally or the cost to have many models printed commercially. Therefore, the most effective way to use the 3D models is for the instructor to meet with students individually or in pairs for short periods during a regular laboratory period. In this way, each student can hold the models and examine them closely while discussing them with an instructor. The simplest model to prepare was that of ethene (Figure 2). It should be noted that the shape of the p orbital isosurface was determined by computation, but the size of the orbital isosurfaces in this 3D model was arbitrary. The isosurfaces in ethene were scaled so that they almost touched, and then that same size was used for all of the other models. The closeness of adjacent lobes in other models thus provides a visual indication of bond lengths in other π systems. In most of the full-color models, red and blue were used to indicate the different phases of the p orbital wave function. While p orbital relationships in ethene are usually evident to beginning organic students, the ethene model provides a convenient introduction to the 3D models so that students can more easily understand other systems. The next 3D model represents the allyl system, and it can help students bridge the gap between valence bond and molecular orbital representations of conjugated systems. For example, the resonance description of allyl in Figure 3 can be problematic to beginning students who primarily conceptualize organic structures as line formulas. When these students are able to rotate a physical 3D model of the allyl system and discover its symmetry (Figure 4), they understand more readily why the allyl cation is a single chemical entity. Similarly, the line formulas for conjugated and nonconjugated dienes (Figure 5) may not seem significantly different to some students. However, the 3D models of these systems (Figure 6) make it clearer to students that the conjugated structure is electronically different from the isolated diene. In addition, students may note that the separation of the p orbital isosurfaces on carbons 2 and 3 of 1,3-pentadiene is greater than that between the p orbital isosurfaces on carbons 1 and 2. Because the models are based on calculated geometries, the orbital separations indicate that the C2−C3 bond length is greater than the C1−C2 bond length. The 3D models can thus be used to stimulate discussions about the relationship of bond length to bond order in conjugated systems. 3D models also help students understand the conformers of 1,3-butadiene and the transition structure for their interconversion. Figure 7 shows 3D models of s-gauche-1,3-butadiene (left), the transition structure for s-gauche to s-trans conversion (center), and s-trans-1,3-butadiene.14 Textbooks may represent

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USE OF THE MODELS IN ORGANIC CHEMISTRY CLASSES There are several ways to use 3D models in introductory organic chemistry classes. Projecting an image of a model with a

Figure 2. 3D model of ethene with p orbital isosurfaces.

Figure 3. Resonance description of the allyl cation.

document camera allows everyone in the class to view the model as it is rotated in space and different perspectives are described by the instructor. However, this approach deprives students of the tactile experience that the models make possible. Having each student examine a model during class is effective only if there are enough models for every student to examine a structure at the same time. This approach may be impracticable, however, because of the time required to print B



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Figure 6. 3D models with p orbital isosurfaces for 1,4-pentadiene (left) and 1,3-pentadiene (right).

Figure 7. 3D models for s-gauche-1,3-butadiene (left), the transition structure for s-gauche to s-trans interconversion (center), and s-trans-1,3butadiene.

Figure 9. Line drawing of COT with p orbitals.

Figure 8. Energy profile calculated with DFT for rotation of 1,3butadiene from the s-cis conformation to the local energy minimum for the s-gauche conformation and then over the energy maximum to the s-trans conformation.

one conformer of 1,3-butadiene as s-cis, with a C−C−C−C dihedral angle of 0°. However, the local energy minimum near 0° was found by DFT to have a C−C−C−C dihedral angle of 33.7°. The instability of the planar s-cis geometry is attributed to steric strain involving hydrogens on C1 and C4.15 Twisting about the C2−C3 bond reduces that steric strain, but at the cost of decreasing the p orbital overlap on carbons 2 and 3. Thus, the s-gauche conformation represents the best

Figure 10. 3D model of the calculated geometry of cyclooctatetraene with p orbital isosurfaces.

compromise between opposing energetic consequences of rotation about the C2−C3 bond. C



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Figure 11. Line drawing of trans-cycloheptene. Figure 13. (left) Twisting of the π bond and (right) pyramidalization of olefinic carbons of trans-cycloheptene.22

Discussing these 3D models of 1,3-butadiene with students leads naturally to a consideration of the energy profile for a 180° rotation about the C2−C3 bond (Figure 8). The s-gauche conformer is lower in energy than the s-cis geometry for the reasons discussed above. The s-trans conformation is lowest in energy because there is no steric repulsion between C1 and C4 and the p orbitals are all parallel. If p orbital alignment were the only determinant of conformational energy, the highest energy along the dihedral angle coordinate might be expected to occur when the dihedral angle is 90° because the p orbitals on C2 and C3 would be orthogonal. However, the energy profile calculated with DFT at 5° dihedral angle increments had an energy maximum at 100°, which can again be related to steric interactions.16,17 This result provides an opportunity to remind students that all chemistry models have limitations and that typical model sets represent atoms as spheres that are much smaller than would be the case if they represented van der Waals radii in direct proportion to bond lengths.18 STL files for 3D models of several aromatic systems that are discussed in introductory organic chemistry courses were also prepared, including benzene, cyclopentadienyl anion, benzyl cation, naphthalene, and phenanthrene. Textbook drawings of the parallel alignment of p orbitals in these planar π systems are generally clear to students, although the 3D models can be helpful for students with limited vision. A 3D model of 1,3,5,7cyclooctatetraene (COT) is beneficial to all students, however. A drawing such as Figure 9 shows the tub-shaped conformation for COT, but it does not convey the different bond lengths and varying p orbital orientations in such structures. As a result, many students do not fully grasp why COT is not considered antiaromatic. The 3D model of COT (Figure 10) helps students understand that there are pairs of carbon atoms with shorter bond distances connected by longer bonds to other pairs of carbons and that the pairs of p orbital isosurfaces on these carbons are twisted with respect to pairs of orbitals on

either side of them. Thus, the 3D model gives students a more complete understanding of why COT does not meet the criteria for antiaromaticity. Understanding the relationship between energy and p orbital isosurface orientations in 1,3-butadiene and COT sets the stage for students to explore the origins of strain in cyclic and bicyclic olefins. As noted, typical molecular model sets cannot accurately depict calculated molecular geometries of highly strained structures. Projecting images of calculated geometries in class has been found to be useful,19 but some students may have difficulty understanding the 3D information in displayed images. Furthermore, while molecular orbitals can be shown with the calculated structures, most computational programs do not display the atomic p orbital isosurfaces that are used to introduce students to π bonding.20 On the other hand, 3D models of strained olefins can be examined closely by students, and the spatial relationships of p orbitals in these models can be considered in detail. The example of trans-cycloheptene illustrates the advantages of the 3D models discussed here. Textbook discussions of small trans-cycloalkenes are often too concise to give students a good understanding of the origins of molecular instability. For example, a line formula such as that in Figure 11, in which the olefinic carbons, their two hydrogen atoms, and the two attached methylene groups drawn with straight lines, suggests that all of these atoms lie in the same plane. An accompanying statement that small trans-cycloalkenes are strained because the two allylic carbons are relatively far apart does not explain the origin of the strain. Thus, students may incorrectly gather from the graphics and text that all of the steric strain resides in the remaining (gray) segment of the molecule.

Figure 12. (left) 3D model of the calculated geometry of the trans-cycloheptene skeleton. The double bond is indicated by the box. (right) Rotated 3D model showing misaligned p orbital isosurfaces. D



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Figure 14. Depictions of π bonding in acetylene (left) and allene (right).

structures, one-color or two-color models were effective when coupled with explanation by an instructor. Because of small class sizes and variations in model development over time, we have not collected objective measures of the effectiveness of the models in introductory organic chemistry courses. However, students consistently indicated that the 3D models gave them a better understanding of the relationship of molecular geometry and π bonding, particularly with regard to acetylene, allene, 1,3-butadiene, COT, and trans-cycloheptene. Even for students who are able to visualize three-dimensional relationships from printed pages or computer images, the sensation of holding and manipulating models with computed geometries and p orbital isosurfaces is the kind of physical experience that helps them understand and remember important concepts.24,25

Figure 15. 3D models of acetylene (left) and allene (right) with p orbital isosurfaces.

Examination of 3D models of the calculated geometry of trans-cycloheptene clarifies the origin of its strain for students. The model of the trans-cycloheptene skeleton (Figure 12, left) shows considerable angle strain in the σ bonds of the olefinic unit.21 In addition, this distortion of the olefin reduces overlap of the p orbitals on those carbons. As detailed by Barrows and Eberlein,22 there are two components to this restricted overlap: (i) misalignment of the p orbital axis vectors due to twisting about the carbon−carbon double bond (Figure 13, left) and (ii) pyramidalization of the olefinic carbons, which causes separation of two p orbital lobes from each other (Figure 13, right). The skeletal model of trans-cycloheptene enables students to see the angle strain, but the 3D model with p orbital isosurfaces (Figure 12, right) is needed so that students can examine the reduced p orbital overlap from a variety of perspectives. 3D models for structures in which bonding is described in terms of sp hybridization were also developed. Typical textbook depictions of π bonding in acetylene and allene (Figure 14) require that some p orbitals be angled in order for all lobes of the orbitals to be seen. For beginning students who are not yet able to visualize the 3D meaning implicit in 2D drawings, it can be difficult to realize the perpendicular orientation of the two p orbitals on C1 and C2 of acetylene and C2 of allene (Figure 14).23 The 3D models shown in Figure 15 provide tactile experiences that clarify the spatial relationships of p orbital isosurfaces. Red and blue were not used to indicate p orbital phases in these models because textbooks often use the same color for all four lobes of the p orbitals that lead to π bonding in these compounds. To avoid confusing students by using colors that had a different meaning in other models, blue was used for all four lobes of the p orbitals responsible for one of the π bonds and green was used for the four lobes that generate the other π bond.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.6b00933. STL files for the models of a 2p orbital, ethene, acetylene, allene, allyl, 1,3-pentadiene, 1,4-pentadiene, sgauche-1,3-butadiene, 1,3-butadiene (100° dihedral angle), s-trans-1,3-butadiene, 1,3,5,7-cyclooctatetraene, the trans-cycloheptene skeleton, and trans-cycloheptene (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 We are grateful to Davidson College for support of this project. REFERENCES

(1) These models also illustrate the bent-bond theory of multiple bonding advocated by Pauling. See: Pauling, L. Kekulé and the Chemical Bond. In Theoretical Organic Chemistry, The Kekulé Symposium; Butterworths Scientific Publications: London, 1959; pp 1−8. For a discussion of bent-bond theory, see: Carroll, F. A. Perspectives on Structure and Mechanism in Organic Chemistry, 2nd ed; Wiley, Hoboken, NJ, 2010; pp 42−47. (2) Blauch, D. N.; Carroll, F. A. 3D Printers Can Provide an Added Dimension for Teaching Structure−Energy Relationships. J. Chem. Educ. 2014, 91, 1254−1256. (3) Carroll, F. A.; Blauch, D. N. A Hands-On, Cooperative Learning, Guided-Discovery Exercise using 3D Potential Energy Surface Models to Enhance Student Understanding of Conformational Energies. Chem. Educ. 2016, 21, 162−165.

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CONCLUSIONS We have used different versions of these 3D models during their development over several semesters and have always found them to be helpful. Although images of full-color models are included here, students indicated that color is essential only for the allene and acetylene models and that even for these compounds, hand-painted models printed locally were as effective as the commercially printed color models. For other E



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(4) Striplin, D. R.; Blauch, D. N.; Carroll, F. A. Discovering Pressure−Volume−Temperature Phase Relationships with 3D Models. Chem. Educ 2015, 20, 271−275. (5) 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). (6) VMD was developed by the Theoretical and Computational Biophysics Group of the Beckman Institute for Advanced Science and Technology at the University of Illinois at Urbana-Champaign. See: Humphrey, W.; Dalke, A.; Schulten, K. VMD−Visual Molecular Dynamics. J. Mol. Graphics 1996, 14, 33−38. (7) Rossi, S.; Benaglia, M.; Brenna, D.; Porta, R.; Orlandi, M. Three Dimensional (3D) Printing: A Straightforward, User-Friendly Protocol To Convert Virtual Chemical Models to Real-Life Objects. J. Chem. Educ. 2015, 92, 1398−1401. (8) netfabb Basic has been renamed netfabb. It is available at http:// www.autodesk.com/education/free-software/netfabb (accessed March 2017). (9) 123D Design was available without charge from Autodesk, Inc. (http://www.123dapp.com/design, accessed March 2017). Autodesk, Inc. subsequently discontinued support for 123D Design but provides Tinkercad, a free, web-based 3D modeling tool (https://www. tinkercad.com/, accessed May 2017). (10) Slightly different isosurface shapes result if a surface enclosing a different percentage of electron density is calculated. (11) Blender is free open-source software released by the Blender Foundation (https://www.blender.org/, accessed March 2017). (12) For a discussion of 3D printing of hydrogenic orbitals, see: Griffith, K. M.; de Cataldo, R.; Fogarty, K. H. Do-It-Yourself: 3D Models of Hydrogenic Orbitals through 3D Printing. J. Chem. Educ. 2016, 93, 1586−1590. (13) Meshmixer is available without charge from Autodesk, Inc., at http://www.meshmixer.com/ (accessed March 2017). (14) Slightly different results were obtained using other computational methods in Spartan ’16: the minimum-energy geometry for the s-gauche conformation was found to be 26.9° with PM3, 39.1° with Hartree−Fock, and 43.7° with molecular mechanics. (15) Wiberg, K. B.; Rosenberg, R. E. Butadiene. 1. A normal coordinate analysis and infrared Intensities. Structure of the second rotamer. J. Am. Chem. Soc. 1990, 112, 1509−1519. (16) This result is in good agreement with the value of 101.7° obtained from high-level ab initio calculations. See: Feller, D.; Craig, N. C. High Level ab Initio Energies and Structures for the Rotamers of 1,3-Butadiene. J. Phys. Chem. A 2009, 113, 1601−1607. (17) Different computational methods can produce slightly different results. The transition state geometry was found to be 92° with molecular mechanics but 107° with both semiempirical (PM3) and Hartree−Fock calculations. (18) As noted by Bent, “Indeed, to be useful, a model must be wrong, in some respects−else it would be the thing itself. The trick is to see with the help of a teacherwhere it’s right.” See: Bent, H. A. Uses (and Abuses) of Models in Teaching Chemistry. J. Chem. Educ. 1984, 61, 774−777. (19) Springer, M. T. Improving Students’ Understanding of Molecular Structure through Broad-Based Use of Computer Models in the Undergraduate Organic Chemistry Lecture. J. Chem. Educ. 2014, 91, 1162−1168. (20) 3D printing of molecular orbitals was reported by Robertson and Jorgensen. See: Robertson, M. J.; Jorgensen, W. L. Illustrating Concepts in Physical Organic Chemistry with 3D Printed Orbitals. J. Chem. Educ. 2015, 92, 2113−2116. However, we believe that physical models incorporating the p orbital isosurfaces that give rise to Hückel π MOs are most helpful to beginning organic chemistry students. (21) Barrows, S. E.; Eberlein, T. H. Cis and Trans Isomerization in Cyclic Alkenes: A Topic for Discovery Using the Results of Molecular Modeling. J. Chem. Educ. 2004, 81, 1529−1532. (22) Barrows, S. E.; Eberlein, T. H. Understanding Rotation about a CC Double Bond. J. Chem. Educ. 2005, 82, 1329−1333. Also see:

Barrows, S. E.; Eberlein, T. H. Cis and Trans Isomers of Cycloalkenes. J. Chem. Educ. 2005, 82, 1334−1339. (23) Additionally, beginning students could misinterpret the depiction of the two π bonds of acetylene as shown in Figure 14 in terms of four slender ribbons of π bonding between the carbon atoms. Thus, the p orbital isosurfaces in the 3D model (Figure 15) lend themselves more naturally to the concept of a cylinder of electron density in discussions of anisotropic shielding of acetylene protons in 1 H NMR spectroscopy. (24) Shams, L.; Seitz, A. R. Benefits of multisensory learning. Trends Cognit. Sci. 2008, 12, 411−417. (25) Kontra, C.; Lyons, D. J.; Fischer, S. M.; Beilock, S. L. Physical Experience Enhances Science Learning. Psych. Sci. 2015, 26, 737−749.

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3D Printing of Molecular Models with Calculated Geometries and p

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