Activity pubs.acs.org/jchemeduc
Using Computational Visualizations of the Charge Density To Guide First-Year Chemistry Students through the Chemical Bond Jonathan Miorelli, Allison Caster,* and Mark E. Eberhart Molecular Theory Group, Colorado School of Mines, Golden, Colorado 80401, United States S Supporting Information *
ABSTRACT: The chemical bond concept is the foundation of the molecular sciences. Therefore, helping students gain a clear physical representation of chemical bonding is necessary for progress in chemistry. Bond Explorer, an activity that utilizes the three-dimensional (3D) plotting functionality of Mathematica, is intended to provide a clear physical picture of electron sharing among atomsi.e., a physical picture of the chemical bond. The app takes advantage of Mathematica’s free-to-use CDF Player, removing the high cost often associated with implementing computational activities in the classroom. Through the course of the activity, students visualize the 3D charge density using both fog and contour plots. Students then go on to describe the density differences that characterize various bonding types, i.e., covalent, polar covalent, and ionic. The activity involves both independent and group work and was designed to guide students as they identify key similarities and differences among the charge densities corresponding to various bond types. Preliminary assessment suggests that students who participated in the activity understand bonding and electronegativity more fully than students who did not complete the activity. KEYWORDS: First-Year Undergraduate/General, Physical Chemistry, Computer-Based Learning, Hands-On Learning/Manipulatives, Internet/Web-Based Learning, Covalent Bonding, Ionic Bonding
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INTRODUCTION
The charge density is difficult to visualize because it is a three-dimensional function with values spanning many orders of magnitude. Understanding and correctly interpreting geometric relations is a common hurdle for students studying the chemical sciences, especially in subjects where molecular structure plays a crucial role.4−9 The problem is exacerbated by the fact that representing 3D objects on a flat surface almost inevitably leads to inaccurate representations.10,11 The importance of having a quality model of charge density structure in introductory courses, juxtaposed with the difficulty involved in visualizing the density using traditional methods, motivated the development of a multipart interactive web and classroom activity that we call “Bond Explorer”. Bond Explorer uses the variety of plotting abilities in Wolfram’s Mathematica to let students manipulate 3D models of the charge density, but this computational exercise is not a solitary educational endeavor. In the variety of modern STEM educational techniques developed over recent decades, one unifying theme is the power of peer-group exploration with instructor guidance.12−17 Thus, in the second module of Bond Explorer, students work in small groups to discuss and articulate similarities among the charge densities for typical bonding types, e.g., covalent, polar covalent, and ionic bonds. This
Modern molecule and materials design is built upon the framework of structure−property relationships. To move toward a future where scientists and engineers tune the properties of materials ranging from pharmaceuticals1 to new types of steel,2 students need an understanding of how fundamental structures mediate bulk properties. As modern quantum physics and chemistry has shown, it is the charge densitythe electron distributionthat mediates intrinsic material properties; it is the physical parameter controlling the location and type of “bonds” in a material. It would be advantageous, then, for students to become familiar with the structure of the charge density and the rules governing the variety of bonding models seen in materials. The bulk of this information is currently conveyed through conventional bonding modelsi.e., covalent, ionic, and metallic bonds and intermolecular forces. Beyond that, though, a vast array of concepts vital to understanding chemical properties, ranging from electronegativity to Lewis acid−base reactions to phase changes, center around the interaction between charge densities of various atoms. In spite of the ubiquity of these concepts in chemistry coursework, students often have difficulty relating these properties to the three-dimensional (3D) charge density distribution.3 Moving from the traditional property-focused model toward a structure-first approach would better prepare students to design materials from first principles. © XXXX American Chemical Society and Division of Chemical Education, Inc.
Received: February 11, 2016 Revised: November 2, 2016
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DOI: 10.1021/acs.jchemed.6b00058 J. Chem. Educ. XXXX, XXX, XXX−XXX
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molecules N2 and LiF, draw contours of the densities they observe, and describe the differences they observe between the two charge densities. The simple calculation of the charge density in Part 1, which is a single-function (non-self-consistent solution) Gaussian basis set, makes detailed investigation of the differences in charge density untenable. For this reason, Part 2 provides highresolution images of charge density contours calculated for a variety of small molecules using modern computational chemistry techniques (see Figure 2).20−24 Part 2 begins by having the students compare the contour plots they drew in Part 1 (for N2 and LiF) with the contour plots provided in Part 2. The students then describe the differences among the contour diagrams for ionic (e.g., LiF and BeO), polar covalent (e.g., CO), and covalent bonds (e.g., N2 and O2) and the differences in charge distribution within these model bonds. Part 2 ends with an exercise in which the student imagines moving through the charge density going from one nucleus to the other, describing what the student would observe. Students answer questions such as “Does the charge density increase/decrease moving along the line connecting the nuclei?” and “Does the charge density increase/decrease normal to the line connecting the nuclei?”. Part 3 finishes out the Bond Explorer Activity. Students analyze a contour plot for H2O, discussing the shape of the charge density in a nonlinear polar covalent molecule. Students then summarize what they learned in Parts 1 and 2i.e., what features in the electron density indicate an ionic, covalent, or polar covalent bond. As a “challenge question” leading to the concept of intermolecular forces, the activity ends with a contour diagram for the very weakly bound Ne2. Students note how the charge density looks in a weakly bound/van der Waals system and make predictions about how strong the Ne2 bond is relative to the previous bonds observed based on the shape of the charge density and the magnitude of the charge shared between atoms.
activity is easy to implement into a variety of early undergraduate chemistry courses.
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THE ACTIVITY The app is written initially as a Mathematica workbook and then exported as a web-embeddable CDF file, allowing the file to be opened using the free CDF Player provided by Wolfram.18,19 The CDF player can run either as a standalone program or within a browser as an add-on. This allows some flexibility in implementation, since students can either download a file provided by the instructor and run the standalone CDF Player or run the CDF Player from a file embedded on a web page set up by the instructor. Once the students have the app running, they are able to generate and view fog plots of the charge density for diatomic molecules (see Figure 1). Students select from a list the atoms participating in the bond (Li, Be, B, C, N, O, F, and Ne), the internuclear separation distance between the atoms, and a visual parameter that toggles the translucency of the fog plot. After taking some time to play around with the app, students are instructed to build the
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DISCUSSION The most crucial prior knowledge students need for this activity is that the electrons within a molecule are not static point charges but collectively describe a 3D function with a value at every point in spacesometimes termed a 3D scalar field. The amount of material covered before the students use the Bond Explorer App is mediated by the specific learning objectives of the instructor and the degree to which this activity is self-guided for the students. In order to preserve the guided discovery character of this activity, the only concepts we mention ahead of time are that charge density is important, that charge density is a 3D function, and how to visualize 3D functions. In our implementation, students work independently on Part 1 as homework. Since the charge density is a 3D function, displaying it on a 2D surfacelet alone having a working concept of how it is physically distributed in spaceis problematic. For this reason, prior to beginning the activity, students are instructed to read a supplemental handout titled “It’s All About the Electrons” (see the Supporting Information).25 The handout provides a brief motivation for fully understanding the charge density (i.e., the charge density mediates material properties), along with some details about what the charge density is (i.e., a 3D function describing the average number of electrons observed within a given volume). The document finishes by describing the various ways one can visualize the charge density using fog plots, isosurfaces, and
Figure 1. Screen capture of Part 1 of the Bond Explorer app with Be (left) and O (right) selected. Students select the atoms and separation distance (in units of bohr) along with some visualization parameters and view a 3D plot of the resulting charge density. The shown plot can be rotated, allowing the students to grasp how the charge is distributed in real space. B
DOI: 10.1021/acs.jchemed.6b00058 J. Chem. Educ. XXXX, XXX, XXX−XXX
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Figure 2. Screen capture of Part 2 of the Bond Explorer App, with a contour of Be (left) and O (right) selected. Here students are shown highresolution calculated contour plots of the charge density for various diatomic molecules. The Be−O separation distance is 2.48 bohr, which is the calculated minimum-energy separation distance.20−24
for the day’s activity is to gain a deeper understanding of covalent, polar covalent, and ionic bonding as well as electronegativity and what all of these terms mean from a charge density perspective. From there, the students break off into groups of 2−4 and work through Parts 2 and 3 of the worksheet. As the students are working, the instructor(s) interact with the groups and probe how well each group is grasping the concepts by way of guided questions, helping students to arrive at accurate conclusions without explicitly giving them the answers. After approximately an hour of group work, the class reconvenes for a short discussion (5−15 min) of the key concepts presented in the activity. The “Bond Explorer” activity was implemented in the fall of 2015 as an in-class activity requiring roughly an hour of class time. The class had 50 students and was cotaught, giving a student/instructor ratio of 25:1. Student responses were assessed for accuracy and thoughtful effort, written feedback was provided to students, and misconceptions were addressed during follow-up class discussions. We have completed an informal assessment to determine how well the activity is meeting the learning objectives and have plans to conduct a more formal assessment in subsequent semesters. On average, students perceived Bond Explorer to be very straightforward, with the understanding of contour plots being the most difficult. Immediately following the completion of this activity (without any other discussion of bonding) each student group was asked to identify the bonding structure for nine different substances (Na, K, Cl2, CH4, H2O, HCl, CuO, NaCl, and Cu(NO3)2). Within 5−8 min, all of the student groups were able to identify and thoughtfully discuss the bonding in all of the substances, including the presence of intermolecular forces and the nature of compounds with both ionic and covalent bonds (Cu(NO3)2). We saw strong evidence through the semester that students utilized these ideas of electronegativity and charge density in their understanding of chemical and
contour plots shown in a plane. This introductory material is crucial because it builds the vocabulary and skillsets required to complete the activity. A brief class lecture could be used to achieve the same objective. In our implementation, we have the students read the material prior to class and follow up with a short lecture (∼20 min) to ensure that the foundational concepts are clear to the students prior to beginning the activity.26 Once the students have a sufficient understanding of what is meant by charge density and how to represent it graphically, they begin with Part 1 of the Bond Explorer App. In Part 1 there are a number of qualitative aspects of the charge density that students should come away with: (1) That the charge density is a maximum near the nucleus. (2) That a ridge of charge density connects bound atoms. (3) That different kinds of atoms have more or less density relative to other atoms along a bond. Manipulating the 3D structures in the Bond Explorer App allows students to visualize these concepts. Physically sketching contour diagrams of the charge densities observed in Part 1 further solidifies these concepts and paves the way toward developing an intuition for how charge is distributed within chemical systems. Prior to having the students work on Parts 2 and 3 during class time, a brief (approximately 10 min) lecture is given to ensure that students came away from Part 1 with the three learning objectives above. The lecture stresses the importance of the charge density for understanding material and chemical properties but does not explicitly explain why this is the case. Once this motivation is provided, we focus on how to view the charge density graphically. The lecture uses videos showing isosurfaces of increasing density for a N2 molecule as well as for LiF (see the Supporting Information). These videos illustrate how charge density is shared in conventional covalent versus ionic (polar) bonding. The lecture then goes on to stress how to view this information using contours of the density. The lecture wraps up by stressing that the main learning objective C
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(5) Barke, H. D. Chemical Education and Spatial Ability. J. Chem. Educ. 1993, 70 (12), 968−971. (6) Gawley, R. E. Chirality made Simple: A 1- and 2-Dimensional Introduction to Stereochemistry. J. Chem. Educ. 2005, 82 (7), 1009− 1012. (7) Ozdemir, G. Exploring Visuospatial Thinking In Learning About Mineralogy: Spatial Orientation Ability and Spatial Visualization Ability. Int. J. Sci. Math. Educ. 2010, 8, 737−759. (8) National Research Council. Learning to Think Spatially: GIS as a Support System in the K−12 Curriculum; The National Academies Press: Washington, DC, 2006. (9) Wu, H.-K.; Shah, P. Exploring Visuospatial Thinking in Chemistry Learning. Sci. Educ. 2004, 88 (3), 465−492. (10) Barta, N. S.; Stille, J. R. Grasping the Concepts of Stereochemistry. J. Chem. Educ. 1994, 71 (1), 20−23. (11) Luján-Upton, H. Introducing Stereochemistry to Non-science Majors. J. Chem. Educ. 2001, 78 (4), 475−477. (12) Handelsman, J.; Miller, S.; Pfund, C. Scientific Teaching; W. H. Freeman and Company: New York, 2007. (13) Handelsman, J.; Erbert-May, D.; Beichner, R.; Bruns, P.; Chang, A.; DeHaan, R.; Gentile, J.; Lauffer, S.; Stewart, J.; Tilghman, S. M.; Wood, W. B. Scientific Teaching. Science 2004, 304 (5670), 521−522. (14) Gaddis, B. A.; Schoffstall, A. M. Incorporating Guided-Inquiry Learning into the Organic Chemistry Laboratory. J. Chem. Educ. 2007, 84 (5), 848−851. (15) National Research Council. Promising Practices in Undergraduate Science, Technology, Engineering, and Mathematics Education: Summary of Two Workshops; The National Academies Press: Washington, DC, 2011. (16) Saitta, E. K. H.; Gittings, M. J.; Geiger, C. Learning Dimensional Analysis through Collaboratively Working with Manipulatives. J. Chem. Educ. 2011, 88, 910−915. (17) Furtak, E. M. The Problem with Answers: An Exploration of Guided Scientific Inquiry Teaching. Sci. Educ. 2006, 90 (3), 453−467. (18) Mathematica, version 10.2; Wolfram Research, Inc.: Champaign, IL, 2015. (19) Wolfram Research, Inc. Wolfram CDF Player for Interactive Computable Document Format. https://www.wolfram.com/cdfplayer/ (accessed October 2016). (20) The charge density contours were calculated using SCM’s ADF computational suite with the M06-2X meta-hybrid density functional and the TZP basis set (see refs21−24). (21) te Velde, G.; Bickelhaupt, F. M.; van Gisbergen, S. J. A.; Fonseca Guerra, C.; Baerends, E. J.; Snijders, J. G.; Ziegler, T. Chemistry with ADF. J. Comput. Chem. 2001, 22, 931−967. (22) Fonseca Guerra, C.; Snijders, J. G.; te Velde, G.; Baerends, E. J. Towards an Order-N DFT Method. Theor. Chem. Acc. 1998, 99 (6), 391−403. (23) ADF 2014; Scientific Computing & Modelling NV: Amsterdam, 2014; http://www.scm.com. (24) Zhao, Y.; Truhlar, D. G. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other function. Theor. Chem. Acc. 2008, 120 (1), 215−241. (25) The handout “It’s All About the Electrons” was written to introduce students to the concept of the electron density and how to visualize 3D functions. As a result, simple anologues are used to introduce these concepts in an attempt to avoid being bogged down in the minutiae of quantum mechanics. For instance, there is an analogy stating that if one were to observe the electrons within a molecular system, they would appear to behave similarly to bees flying around a bee hivemoving in seemingly random trajectories. The time average of all of these electron movements is used to convey the idea of having a time-averaged number of electrons per unit volumean electron density. At first glance, this analogy seems to betray the wavelike behavior of electrons that characterizes molecular systems, but the wording in the handout was carefully chosen. Observing the electrons would cause the wavelike nature of the electrons to be lost, and they
physical properties. Thus, it provided a simple and sturdy framework upon which students built their understanding of the fundamentals of chemistry. The students who completed Bond Explorer (and related work) scored higher on bondingrelated questions on the midterm and final exam than students who did different activities, but more formal assessment is needed to verify these results.
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CONCLUSION The goal of activities such as Bond Explorer is to provide students with a firm foundation from which to think about the electron density of molecules and materials. Presenting concepts of the nature of the charge density in introductory courses provides students with the tools to imagine how electron sharing mediates properties, allowing for easier abstraction of these concepts in later classes, without overloading them with the complicated nuance of electronic structure theory (e.g., valence bond theory or molecular orbital theory). This activity moves us toward a long-term goal of training students in a modern approach to material design: achieving desired properties by tuning the charge density explicitly via changes to the chemical environment within a material.
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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.6b00058. “It’s All About the Electrons” handout; Bond Explorer assignment, Parts 1, 2, and 3; Mathematica code and individual CDF files for all parts of the Bond Explorer app; and videos showing isosurfaces of increasing density (ZIP)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Jonathan Miorelli: 0000-0002-2849-7739 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS Support of this work under ONR Grant N00014-10-1-0838 is gratefully acknowledged. The authors also acknowledge the assistance in implementing Bond Explorer as well as the thoughtful advice of fellow faculty member Renee Falconer.
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REFERENCES
(1) The Quantum Theory of Atoms in Molecules: From Solid State to DNA and Drug Design; Matta, C. F., Boyd, R. J., Eds.; Wiley-VCH: Weinheim, Germany, 2007. (2) Jones, T. E.; Eberhart, M. E.; Imlay, S.; Mackey, C.; Olson, G. B. Better Alloys with Quantum Design. Phys. Rev. Lett. 2012, 109, 125506. (3) Dhindsa, H. S.; Treagust, D. F. Prospecitve pedagogy for teaching chemical bonding for smart and sustainable learning. Chem. Educ. Res. Pract. 2014, 15, 435−446. (4) Burrmann, N. J.; Moore, J. W. Omplementations and Student Testing of a Web-Based, Student-Centered Stereochemistry Tutorial. J. Chem. Educ. 2015, 92, 1178−1187. D
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would appear to be strictly particle-like. Through observation the electron’s position is known with greater certainty, and hence, the Heisenberg uncertainty principle requires a corresponding increase in the momentum of the electron (e.g., confining an electron to a volume of 10−36 m3the volume of a cube with each edge 1 picometer in lengthforces an uncertainty in the momentum corresponding to a velocity of at least 1.0 × 107 m/s). It is the act of observation that makes the bee anology compatible with quantum mechanics. What is not addressed in the analogy is that observation would alter the energy state of the electron. Such complications and detail could confuse some students, and hence, such a nuanced view of molecular electrons is left to a more advanced course. (26) Crouch, C. H.; Watkins, J.; Ragen, A. P.; Mazur, E., Peer Instruction: Engaging students one-on-one, all at once. In Reviews in Physics of Physics Teachers; Redish, E. F., Cooney, P., Eds.; American Association of Physics Teachers: College Park, MD, 2007; pp 1−55.
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