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Interdisciplinary Learning with Computational Chemistry: A Collaboration between Chemistry and Geology Kenny B. Lipkowitz,*† Mehran Jalaie, Daniel Robertson Department of Chemistry, Indiana University-Purdue University at Indianapolis (IUPUI), Indianapolis, IN 46202-3274; *[email protected] Andrew Barth Department of Geology, Indiana University-Purdue University at Indianapolis (IUPUI), Indianapolis, IN 46202

Chemistry is often touted as “the central science” (1). While this claim may be true, in part because many scientists in other disciplines are now beginning to focus their studies at a molecular level (a domain that has traditionally belonged to chemists), such a proclamation rings somewhat hollow particularly in the area of chemical education. In fact, a perusal of this Journal reveals that, with the exception of biochemistry (a subset of chemistry), relatively few papers, pedagogical or otherwise, are directed to other disciplines— with, perhaps, the exception of forensics or art restoration. Why is it that so few chemical educators attempt to reach out to other disciplines, especially in these times when so many scientists and educators in those other disciplines have a desire to carry out their research and to begin teaching from an atomic and molecular level? One reason is that it takes a lot of work to learn about another discipline and, so, the momentum required to get started can be enormous. Another reason for our lack of reaching out from chemistry to other areas of education is that many subdisciplines in chemistry are not really geared for such an adventure. Perhaps if there were more overlap between the subdisciplines of chemistry and disciplines outside of chemistry we would be more willing as a group to make the connection. Computational chemistry is inherently a multidisciplinary area of study that transcends the traditional barriers separating biology, chemistry, physics, and mathematics. Accordingly, computational chemistry is a perfect tool for making the interconnections between chemistry and other sciences. In this paper we describe how we have integrated computational chemistry into a mineralogy course taught by our geology department. The Departments At IUPUI the chemistry department offers a variety of degree options including an ACS-certified B.S. degree; the geology department offers B.S. and B.A. degrees. The chemistry department (17 faculty) neither has a geochemist on its staff nor does anyone carry out research in geological or environmental sciences. The geology department (10 faculty) has no faculty members with a degree in chemistry. While the chemistry department does not require its students to take a course in geology, geology students are required to take two semesters of freshman chemistry to prepare them for courses in geochemistry, mineralogy, and petrology. The chemistry department has already integrated computational chemistry into its curriculum, in part from the efforts of two †

Mailing address: 402 North Blackford Street, Indianapolis, IN 46202.

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of the coauthors of this paper (2–6 ). The geology department makes some use of computing for statistics and word processing, for classes on the Internet, for map making, and in some instances for running and manipulating data from instrumentation, but no compuational chemistry existed before this collaboration began. The geochemistry course taught at this institution is not typical of what might be found in a chemistry department or even in most geology departments where the emphasis is on chemistry. Rather, the course offered here focuses on global and environmental aspects of geochemistry, foregoing the atomic-scale view of things. A more appropriate course for our collaboration thus became Mineralogy 221, a sophomorelevel course required of all geology students. The book used in that course is Manual of Mineralogy by Klein and Hurlbut, in its 21st printing (7). Our institution is fairly well endowed when it comes to technology because we have instituted a “technology fee”. The school of science maintains several student clusters containing PC and Macintosh computers and the chemistry department uses those machines for molecular modeling, especially for organic chemistry classes and their associated labs. We also maintain a high-end research laboratory that is used for departmental research activities but also for upper-division computational chemistry projects in our curriculum. This is the facility we use for the mineralogy classes simply because it is configured for in-lab tutorials and also because it has the equipment and software we need (see below). Computational Chemistry in Mineralogy Introducing computational chemistry into mineralogy was challenging partly because we had to learn some basic mineralogy nomenclature and concepts, but also because there actually exist too many possible applications of computational chemistry to that discipline. Also, because this is a course in geology, not chemistry, we had to meet the needs of the geology department; that is, we were not going to tell them what they should do. Rather, we read their textbook, evaluated their syllabus, and then made some recommendations for them to consider. Our initially agreed-upon project was to use the facilities only for visualization. Their students, like ours, have a difficult time seeing chemical structures in three dimensions, especially when complex lattices are involved, and the possibility of using molecular graphics to assist in their teaching endeavors was as appealing to them as it is to us. (This is a sophomorelevel course, so their students’ understanding of chemistry is comparable to that of a typical sophomore organic chemistry student.) The big advantage of computer graphics over hand-

Journal of Chemical Education • Vol. 76 No. 5 May 1999 • JChemEd.chem.wisc.edu


held mechanical models was, for the geologists, that the mechanical models they were using could be done away with (they are prone to damage and are exceedingly expensive). Additionally, we convinced them that other types of structural features such as molecular electrostatic potential surfaces and polygon representations for rendering could be implemented in a way not possible with mechanical models. Eventually, more than simple viewing was embedded into the course, but much of what the students do involves generating lattices from unit cells, visualizing the nanocrystallites, and then making measurements and formulating arguments about minerals based on those structures being viewed. To help direct our efforts we focused our attention on the laboratory part of the course (we also have routine homework assignments, but those are not described here). Four lab exercises were developed and integrated into the mineralogy curriculum. Each experiment is scheduled for two hours per week as are the other mineralogy experiments, but the modeling facility is available during off-hours as well. Two of the computational chemistry labs are instructed by a chemist along with a geology professor who also serves as a teaching assistant. The remaining labs and homework assignments are taught completely by the geologists. The experiments we developed for our curriculum are described below and they are available from the authors upon request. The computers we use are Silicon Graphics workstations (a mixture of models but typically containing MIPS R4000 chips); the software we use is Cerius2 from MSI (8). Almost any major researchgrade molecular modeling package would suffice. This just happens to be the software we have in the chemistry department, but it is especially good for this mineralogy course because of its many advanced features for inorganic systems (lattice generators; complete databases of minerals, ceramics, and other relevant materials) and because of its reasonable cost and ease of operation. Laboratory 1. Introduction to Molecular Modeling

The exercises focus on halite (NaCl) because of its simplicity but also because it is a material that the geology students had just finished working with. In a previous lab they collected X-ray diffraction data (the “XRD” above) and had computed the unit cell dimensions of this mineral and estimated the Na+ radius on the basis of symmetry arguments. The connection between crystallography and diffractometry commonly used in mineralogy is thus made. Other options such as viewing Miller planes are also introduced here, but most of the laboratory assignments are made so as to reconnect the geology students with many of the topics they had in freshman chemistry. This was also a crucial exercise because it reinforces concepts of “scale” that are important to geologists (see below). Here, students crush macroscopic halite crystals, measure unit cell dimensions, and view the cell with its constituent atoms with molecular graphics on a microscopic level. Laboratory 2. Polyhedral Models of Silicates Two goals are achieved in this laboratory experiment. First, students are made aware that various representations of molecular structures exist (e.g., wire-frame, ball-and-stick, and space-filling presentations of atomic connectivity) and also that one can present surfaces such as van der Waals’ and molecular electrostatic potential surfaces and map out properties like lipophilicity. More important for this course, though, is that students become accustomed to working with polyhedral representations, especially tetrahedral and octahedral clusterings of atoms. Without this simplification of the lattice, mineral structures can be both difficult to see and intellectually prohibitive to comprehend for most novices (these structures are usually more complex than those a typical organic chemistry student would struggle with). An example of this is depicted in Figure 1. The second goal is to remind students about the various kinds of intermolecular forces that exist in nature and to recall for them the relative strengths and characteristics of those

This is the beginning molecular modeling exercise. Here the various types of molecular modeling techniques used in different disciplines throughout science and technology are brought to light, the computational tools used for those purposes are mentioned, and the students learn how to use the Cerius software. This lecture is comparable to what we teach our undergraduate organic chemistry students, but with an emphasis on inorganic solid-state systems. In this course we do not train students about the UNIX platform; the machines are simply made available to them and the software pops up upon login to that course number. Some representative elementary exercises taken directly from the first lab handout are listed below. • • • • • • • •

Use CERIUS to pull up the unit cell of HALITE. Rotate, translate, and zoom into and out of the unit cell. Turn on atom labels. Measure the Na+ Na + distances. How many different distances exist? Measure the Na+ Cl{ distances. Measure the Na+ Cl{ Na+ angles. Compare the measured distances and angles with your XRD values. Are they the same? Make a graphics plot of that structure.

Figure 1. The tremolite lattice, a typical complex structure students work with. Opposing chains comprised 6-membered rings of polymerized SiO4 tetrahedra, linked by octahedra and cross linked by distorted cubic Ca2+ sites. The ability to zoom in, expand, rotate, and highlight atoms and symmetry-related groupings and to visualize such complex structures in stereo is a compelling reason for using computer models rather than hand-held mechanical models. (This figure appears in color on the cover of this issue.)

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interactions. With this knowledge students are then expected to make predictions concerning properties of minerals. An example is to predict cleavage planes in crystals that are subjected to shear-induced stresses. How minerals cleave, together with influences of “weathering” described later in the course, affect things like oceans and climates. A connection between atomic and global views of the world is thus made. (The dynamic range of scale that a geology student must be cognizant of is much greater than that for most chemistry students; we find these computational chemistry exercises a good way to make the connection between macroscopic objects like rocks, boulders, and continents and the microscopic atomic world that is otherwise difficult for students to comprehend.) Learning how to concisely describe a visual image of such complex solid solutions containing multiple ions and varying types of interplanar bonding is a difficult but important task. Because of our commitment to “writing across the curriculum”, laboratory reports contain brief (less than 1 page) written descriptions comparing the structures and bonding motifs of the minerals being studied (fayallite and almandine, in our case). Laboratory 3. Double- and Single-Chain Silicates This laboratory is an extension of the second laboratory experiment. In it students examine far more complex minerals and then compare and contrast minerals containing double and single polymeric strands of siloxanes. Again, predictions concerning cleavage planes are made. In this experiment, though, students return to the geology laboratory with their predictions. There they carry out fracture experiments to verify that the predicted and observed cleavage planes are the same. They also make measurements of the angles between such planes for comparison with their modeling studies. An example of a predicted cleavage plane is presented in Figure 2. Figure 3 illustrates the interplanar bonding of micas; it is clear that only van der Waals’ forces hold the planes together, making the formation of atomically smooth surfaces possible. Finally, based on (i) the types and number of interplanar forces, (ii) the kinds of interatomic interactions in those planes, and (iii) the spatial placement of ions in minerals, our students are asked to rank-order the “hardness” of several minerals. They then compare their predictions with the Mohs hardness test (a standard measure of hardness in geology) and defend their findings, both in written form and orally in front of their peers.

placement of cations in mineral matrices, how this arises in nature, the relationships between classes of minerals related by these small differences and the relative stabilities (heats of formation) of these classes of minerals. The systems we direct our attention to are classified under the superfamily of feldspars. In the albite crystal 1/4 of the Si 4+ atoms have been replaced by Al3+. To maintain a charge balance, nature inserts an alkali metal atom of suitable size (Na + in this case) into holes near the Al3+. The high-temperature form of this mineral has the alkali cations centered in the cubic holes, but in this lowtemperature structure the cations are snuggled up close to the aluminum. This type of replacement is represented by the following equation: Na+Al3+ Si4+ ❒, where the square refers to the square vacancy of the lattice. Albite and anorthite form the two end points of a range of minerals found in nature. At the one extreme (albite) the Si 4+ atoms are replaced by Al3+ atoms along with a charge-compensating M+ alkali metal atom to maintain charge neutrality. At the other extreme (anorthite), half of the silicons are replaced by aluminum, making the crystal negatively charged, and to compensate for this, calcium ions (Ca2+) are inserted. The corresponding equation here is Na+ Si 4+ Ca2+ Al3+. These idealized end points (albite and anorthite) can be made in pure form in a laboratory but they cannot be found in nature. There exists a range of minerals between these end points and taken together these minerals show a gradient of mole ratios of metal and oxygen. Each mineral has its characteristic mole ratio; some of these species have common names such as labradorite and

Laboratory 4. Cationic Ordering in Framework Silicates This experiment contains two parts. The first extends the ideas of previous labs (where isolated tetrahedra and linked tetrahedra of silicates were studied). It may be perceived as somewhat trivial, but searching for and analyzing networks of chains in silicates completes a theme of [Si–O–Si–O]n bonding patterns we have our students focus on. In this experiment nanocrystallites of minerals containing cross-linked silicates are generated and studied. The emphasis is on α and β forms of quartz along with spessartine. The nature of the crosslinking is evaluated and predictions of mineral durability under stress and of ordering of melting points are made. The second part of this laboratory experiment involves solid solutions. In particular we stress here the relative 686

Figure 2. A nanocrystallite of hornblende depicted with a ball-andstick presentation for clarity. In this figure we note that some areas have spaces and gaps in addition to regions that are inherently less well bonded to neighboring atoms than others. These regions in turn correspond to places where stress-induced fracture and parting will appear. Students locate those regions and predict where macroscopic cleavage will occur. In this case the smaller, vertical lines are highlighting the microscopic fracture zones while the larger diagonal line highlights the predicted cleavage plane. Students then verify these predictions with appropriate laboratory experiments.



andesine (from Labrador and the Andes, respectively), while others have more exotic names. We initially wanted our students to calculate the heats of formation of these systems quantum mechanically. The idea here was that the relative stabilities of minerals would be compared with tabulated experimental values and students would again be asked to make arguments concerning mineral durability, the influence of weathering, and so on. The logical quantum-based approach would be to implement a semiempirical Hamiltonian. Unfortunately the computed results were poor at best (the geometry of the lattice is poorly reproduced when energy is minimized), and this part of the experiment was not implemented. This laboratory experiment is followed by one in the mineralogy laboratory, where students select pure starting materials (magnesium oxides, carbon, silica, etc.) and then mix them in mole ratios that would lead to the formation of a desired mineral upon heating in a furnace (mineralogical synthesis). Upon synthesis the students verify their products with X-ray diffraction spectrometry. Discussion The laboratory experiments described above are part of Mineralogy 221. This is a sophomore-level geology course and the laboratory experiments we codeveloped constitute 33% of the entire laboratory syllabus. The experiments are interspersed among other mineralogy experiments, so while

Figure 3. A ball-and-stick representation of talc showing layers of SiO4 tetrahedral groups sandwiching MgO6 octahedral groups bonded only by weak van der Waals’ forces. Visualizing this mineral allows students to bridge the gap between the microscopic world depicted here, and the macroscopic world in which talc is known to be a soft, lubricant-like material. Another example of layers held together exclusively by weak van der Waals’ forces is the micas. Again, the macroscopic world of peeling mica layers to make atomically smooth surfaces can be connected to the microscopic underpinning of what gives rise to that phenomenon.

they follow the order presented here, they are not concatenated. Rather, they are offered when that part of the lecture covers those topics. The experiments we have developed maintain a theme of silicate chemistry, but this is just our local preference; other ideas would no doubt be welcomed by geology instructors. The computational laboratories bring basic concepts in structural chemistry together with real-world mineralogy. In particular, we strive to make the connection between chemists’ microscopic, atomic-level views and macroscopic (sometimes global) scales that geologists work with. Students build, measure, and predict the properties of nanocrystallites and then make predictions about mineral durability, stress fracturing, weathering, and so on. We have attempted to use the available force fields of Cerius to optimize mineral lattices, but we have found these force fields to be uniformly incapable of reproducing known mineral lattices with a suitable root-mean-square deviation. Similarly, geometry optimizations with the semiempirical Hamiltonians have failed, so we do not predict lattice geometries in this course. We do find, however, that ion replacement calculations (e.g., Mg2+ for Ca2+) do predict the correct trends in stability and students can use these computational tools to begin thinking about thermodynamic implications of minerals in high- vs low-temperature phases as well as to foster an understanding of why minerals deposit as they do in nature. This aspect of the laboratory is still under development. Most of these laboratory experiments are based on relatively simple computational techniques, relying heavily on visualization. Molecular graphics allows us to use, relatively cheaply, a greater number of models than we could ever purchase from our limited budget. (MSI now supplies hundreds of minerals and ceramics in their materials database, along with numerous other polymers and organics.) Moreover it allows us to see things such as electrostatic fields, Miller planes, and the like that are not otherwise possible to see from mechanical models. Several other aspects of this interdisciplinary curriculum also need to be highlighted. First, we have focused on bridging the “size” gap where the connections between macroscopic and microscopic worlds are made. In contrast to chemists, geologists have a far greater range of scales to think about. For example, they need to make the connections between atomic-level details and how these affect weathering of minerals, which in turn affects oceans and climates. Computational chemistry has proved capable of helping students make those connections. Second, we were taken aback by the eagerness of our students for manipulating and viewing the models computationally in comparison to using the handheld mechanical models. Students seemed apprehensive about using the mechanical models, perhaps for fear of breaking them or maybe because they hadn’t seen such models before. In contrast, they were very eager to use the computer models (and clearly expressed their opinions of this), perhaps because they felt comfortable using a computer and knew they couldn’t damage the models. Third, we reiterate that the students in this course are at a similar level of comprehension of molecular structure as first-semester organic chemistry students, so one cannot raise the level of computational difficulty beyond what would be presented in an organic chemistry class. Finally, we point out that this collaboration is interdisciplinary and forces students in geology to make


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use of the chemistry they have had. We notice that students tend to compartmentalize their knowledge, in part as a defense mechanism when being overwhelmed by class work, and this combined geology-chemistry experience helps shed those shackles. In our opinion, the earlier we begin to remove the barriers between disciplines (in this case in the sophomore year) the easier it will become for students to understand how the sciences are all interconnected, and especially for them to see the commonalties rather than the differences. Summary If chemistry is “the central science”, one would expect to see more interdisciplinary learning partnerships between chemistry and cognate disciplines of science and technology. Computational chemistry is inherently multidisciplinary and capable of conveying important pedagogical messages to students of chemistry as well as to students of other disciplines where knowledge at an atomic or molecular level is desired. In this paper we have documented how we used computational chemistry in a collaborative effort with a geology department. Specifically, we have developed a set of tutorials, homework

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assignments, and laboratory experiments for use in a mineralogy course. If we, as a group of chemists, intend to make the claim that chemistry is the central science, we need to reach out to other disciplines to provide guidance for those who wish to learn about what we already know. There are many pathways for achieving such an intellectual collaboration and we have demonstrated one such way here. We encourage others to do likewise. Literature Cited 1. See for example Brown, T. L; LeMay, H. E. Jr.; Bursten, B. E. Chemistry The Central Science, 5th ed.; Prentice Hall: Englewood Cliffs, NJ, 1991. 2. Boyd, D. B.; Lipkowitz, K. B. J. Chem. Educ. 1982, 59, 269. 3. Lipkowitz, K. B. J. Chem. Educ. 1982, 59, 595; 1984, 61, 1051. 4. Lipkowitz, K. B. J. Chem. Educ. 1989, 66, 275. 5. Lipkowitz, K. B. J. Chem. Educ. 1995, 72, 1070. 6. Lipkowitz, K. B.; Robertson, D.; Pearl, G.; Schultz, F. A. J. Chem. Educ. 1996, 73, 105. 7. Klein, C.; Hurlbut, C. S. Jr.; Manual of Mineralogy, 21st ed.; Wiley: New York, 1993. 8. MSI Inc., 9685 Scranton Road, San Diego, CA 92121-3752.



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