Article pubs.acs.org/jchemeduc
3D Printing of Molecular Potential Energy Surface Models Phalgun Lolur* and Richard Dawes* Department of Chemistry, Missouri University of Science and Technology, Rolla, Missouri 65409, United States S Supporting Information *
ABSTRACT: Additive manufacturing, commonly known as 3D printing, is gaining popularity in a variety of applications and has recently become routinely available. Today, 3D printing services are not only found in engineering design labs and through online companies, but also in university libraries offering student access. In addition, affordable options for home hobbyists have already been introduced. Here, we demonstrate the use of 3D printing to generate plastic models of molecular potential energy surfaces useful for understanding molecular structure and reactivity. KEYWORDS: Upper-Division Undergraduate, Physical Chemistry, Hands-On Learning/Manipulatives, Atmospheric Chemistry, Gases, Kinetics, Thermodynamics
and topography of a PES determines spectroscopically observable states and dynamics. Accurate PESs can often be generated for small molecular systems (typically 2−6 atoms) using ab initio quantum chemistry methods. A number of discrete ab initio data (ranging from a few hundred to tens of thousands) are computed and then represented as a PES by some chosen method of fitting or interpolation.9−15 The surfaces can then be used either for qualitative interpretation or as the basis for various calculations or simulations. Dynamics calculations using a PES might range from full quantum scattering calculations to quasi-classical trajectories (QCT)16,17 commonly used to make molecular movies (animations of classical dynamics), where the forces come from the gradients of the PES at each time step. Potential energy surface models have a long history in chemical education. A 1957 paper by Dye describes using plywood and clay molds to construct plaster models and discusses using shim-stock to build the model layer-by-layer.18 Another plaster model appears in a 1974 paper by Hulse et al.19 and other authors refer to contour diagrams for teaching purposes.20,21
3D printing or additive manufacturing is a technology that has been around for almost 30 years1,2 but has recently seen a huge growth in interest and popularity.3,4 It involves creating a 3D model of an object designed on a computer, often using computer aided design (CAD) programs. The object is represented in a digital format, for example, stereolithography (STL) and then built into a real physical object layer-by-layer in a chosen material by the 3D printer. The resolution (thickness and detail of each layer) depends on the printer and the material being used. Additive manufacturing not only reduces waste of raw material, but also can create objects that are not easily manufactured using other techniques. The capability to rapidly construct useful objects in a variety of environments is expected to have a large impact on society in the next few decades. Here, we provide an illustrated tutorial demonstrating how 3D printing helps us teach and understand chemistry by making models of molecular potential energy surfaces. Traditionally, the study of chemical reaction rates is attributed to chemical kinetics, but a fundamental understanding of the factors contributing to reaction rates is made possible via the study of reaction dynamics.5 Molecular reaction dynamics is the field of chemistry that studies reactions as the underlying processes in reactive collisions between molecules and predicts thermal rates from sums over detailed state-to-state reactive cross sections. Dudley Herschbach, Yuan T. Lee, and John C. Polanyi helped develop techniques to probe reactive molecular collisions experimentally and received the Nobel Prize in chemistry in 1986 for their contributions to this field.6 Theoretically, dynamics are commonly interpreted in the framework of Born−Oppenheimer potential energy surfaces (PES).7,8 A PES gives the electronic energy of a system as a function of the geometry of its nuclei. Minima (wells) on the PES correspond to stable isomers, saddles between minima represent barriers to isomerization or reaction, while the shape © XXXX American Chemical Society and Division of Chemical Education, Inc.
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TUTORIALS Our research group develops accurate PESs for systems of interest to atmospheric, interstellar, and combustion chemistry, including two recent studies that are used here as tutorials: (1) a new PES for ozone22,23 and (2) three coupled PESs describing the spin-forbidden reaction of CO + O(3P) → CO2.24 The topography of our new PES for ozone is the key to interpreting the improved description of low-temperature reactivity. Previous ozone PESs have a submerged reef feature
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for the approach of O atom to the O2 fragment in the ozone formation process, which led to large discrepancies between calculated and observed low-temperature rates of formation.25,26 At long-range (R > 8 bohr) where electrostatics (quadrupole−quadrupole) provide a good description of the atom−diatom interaction, a colinear approach is slightly favored.27 At shorter distances, the colinear arrangement becomes repulsive (as is the T-shaped, side-on approach). In fact, there is only a small cone of acceptance about the equilibrium bond angle of about 117°. In addition to this angular bottleneck, in many ozone calculations, a spurious reef appears along the minimum energy path (MEP) due to an avoided crossing with an excited electronic state. We have created plastic models (Figure 1) of our new PES (without the
Figure 2. STL file representing three intersecting PESs describing the spin-forbidden CO + O(3P) → CO2 reaction. Three individual PESs were generated in a mesh. Finally, the three mesh surfaces were combined into a single multisurface object illustrating the seams of intersection between the PESs. Details of how this was done are provided in Supporting Information.
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METHOD TO CREATE PES MODELS WITH 3D PRINTERS To make a model of a PES (or any other data that might be represented as a surface plot), one must generate a digital file that can be interpreted by the printer. Typically, when one makes a surface plot of a PES, two coordinates are varied and represented in two axes of the plot while other internal degrees of freedom of the molecule are held fixed (or perhaps minimized). The height (third axis) represents the value of the function (potential energy in this application) and is most often also color-coded. For each of the two examples here (O + O2 and O + CO), the diatomic bond distance is held fixed, while the two active coordinates represent x and y Cartesian coordinates for approach of the O atom. An important step is to add a chosen finite thickness, so that the function defining the 2D surface becomes a 3D object with volume. A common format accepted by most printers is stereolithography (STL). STL files contain a triangulated representation of a model in terms of unit normal and vertices of triangles that make up the model (Figure 3). If one has a rectangular array of data typically used to generate a surface plot, then it must be converted to a triangulated form. This is easily done in Matlab.28 A Matlab script is included in Supporting Information that employs the Delaunay triangulation scheme,29 which maximizes the minimum angles of the triangles in the triangulation, minimizing the number of small and acute triangles, and is commonly used for this purpose. To create a model with a specified thickness, once the triangulated surface has been prepared, a duplicate surface is created by projecting the vertices of all the triangles along their respective normals. The two surfaces (set apart at a distance corresponding to the desired thickness) are then connected by a third “border” surface, making it a closed three-dimensional object (Figures 3 and 4). Note that STL files do not contain the absolute size of an object’s dimensions. These are set later (to user specifications) by the software driving the 3D printer. Once the STL file is loaded by the printer software and the overall dimensions are specified, the cost to print (which is typically based on volume) can be determined. The mesh model in Figure 2 costs only $7 to print at our campus library, but it is a good idea to get an estimate in advance. Some printing facilities charge additional fees for temporary support
Figure 1. Plastic models of two different PESs for ozone produced by 3D printing are shown in a wooden display box. For the model at the back of the box, a reef feature traps the marble (representing an O atom), while the absence of a reef in the model at the front allows the marble to reach the well, thus “forming ozone”. The O2 fragment (painted red in the back model) was also produced using 3D printing.
reef feature) and another PES by Ayouz et al. (with the reef feature),25 that make for a dramatic and easily interpreted demonstration when students roll marbles (representing the approaching O atom) on the two surfaces. With one model, the marble is trapped by the reef, whereas on the other, the marble rolls directly into the well, thus “forming” ozone. This demonstrates the importance of small potential barriers on low-temperature reactivity. The second tutorial demonstrates the spin-forbidden CO + O(3P) → CO2 reaction.24 Ground state O(3P) atom being a spin triplet is only “allowed” to combine with singlet CO to form triplet molecular states and is therefore “spin-forbidden” to form singlet CO2. In fact, nature finds a way through spin− orbit coupling between the singlet and triplet PESs. We have generated three PESs for this system, one for the spin-allowed formation of CO2 describing approach of an excited O(1D) atom, and two frustrated triplet states with shallow wells hanging high above the deep well of singlet CO2. We then make a model combining the three surfaces represented as a mesh (Figure 2), which illustrates the seams of intersection where spin−orbit coupling permits the trajectory to hop from one surface to another in the spin-forbidden reaction process. Here, we show how these PESs were made into 3D plastic models suitable for demonstrations. In the Supporting Information, we provide example data files and scripts that can be used by anyone to create their own. B
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Figure 3. (Left) A surface plot generated in Matlab representing the ground singlet state of CO2 as a 40 × 40 rectangular mesh. (Middle) The intermediate step of a triangulated mesh is shown. (Right) The solid object with specified thickness is represented in STL format ready to be printed into a plastic model.
Figure 4. (Left) A surface plot of the ozone PES representing the energy landscape for approach of an O atom to an O2 fragment describing ozone formation. (Right) The STL file representing the 3D model that was printed in plastic. The dimensions of the final model are 8 in. × 4 in. × 6 in. (height) and a thickness of 0.125 in.
triplet wells and have numerous opportunities to hop onto the singlet surface.
material that might be needed to support complex architectures during the printing process. Once finished, any support material is washed away in an ultrasonic bath.
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CONCLUSION We have shown that 3D printing can be used to print plastic models useful in demonstrating molecular structure and dynamics through visualization of potential energy surfaces. An interactive Matlab script requiring no programming or coding knowledge is included as Supporting Information and is straightforward to use (even by novice users of Matlab). It can be used by a wide range of people including mathematicians, scientists, and engineers to create and showcase threedimensional realizations of surface plot data. This has proven very useful for chemical education as students immediately appreciate aspects of a model they can hold in their hands. We plan to use the same approach to create mesh models of molecular orbitals.
HOW THE MODELS CAN BE USED IN THE CLASSROOM Plastic models of the ozone and CO2 PESs were printed and have been used in a number of classroom demonstrations as well as at an Educause workshop30 focused on the use of technology in education and at cutting-edge scientific meetings including a Telluride workshop on New Challenges for Theory in Chemical Dynamics.31 The models fit well into physical chemistry courses once the concepts of PESs and transition-state theory have been introduced. When a red marble (representing an O atom) is placed onto the ozone model, it becomes immediately clear where the dynamical bottleneck is and how approach outside the cone of acceptance becomes repulsive at close range (Figure 1). The second ozone model representing data with a spurious reef feature actually traps the marble outside the main well and facilitates discussion of van der Waals states and the significance of small barriers to kinetics at low temperature. It is particularly difficult for students to visualize how multiple PESs behave and intersect when relying solely on figures or diagrams. We have printed the three CO + O PESs separately as well as combined together in a transparent mesh (Figure 2). The size of the singlet−triplet gap relative to the well depth is immediately clear. It is easy for students to see how a trajectory on the triplet surfaces might oscillate in the
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ASSOCIATED CONTENT
S Supporting Information *
Description of an interactive Matlab script; example data files and scripts. This material is available via the Internet at http:// pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected]. *E-mail:
[email protected]. C
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Notes
(22) Dawes, R.; Lolur, P.; Ma, J.; Guo, H. Highly accurate ozone formation potential and implications for kinetics. J. Chem. Phys. 2011, 135, 081102. (23) Dawes, R.; Lolur, P.; Li, A.; Jiang, B.; Guo, H. An accurate global potential energy surface for the ground state of ozone. J. Chem. Phys. 2013, 139, 201103. (24) Jasper, A. W.; Dawes, R. Non-Born-Oppenheimer molecular dynamics of the spin-forbidden reaction O(3P) + CO(X 1Σ+) ∼> CO2(X 1Σg+). J. Chem. Phys. 2013, 139, 154313. (25) Ayouz, M.; Babikov, D. Global permutationally invariant potential energy surface for the ozone forming reaction. J. Chem. Phys. 2013, 138, 164311. (26) Siebert, R.; Fleurat-Lessard, P.; Schinke, R.; Bittererová, M.; Farantos, S. C. The vibrational energies of ozone up to the dissociation threshold: Dynamics calculations on an accurate potential energy surface. J. Chem. Phys. 2002, 116, 9749−9767. (27) Lepers, M.; Bussery-Honvault, B.; Dulieu, O. Long-range interactions in the ozone molecule: Spectroscopic and dynamical points of view. J. Chem. Phys. 2012, 137, 234305. (28) MATLAB, Release 2013a; The MathWorks, Inc.: Natick, MA, 2013. (29) Lee, D. T.; Schachter, B. J. Two algorithms for constructing a Delaunay Triangulation. Int. J. Comput. Inf. Sci. 1980, 9, 219. (30) Educause Learning Initiative Annual Meeting, Feb 3−5, 2014, New Orleans, Louisiana, USA. (31) Telluride Workshop. New Challenges for Theory in Chemical Dynamics; Telluride, CO, Jan 13−16, 2014.
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors gratefully acknowledge Sven Holcombe (University of Michigan) and Paul Kassebaum, Ph.D., Maker Community Relations, MathWorks for help with developing the scripts. R.D. is supported by the National Science Foundation (CHE-1300945) and the Office of Basic Energy Sciences, U.S. Department of Energy under Contract No. DESC0010616.
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