A Lab Course in Computational Chemistry Is Not About Computers

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A Lab Course in Computational Chemistry Is Not About Computers Downloaded via UNIV OF ROCHESTER on May 14, 2019 at 13:29:46 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

Alexander Grushow* Department of Chemistry, Biochemistry & Physics, Rider University, 2083 Lawrenceville Rd., Lawrenceville, New Jersey 08648, United States *E-mail: [email protected].

A laboratory course in computational chemistry is described. The course is taught for chemistry and biochemistry majors who have had at least one semester of basic physical chemistry that includes some quantum mechanics, but not a full theoretical description of molecular quantum mechanics. In the lab students are first introduced to basic concepts and techniques. Later experiments in the course use more advanced techniques or longer calculations to provide chemical insight or reinforce prior understanding. At the end of the semester each student will develop a chemistry question and learn how to perform the necessary computations to answer that question. Student and instructor reflections on the course will be provided throughout.

Introduction The Chemistry program at Rider University was being revised in response to changes in the ACS Guidelines (1) for approved programs. The department was working to diversify upper-level course and laboratory offerings. As a result of many discussions, it was clear that we needed to include computational chemistry more prominently in our curriculum. We wanted students to learn about computational methods, but for many of our students, the high-level theoretical underpinnings of textbooks (2–4) in computational chemistry at the time seemed to be more detailed than even our senior undergraduates would be prepared for. After participating in a workshop with Center for Workshops in the Chemical Sciences (known as cCWCS) (5), I began to realize that a large part of introductory computational chemistry should really be about “doing” computational chemistry. This workshop provided the initial ideas for how to develop a computational chemistry course. I also realized that a large part of the course would have to involve students doing computations and exploring the results rather than developing a deep theoretical understanding. To my department this sounded more like a laboratory course than a lecture course. Indeed, we decided that it was more suited to be a laboratory only. We have a mechanism to create two-credit laboratory courses that meet for six hours per week. Our scheduling is flexible enough that those six hours can be broken up © 2019 American Chemical Society

Grushow and Reeves; Using Computational Methods To Teach Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 2019.

into whatever time frames are best suited for a particular subject. For the computational chemistry laboratory, it was decided that two meetings of three hours each per week would work the best. All that was needed was a strategy for the course. Examples of other courses (6–9) and lab modules, as evidenced by several chapters in this book, do exist in the literature, but the description of an entire lab course devoted to computational chemistry as a means to learn about chemistry is not found in the literature. Before I describe the course, some context of the setting is in order. Rider University is a private regional comprehensive institution in central New Jersey with an undergraduate population of over 4000 students. There are a couple of different college units within the university, and the Department of Chemistry, Biochemistry & Physics resides within the College of Liberal Arts & Sciences. We offer an ACS approved B.S. degree in chemistry. We also offer a B.S. in biochemistry. Students with other scheduling constraints (double majors, usually) can elect to obtain a B.A. degree in chemistry which is not approved by the ACS but follows a similar structure with a few less upper-level lab and course credit requirements. The department graduates between five and fifteen chemistry and biochemistry majors each year. In any given semester we will offer one of our two-credit lab courses. We also offer some one-credit lab courses each semester that are usually tied to a specific lecture course. Most majors will take 1-3 lab credits per semester. Students will mix and match the lab courses that fit their interests and provide the required number of lab credits to graduate. As a result of this environment, there is a mix of chemistry and biochemistry majors in the computational chemistry lab, and there is a mix of experience with mathematics and physical chemistry. Some students will have had two semesters of physical chemistry and the lab and three semesters of calculus. Others may have had only two semesters of calculus and just the first semester of physical chemistry, which is the minimum prerequisite for the computational lab. I should also mention that the first semester course in physical chemistry is an introduction to both quantum mechanics and thermodynamics. In this course, students learn how the Schrödinger equation works and they develop solutions to the solvable problems up to the hydrogen atom. In the thermodynamics side of the course, we begin to explore a statistical approach to developing thermodynamic functions. We start with energy and entropy and begin to develop the concept of thermodynamic driving forces.

Guiding Principles to Course Structure With the recognition that many of the students in the computational chemistry lab have not had a lot of physical chemistry background but will have at least been exposed to the mechanism of solving the Schrödinger equation, I try to introduce computational chemistry from the ground up. I have developed four guiding principles for the lab course: 1. Students should learn how to develop some of the basic mathematical models to recognize that there is a theoretical and mathematical underpinning to the models. 2. Students should recognize the need to have a basic understanding of the computational chemistry tool they want to use. 3. Students should recognize that computational chemistry is not a panacea for all chemistry questions. They need to understand the limitations of computer modeling. 4. Students should learn how to frame a chemistry question that can actually be answered by computational methods. In a semester-long course, one cannot teach or even introduce all of the areas of computational chemistry and do them justice. Thus, some choices have to be made. I decided that the course would 212 Grushow and Reeves; Using Computational Methods To Teach Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 2019.

primarily examine quantum mechanical computer modeling. This was done primarily because the platforms exist to make quantum computational chemistry fairly easy to access and there are relatively easy-to-use visualization tools for quantum computational chemistry. The world of molecular mechanics and statistical mechanics is also of value. However, I have found that students have a little more difficulty with the interfaces used for visualization of results of these calculations. I should indicate that the four principles above are given in reverse order of importance to me, with the fourth principle being the most important point in this course. Even though the course is about computational chemistry, the key delivery that I want to provide for the students is that computational chemistry is a tool to answer chemistry questions. A good part of the semester is spent probing what kinds of chemistry questions can be reasonably answered using computational methods. Here too, the questions that quantum mechanical computations can answer are often more accessible to undergraduates who have not had any prior exposure to computational methods. The primary tool that I use in the laboratory is Gaussian 09 rev. B.1 (10) that resides on an 8processor server. Students access Gaussian using the WebMO (11) interface that also resides on the same server. WebMO is used because it provides enough information for basic introduction to using Gaussian, but also provides enough flexibility to utilize advanced features. The structure of most of the lab periods is also important. Before each period I usually have some reading assignment that may come from a couple of sources. I suggest that the students purchase Cramer’s Introduction to Computational Methods text (2), and many readings come from that. While the math and physical chemistry level of the text is a little higher than my students are usually ready for, it does provide decent descriptions of the methods in text form and also provides quite of bit of descriptive data for method comparison. After a short discussion (usually less than 30 minutes) of the methods or questions to be explored in the day’s activity, the students are given a set of instructions of how to develop the computation of interest for the day. Within the instructions I embed questions that students will need to answer to both move forward and also to develop some conceptual understanding of either the computations being performed, or later on in the course, to understand some of the chemistry being explored. Examples will be provided later in this chapter as I discuss the course sequence. For introductory and exercise materials I have adapted some materials from the cCWCS course that I previously mentioned. In addition, some of the exercises were adapted from the book by Foresman and Frisch (12) that provides many useful examples. At the end of each lab session, there is a series of reflection questions that students must answer and submit (electronically, of course). These reflections should take a student no more than 15-20 minutes and can sometimes be answered in the lab period or just after. Later in the semester as the computations become more involved and require more computing time, students must often reflect on their results long after the lab period is over. The computational server is accessible through any browser that is connected to the university internet domain, so that students can complete their work anywhere on campus. Again, later in the semester this is a very important consideration.

Initial Exercises I begin the course with the discussion of the use of parameters to fit data and the rule of diminishing returns of added parameters. We start by using a Mathematica (13) notebook to fit actual infrared spectroscopic data that contains weighted spectroscopic transitions for the fundamental and overtone absorptions of H35Cl. The students are familiar with this system from the physical chemistry course even if they have not done the physical chemistry laboratory course. Based on our curriculum, they are also familiar with fitting data to a function by the time they take this course. The Mathematica 213 Grushow and Reeves; Using Computational Methods To Teach Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 2019.

notebook performs a nonlinear optimization on as many parameters that are put into the function to be optimized. Initially, the students are asked to fit the data to a vibrational frequency and rotational constant and observe that the residuals of the fit take on a form that does not appear to have random behavior. They are then asked to add some parameters to their function for centrifugal distortion and vibration-rotation interaction. As more parameters are introduced the residuals get smaller and take on a more random appearance. Students then usually obtain the false notion that the addition of any new parameters will simply improve a fit. They are asked to add further terms to their function and they find that not only do additional terms not improve the fit, they can sometimes decrease the precision of the fitted parameters. This lesson, while not directly related to computational chemistry, is an important initial lesson in the thoughtful use of parameters. The next two exercises utilize previously developed computations to explore the nature of molecular mechanics as a means to understand both internal motions and the concept of geometry optimization. In the first example, the students look at energies of molecular systems as function of a change in one internal coordinate, such as a vibration or internal torsion. This is done using a table of previously computed energies as a function of a coordinate scan and examining them using MS Excel. In these exercises, students are asked to examine how these motions are most easily modeled with harmonic potential functions that rely on a small number of parameters. They then explore the role of optimization by calculating the slope of a potential function as a result of a change in one parameter, such as bond length or bond angle. Students directly observe how changes in a parameter value will affect the energy of the system. They do some basic optimization sequences “by hand” using Mathematica to explore the idea of function minimization, with an eye toward minimizing the energy of a molecule to find the “best” set of internal coordinates of a simple molecule, such as water or carbon dioxide.

Early Explorations with Gaussian With these initial explorations, students still don’t have much context for computational chemistry, but in the next lessons, they are introduced to WebMO and the use of Gaussian. Initially, we explore the mechanics of how to draw molecules, perform initial molecular mechanics minimization and submit a basic quantum mechanical geometry optimization. They explore the differences in results from molecular mechanics versus quantum mechanics. The difference between a parametrized calculation (such as molecular mechanics or semi-empirical methods) and an ab initio calculation. The server is fast enough that simple molecules even with 8-10 heavy atoms still run fairly quickly, so these exercises have very little lag time in the lab. After students learn the basics of using the WebMO interface to draw structures, develop and submit jobs, and then read and interpret the various kinds of output information, we move on to basic aspects of calculations. In each of the next several lab sessions the students explore the effect of basis set and model chemistry, calculations of vibrational energies and their importance, and the importance of finding global minimum structures. The activity on basis sets first explores the need for approximations. We also discuss the variational method. Because the first course in physical chemistry only explores the solvable problems in quantum mechanics, some students have not yet experienced the use or description of approximate methods in quantum mechanics. In this exploration students examine how a Slatertype orbital can be approximated by the sum of carefully chosen Gaussian-type orbitals. This exercise is also done using MS Excel and Mathematica to examine both visually and numerically how well various basis functions can approximate a particular Slater-type orbital. The students then perform basic minimization calculations on small diatomic molecules to find a minimum structure. This 214 Grushow and Reeves; Using Computational Methods To Teach Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 2019.

activity can also be extended to spreadsheet examination of structural properties calculated under different model chemistries (14). In subsequent exercises, the students explore graphical depictions of molecular orbitals on diatomic or larger molecules. Because some of the students have not yet been exposed to molecular quantum mechanics in physical chemistry, the concept of a linear combination of atomic orbitals is explored in the exercise by asking the students to pick out specific non-bonding orbitals and compare their shape with atomic orbitals. Students are also asked to use their experiences with the concepts of bonding, anti-bonding, sigma and pi orbitals that have been developed in prior courses to help them interpret molecular orbital pictures. This particular exercise, while simple at the start, leads them to the recognition that molecular orbital pictures are not always the simple cut and dry diagrams that they might have seen in their organic chemistry textbook. As an example, Figure 1 shows the HOMO-2 orbital of formaldehyde which is the molecular orbital that is two below the HOMO in an energy level diagram. Initially, students have a very difficult time determining if this MO is a bonding or antibonding orbital. While it does look like sigma bond between the carbon and oxygen, as students recognize it, the presence of the nodes perpendicular to the bond axis seem at odds with the definition of a sigma bond until they recognize that the nodes occur over the atoms and not on the line in between the atoms. Also, the shape of the lobe that covers the carbon and both hydrogens also seems a little unusual until the students get more comfortable a with molecular orbital being a linear combination of multiple atomic orbitals.

Figure 1. The HOMO-2 orbital of formaldehyde. The third exploration is the calculation of vibrational frequencies. This exercise actually stems directly from the early exploration that used the harmonic oscillator model to describe internal motions. In this exercise, students explore a couple of specifically chosen examples for the determination of vibrational frequencies to compare with spectroscopically observed measurements. These examples serve to show the utility and limitations of the harmonic oscillator model used by programs like Gaussian to model not just vibrational frequencies, but also internal vibrational energy – a topic to be discussed later in the semester. A final example serves to show the importance of searching for imaginary frequencies after performing a geometry optimization or attempting to find a transition state geometry. In particular, we begin to explore the more complex ideas of molecular motions between to stationary points across a transition state. For example, the students explore the isomerization between 1-fluoropropene and 3-fluoropropene adapted from Foresman and Frisch (12). The transition state for this isomerization is shown in Figure 2. In this exercise, students compare the isomers to one another and then calculate the transition state between the two, exploring the atomic motions through the transition state and the nature of the imaginary or “negative” frequency of that motion. 215 Grushow and Reeves; Using Computational Methods To Teach Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 2019.

This section of the course takes about 3-4 weeks of the 13-week semester. Between this and the introductory materials, we are almost at the halfway point of the semester. What I have not spent a lot of time on is distinguishing between various methods, such as Hartree-Fock, MøllerPlesset, Density Functional methods, not to mention the higher order methods for developing higher accuracy calculations. We have used some of these methods, but the students at this point only recognize that there are a number of different model chemistries, and that the choice in method seems to be dependent upon the calculation of interest. The reason for not emphasizing the modelchemistry choices, is because the second half of the semester is spent looking at applications of quantum calculations, and quite often the application will dictate the type of calculation that should be performed. The key for the first half of the semester, is to get students comfortable using the WebMO interface both for input and output. In many of the examples, I have students alter the basis set to something that is not in the dropdown menus of WebMO, forcing the students to learn how to modify an input file. In other examples students need to find results from the full output file rather than simply recording numbers or pictures off of the GUI interface of WebMO. As the students perform more detailed computations, I am able to provide them with guidance and questions that requires less and less step-by-step instruction. This is an important scaffolding technique that allows the students to use Gaussian with more ease and comfort giving them more expertise in using the tool.

Figure 2. Transition state of fluoropropene.

An Initial Chemistry Question While there are a number of other investigations that could be done to explore various methods and model chemistries, at the midpoint of the semester is it time to have the students actually explore some chemical questions. Along the way, we will discuss other computational methods, but at this point in the semester, the students are now comfortable using the WebMO interface, modifying input files and digging into a lengthy output file looking for a specific result or descriptor. The first chemistry question that is addressed using computations is “What makes an electron a valence electron?” This experiment was developed by Melissa Reeves and has been described elsewhere (15). The experiment was developed as part of an NSF-Sponsored project that is also described elsewhere (16). This experiment leads students through a series of computations on atoms and diatomic molecules and a subsequent analysis of the energies of various orbitals in these systems to have students recognize that a primary characteristic of valence electrons is that they are more easily ionizable than other electrons in an atom. Students also find that in a molecule, the valence electrons are those found in orbitals that change energy quite a bit as a function of bond formation. Whereas core electrons reside in orbitals that don’t change energy during bond formation. The key 216 Grushow and Reeves; Using Computational Methods To Teach Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 2019.

aspect of this two-lab period activity is that the students are learning to use the computational tools to answer chemistry questions. Clearly, there is a great deal of scaffolding in this experiment. While students do have some choices to make in terms of the computations to run, the goal is to guide the students to the learning goals through a carefully designed line of questioning that goes along with a series of specific calculations to answer those questions. It is important to note that the model chemistries used to perform most of the computations in this experiment are low-level, because while the accuracy of the orbital energies may be suspect, the qualitative trends seen in the results are similar to those found in much higher-level calculations. And this brings up another important aspect of the laboratory course; it is billed as an introduction to computational chemistry. While computational accuracy is emphasized in some of the activities, it is not stressed in every experiment. At several points in the semester, we discuss when computational accuracy is important and when expedient computations will provide a reasonable answer for our chemistry question. The “Valence Electron” experiment has undergone extensive testing by faculty who were part of the NSF-Project (16, 17) and numerous revisions were developed as a result. Many of the subsequent activities in this computational chemistry laboratory follow along a similar line of asking the students a chemistry question, providing them with some guided instruction on how to develop an appropriate computation to find the answer and then asking the students to provide some analysis of the data and reflection on the process.

The Final Project Introduced After the “Valence Electron” experiment, students are introduced to their final project for the laboratory course. Simply put, it is up to the student to develop a chemistry question that they can answer using computational methods available to them through Gaussian. Initially this is a very daunting task because we have not learned all the possible techniques and considerations or computational methods. As I will describe further, the next several weeks of the semester are spent examining systems of chemical interest and learning how to use techniques to answer a particular question about that system. I have found from experience that giving the students time to develop a question of their own while we explore advanced techniques better prepares them to pursue a line of questioning that might parallel a topic they are studying in this or another class. This helps to scaffold the development of their experimental question. Two weeks after the final project is introduced, the students must discuss their initial ideas with me to determine the validity of the question and how they might use a computational method or methods to develop an answer. In many cases, a student develops a question that can be pursued using a method that we have already discussed in the lab (or will be discussing in the coming weeks). Most of the time, I will send the student to explore the question in the research literature to find resources about their question or find if a similar question has been addressed. While these students are still novices at reading the literature in computational chemistry, they are often surprised by how much of a basic research paper in computational chemistry that they can understand at this point in the semester. For those students who rely on work based off of the research literature, we spend a good bit of time in the intervening weeks working to understand what is described in the literature. A number of students have reported this as being a very powerful learning experience. For those students who decide to build from one of the exercise or lab questions that they have done in the semester, their work is similarly daunting because they must use what they have learned to develop their question and explain how a chosen computational method will answer that question. Whether the question is one of the student’s choosing or an extension from research literature, each 217 Grushow and Reeves; Using Computational Methods To Teach Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 2019.

student must have a finalized proposal of their question by week eleven of the thirteen-week semester. I will discuss the nature of some of these questions and projects later.

Other Chemistry Questions The remainder of the instruction in the laboratory (about four weeks) is spent exploring other chemistry questions as a means to introduce more complicated methods of analysis or to determine other properties. In all cases I try to have the students explore the utility and limitations of each method. In the next experiment, students examine the structural features of malonaldehyde and explore the computation of internal coordinates of a molecule that also undergoes an internal conversion (proton transfer). Their first set of calculations explores the precision of the computed bond lengths and angles as a function of model chemistry. In particular the students examine the value in increasing the size of the basis set to the precision and accuracy of the structure and examine the trade-offs in increased computing time. In a subsequent exercise, the students examine how the computation of vibrational frequencies and internal motions are affected by model chemistry as well. This activity is followed by another discussion of the trade-offs of computationally expensive calculations. Exploration of structural features is then followed by an examination of how to calculate reaction energetics. In this section, the students are shown how to use the technique of isodesmic reactions to determine either a Δ f H° for a compound of interest or a Δ r H° for a specific reaction. After examining a couple of known reactions to compare with literature values, the students choose a question of their own to answer. Most explore the changes in Δ r H° as substituents are changed. The scheme shown in Figure 3 represents an isodesmic reaction and students can replace the –X with a hydrogen or a halide very easily. However, they do begin to see some troubles if the group is larger than an atom. This exercise is also modified from the examples in Chapter 8 of Foresman & Frisch (12). Along with this exercise, the students spend some time examining how the size of the molecules affect the accuracy of a calculated enthalpy or Gibbs energy. In particular we explore the nature of the computation of the zero-point energy (ZPE). This leads to the discussion of one of the limitations of quantum calculations in the determination of thermodynamic quantities. Often quantum calculations of thermodynamic properties are more useful in examining a series of compounds or reactions rather attempting to determine a highly accurate value of a single molecule or reaction. At the end of this exercise, the students find that for larger systems it is very important to design the series of calculations to reduce the effect of the limitations mentioned above.

Figure 3. A simple isodesmic reaction. We next explore the use of simple solvent models to examine the effect of solvent environment on the structure and properties of a compound. While quite a bit of work has been done on modeling solvents in quantum calculations, I don’t spend a lot of time exploring all the methods and types of models. I have found that simply exploring the nature of solvent cavity calculations in continuum models is sufficient for students to understand the effects of solvent in a quantum computation. In the past, I have had students perform additional modeling using one or more explicit solvent 218 Grushow and Reeves; Using Computational Methods To Teach Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 2019.

molecules. While this can provide more accurate results, the time for students to develop successful computations of this type has seemed to outweigh the additional learning gains from the exercise. In one lab period the students compare the results of prior gas-phase computations with computations done in various solvents. They explore the effect of solvation on structure, conformation, and vibrational energies. One or two students have explored solvent effects further in their final project and that has produced some interesting results and discussion for the class. Students explore coordinate scanning over a couple of laboratory sessions. In the first session, they examine the effect of scanning bond angle coordinates on the molecular orbital energies and shapes within triatomic molecules such as H2O, BeH2, CO2, and H2S. The chemistry question is why are some molecules bent and others are linear? To answer this, students compute molecular orbital energies as a function of bond angle. Many students come into the course with a mindset developed in organic chemistry that hybrid orbitals govern the shapes of molecules. While they did see some familiar shapes in our earlier exploration of MO diagrams, there were many that were unfamiliar. Most of my students have already heard about my views on the teaching the hybrid orbitals (18). I take this time to have them find an sp3 orbital on the water molecule or the alternating pi bonds that a valence bond model would predict for CO2. When they can’t find these, it provides a more powerful teaching moment. When the students further see how the orbital energies change as a function of bond angle for all four of the molecules, they begin to understand that the molecule shape is not determined by one orbital or hybrid orbital, but the collection of the orbitals that are produced from atomic orbitals that contain valence electrons. This also provides an interesting connection to our earlier exploration of the valence electrons in atoms. In the next exercise, we examine reaction coordinate scanning and discuss some of the difficulties and limitations of performing this kind of calculation. A very nice and simple exercise involving the SN2 reaction is provided in Foresman and Frisch (12). However, I have different student teams then tackle multiple variants of the methyl chloride to methyl fluoride calculation. We then discuss issues of complexity in the calculation and the fact that these were done in the gas-phase resulting in the unexpected weakly bound ion-neutral reactants and products which would not be observed in the solution phase. Indeed, this has also led a couple of students to explore the effect of solvent in their final projects. One of the last explorations in the semester involves the calculation of charge densities. The students compare the Mulliken population analysis for a couple of small molecules and ions that are simple and straightforward. When they look at molecules that might have an organic resonance structure, the students find that the electron populations are not always what they expect, particularly for ions with a double bond nearby such as an allyl ion or acetate. The students then explore other methods for calculating a charge density such as Natural Bond Order (NBO) analysis or CHarges from ELectrostatic Potentials using a Grid-based method (CHelpG), and we discuss the advantages and limitations of each. However, through these analyses, the students are also pursuing questions that are often related to their understanding of organic chemistry to test how different substituents may affect the resulting charges. In a subsequent set of experiments students may examine the effect of a solvent model discussed above on the nature of the electronic population. Another exercise looks at an estimation of bond order. This has been done in two ways. The simplistic method uses the sum of the product of molecular orbital coefficients on adjoining atoms to determine a bond order. This exercise, while simple, does require the use of a spreadsheet to analyze contributions. I have found that this exercise can be lost on some students because they have not yet had a formal exposure to molecular orbital theory. Therefore, I have introduced calculations using the Atoms In Molecules 219 Grushow and Reeves; Using Computational Methods To Teach Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 2019.

(AIM) approach to compare with the atomic charge analysis and find that students seem to appreciate the more black-box nature of this calculation. If time in the semester permits, I also have the students explore spectroscopic calculations. Students are often interested in predictions of NMR spectra and, to a lesser extent, UV/Vis spectra. The nature of these computations are strongly dependent upon basis set size and the accuracy of the optimized geometry (particularly for NMR). As a result, these computations can be time consuming for the medium sized molecules that are of interest to my students. After going through a series of computations and comparing them to known experimental values, they are encouraged explore other molecules that they might be interested in. Most students will choose molecules that they have made in other laboratory courses or are performing research on as part of their independent study. Exploring the use of computational chemistry to calculate something that might be of value in their own research project has proved to be highly motivating and engaging.

The Final Project and Presentations The last two weeks of the semester are then reserved for students to work on and then present the results of their final project that was described earlier. Most student have had their proposed questions approved a couple weeks earlier and will have begun to develop a research plan and decided on the type of computations they will need to perform. Some students will perform initial work earlier, but the twelfth week of the semester is reserved for the students to work on their questions in the computer lab. I am available for the entire lab period for both sessions that week to assist with questions and troublesome calculations that don’t proceed as planned. Some students opt to work outside that time frame, particularly if they have a computationally intensive series of calculations that will be take up a quite a bit of time on our small server. It is of interest to note that early in the semester, the students do not really notice how much time computations take, because they are relatively quick. But as the semester wears on and we are doing computations in solvents, or with much larger basis sets, they become acutely aware of computing time resources. For the last week of the semester, students prepare a 20-30 minute presentation of their question and the results they obtained. They must clearly articulate their question and the computational method(s) they chose to answer the question. In the cases where the students are pursuing a question based on research literature, they also spend some time explaining the background of the methods they have employed if there are differences from what we have done so far in the laboratory. The rest of the class provides review feedback for these presentations as a way for me to (a) make sure they are paying attention to their peers and (b) assess the clarity of the presentations. The final grade for the presentation is a combination of my review and the peer reviews. Students are also graded on their performance in their review of their peers. The last graded piece of the project is a report that provides greater details of the work on their project. This report is due during the final exam period of the semester. As indicated earlier, I will provide a couple of examples of research questions that have been pursued to greater or lesser success. Some student projects result from extensions of exercises performed earlier in the semester. One student chose to examine bond angle and bond lengths for the analogs of water from H2O to H2Te. What surprised the student more than the structural changes was the fact that she had to use different basis sets to effectively calculate the results for the selenium and tellurium compounds. The exploration of basis-set effects proved to be challenging as she had to dig deeper into the Cramer text and the research literature. And she thought she was choosing a simple extension! 220 Grushow and Reeves; Using Computational Methods To Teach Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 2019.

A couple of student projects have explored further the charge density and bond order questions in larger molecules; often heterocyclic molecules or those containing pi bonds that may have electron withdrawing or donating substituents on them. Similar projects have examined the charge density of a series of carbocations or carbanions that have sometimes piqued the curiosity of the students. It should be noted that in the last few times when the computational chemistry laboratory was offered the department has offered in the same semester a course in physical organic chemistry with a lab component. For those students taking both, this course has provided numerous examples for students to cross-fertilize their pursuit of chemical questions. Other examples of this crossfertilization are evidenced by an examination of the transition states and reaction coordinate calculations. Two that come to mind are the exploration of a Grignard reaction scheme and pathway of a Diels-Alder reaction. Both of these initially seemed relatively straight forward, because there are examples of each in the research and education literature. However, when a student picks something that is not exactly the same as in the literature, they often find that pursuing their question leads to some challenges. Along the lines of advanced structural calculations, one student was fascinated with organometallic chemistry and found a research paper on computing structures of organometallic reaction intermediates. The student wanted to see how changing substituents on the metal center changed the structure of the intermediate. Again, he had to explore using alternate basis sets, and the molecules themselves were not small. These computations were often done over night when others where not using the server. Another biochemistry student was interested in peptide structure. While larger peptide structures are better determined using methods other than quantum computations, the student was able to explore structures of a couple amino acids, both charged and uncharged and then explore their structures when they formed dimers and trimers. Another area that did get some attention from students was spectroscopy. While the NMR spectroscopy proved pretty straightforward in the previous exercise provided that an accurate structure was determined, a few students found an interest in electronic spectroscopy. A couple of projects have looked at absorption profiles of substituted coumarin dyes to explore how substitution affects the apparent λmax. One project of particular interest was the exploration of the fluorescence spectrum of substituted naphthalenes. This also proved interesting for the student since she had to learn about the potential energy surfaces for the ground and excited electronic states in order to fully understand how to calculate the energy of the fluorescence transition. Her research led her to a number of literature papers and I would say that she learned just as much about fluorescence spectroscopy as she did about computing a fluorescence spectrum!

Summary of Learning Goals and Activities One of the more attractive aspects of this lab course for the students has been the fact that they don’t need to write full lab reports for a lab course! But to revisit the guiding principles, having students perform a lot of writing was not one of my key goals. In Table 1, I have summarized the activities in the order they were done along with the methods used and learning goals for each. As indicated in the text above, some activities took one lab period, others took two, i.e., an entire week. In addition, there is a visual time-line for the 13-week course given in Figure 4. These activities are more thoroughly described in the preceding sections. While most of the learning goals for each activity listed in Table 1 do not directly match the four guiding principles provided at the start of this chapter, I would suggest that they do map onto the main streams given in Figure 4. The basics of mathematical modelling and theory are given in the first 221 Grushow and Reeves; Using Computational Methods To Teach Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 2019.

stream. The second and fifth streams address the need to understand the basic tools of computational chemistry. In all the activities, particularly those in the fifth stream, we address the care that must be used when interpreting the results of a computation. Indeed, during the final project, which mainly covers the fourth guiding principle, many students learn while developing their methods for addressing their chemistry question, that almost every theoretical computation has its limits. I have highlighted the Valence Electron experiment in Figure 4 because this experiment is indeed the turning point in the course when we move from emphasizing the learning of methods and techniques to the ability to answer a chemistry question using a method or technique. It is during the fifth stream and work on their project when the student develops the experience that enables them to pose a chemistry question that can be answered by computational methods. Table 1. Summary of the activities in the lab course as described in previous sections of this chapter. The sequence shown here follows the syllabus for the course. Exercise

Computational Method

Target Learning Outcome

Exploration of the HCl spectrum

Non-linear least squares fitting

The value of descriptive parameters

Model computational methods

MS Excel and Mathematica to examine parametrization

The process of energy minimization and structural determination

Using the WebMO interface Molecular mechanics, semi-empirical Exploring the advantages and and ab initio calculations and Gaussian disadvantages of each method Examination of basis sets

Mathematica and Excel-modelling of basis functions

The approximation of wavefunctions

Graphical depiction of molecular orbitals

Gaussian minimization and single point calculations

Comparing calculated wavefunction “shapes” to prior experiences

Vibrational frequencies

Vibrational frequencies and use of scaling factors

The utility and limitations of vibrational calculations

Transition state geometries

Computation of imaginary vibrational Observation of an unstable stationary frequencies state

Valence Electron Experiment Single point and scanning computations

How to pose and answer a chemistry question

Determination of internal coordinates

Use of various model chemistries in computation

How basis sets can affect simple computations

Can I calculate a reaction energy?

Calculation of thermodynamic properties

Difficulties and limitations of thermodynamic computations

How does solvent affect a calculation?

Addition of solvent-continuum models to previous computations

Effect of solvent on a computation in both time and quality

The bond angle of water is not 109.5°

Coordinate scanning

How orbital energetics determines structure

Where is the electron density?

Calculation of charges using various methods

Charge density can be a complex calculation

222 Grushow and Reeves; Using Computational Methods To Teach Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 2019.

Table 1. (Continued). Summary of the activities in the lab course as described in previous sections of this chapter. The sequence shown here follows the syllabus for the course. Exercise

Computational Method

Target Learning Outcome

Spectroscopy

NMR or UV/Vis computations

Using electronic structure to determine a spectrum

Final project question

Determined by the question

Developing and answering a chemistry question

Figure 4. Timeline for general activities during the 13-week semester. Students work on their topic at various open times and outside class during the second half of the semester, with week twelve entirely devoted to work on the project and week thirteen to the presentations.

Responses and Reflections About half the students that have taken the computational chemistry laboratory did so because they needed additional laboratory credits to complete their degree program and this course fit their schedule and other constraints. I am well aware of the fact that many students were a little dubious of taking a course that looked as if it was another physical chemistry lab just with computers. However, as evidenced by the comments in the course evaluations, most of the students changed their tune by the end of the course. They were very appreciative of the fact that there are no full reports except for the project report at the end. Yet they also gained new insight from the reflections that they had to write after each set of activities. Many felt that they had learned some important techniques and yet still respected the difficulty of computational chemistry. Early in the semester the printed procedures were very detailed to make sure students could get results without too much frustration. Later on, the level of detail in the instructions diminished as students became more accomplished with using WebMO and Gaussian to find the appropriate results in the output. This was also noted by a number of students in their course evaluations. Students also commented on their ability, in a number of cases, to pursue chemistry questions of their own interest, not just in the final project. While this was indeed my design in the course, it was nice to know that some students recognized that aspect! I have also found that most students did not mind the challenging cases later in the semester, particularly in their final projects because that had some ownership of their experiments. It is good for students to engage in some challenges. You want them to have a little frustration to ensure that they recognize that computational chemistry is not a simple panacea for all chemistry questions. Furthermore, it is 223 Grushow and Reeves; Using Computational Methods To Teach Chemical Principles ACS Symposium Series; American Chemical Society: Washington, DC, 2019.

important for students to recognize that one needs to understand the requirements and limitations of a particular calculation in order to properly understand the value of the results. Indeed, that was another discovery that a couple of students voiced in their evaluations. The two-credit lab course is an unusual format that I have not heard of at many other institutions. That said, this course could be modified into a course that was a four-credit lecture-lab course, where a significant portion of the “lecture” time would be used for computational work in the presence of the instructor similar to that which was reported elsewhere (6). A significant enough portion of time was spent doing computations, that it is still appropriate to call this a two-credit lab. I also don’t see any reason that this course couldn’t be scaled up from the 8-15 students I have had to 20 or more. The key factor is that whatever software is used needs to be accessible by all students in the course at the same time. They need to be able to explore separately as much as possible so that they can individually learn how to do the different type of computations described. But they also need an environment that allows for collaboration as well, because I found that just as in a traditional lab environment, students learned how to fix their “experimental” mistakes by talking with one another. The key limiting factor is to have the instructor coverage for all students in the lab readily available to help out when input errors cause calculations to go wrong. My final thought on this course is that while I realized early on that I wanted to make this course about chemistry and not about computers, it was a pleasant result that students have also eventually recognized that as well.

Acknowledgements The author would like to thank all the students of CHE 375 who have been patient with the technology and have worked hard to learn some new chemistry as a result.

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