Teaching AP chemistry is hard. It’s a race to cover all of the material between the start of the school year and the AP exam in early May. Conversations with numerous AP chemistry teachers over the years have suggested, however, that many teachers struggle most during the period between the completion of the exam and the end of the school year. In many places there may be 3-5 weeks of time between the AP exam and the end of the academic year, where the challenge is to keep the students engaged and motivated. So what do you do?

One idea is to offer a “short course” in a specialized topic or one that fits into your personal expertise. If, for example, a teacher has some experience with a branch of chemistry that is not typically taught in AP Chemistry, such as polymer chemistry or analytical chemistry, a short course in those topics might be of interest. Students could also do small research projects, perhaps with an emphasis on a review of the literature if suitable laboratory resources are not available. Other topics, such as the history of chemistry or conducting a review of Nobel scientists in chemistry, might be of interest. The potential short course idea presented in this article is an introduction to computational chemistry.

The foundations of computational chemistry were laid in the 1920s and 1930s, when a group of mostly physicists developed the theoretical underpinnings of modern computational chemistry. Scientists such as Niels Bohr, P.M. Dirac, and Edwin Schrodinger developed a wide variety of theoretical (mathematical) descriptions of the behavior of electrons at the quantum scale. The issue, however according to Dirac? “The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble.” This quote, from the Proceedings of the Royal Society of London in April of 1929, was basically saying that, given 1929 technologies, these equations could not be solved.

However, with the advent of modern computing technologies, these equations were now “soluble,” a reality now manifested in the field of computational chemistry.

Computational chemistry can be described as the application of mathematics and computer science to the study of interesting and challenging problems in chemistry. Computational chemistry is considered by some to be the “third leg” of modern research in chemistry,¹ joining experimental and theoretical approaches.

Figure 1. Knowing chemistry: a concept map

Computational chemistry can be used in a wide variety of ways to study chemistry. Figure 1 shows a concept map describing one view of what it means to “know” chemistry. Chemistry can be described as the study of the characteristics – structure, properties, and (re)activities – of molecules. All of these characteristics are easily and readily studied using a computational approach. For example, using computational chemistry students can build and optimize a water molecule, study its bond lengths and angles, and look at the energy, partial charges and dipole moments of the molecule. For example, the water molecule on the left (Figure 2) shows a bond angle of 77.854 degrees, an unoptimized molecular structure. The water molecule on the right (Figure 3) shows the same molecule optimized (using the semi-empirical software package, MOPAC) with a more realistic bond angle of 107.692 degrees.

Figure 2. Bond angle 77.854 degrees	Figure 3. Bond angle 107.692 degrees

Students can calculate and visualize the three vibrations for this and any other molecule. They can also calculate a number of other properties, such as: the electrostatic potential, a measure of where electrons are congregated on a molecule; the electron density of the molecule, showing the general distribution of electrons; the ionization potential and electron affinity, showing where electrons can leave and be attracted to the molecule; and molecular orbitals, which can be used to understand and explain chemical reactivity. We can study how chemical reactions occur by looking at the thermochemical and thermodynamic properties, such as the heats of reaction, Gibbs free energy, and entropies of a given reaction system. Why are these calculations important? The answer is that they allow chemistry students to conduct actual (computational) experiments and visualize the results, confirming and expanding on the visualizations they might see in a standard chemistry textbook.

The likelihood of your students encountering computational chemistry at the undergraduate level at most universities is quite high, and preparing them for that reality is worth considering. There is little doubt that most if not all chemistry teachers have that one topic or content idea that they hate not being able to teach, given the finite amount of time in any chemistry course. We certainly can’t teach all of college chemistry during high school! Given that, however, a topic such as computational chemistry has the ability to allow students to get a taste of many other topics in chemistry, including computational organic chemistry, drug design (medicinal) chemistry, and other current topics.

The sample course layout is based on a teaching schedule in which students meet for 90-minute blocks every other day. It also estimates that there are 10-15 days of contact time after the completion of the AP chemistry exam and the end of the school year. Given the many different schedules, both in terms of number of meeting blocks per week and the number of days available post-AP exam, the course could be tailored to meet the needs and desires of the students, instructor, and available time.

There are two common themes in a computational chemistry short course:

• Basic conceptual foundation of computational chemistry: in this theme, students learn some of the foundational concepts in computational chemistry. These include topics such as model chemistries, a description of the different types of mathematics (levels of theory) and the different basis sets that are commonly used in computational chemistry. For example, we want students to recognize different levels of theory, such as learning the difference between molecular mechanics/molecular dynamics (where we study the behavior of nuclear interactions), semi-empirical methods (where we only consider electron behavior, with some data calculated and stored in the software), ab initio methods (where 100% of the electronic properties are calculated in real time), and density functional theory (DFT, where we use the electron density as the starting point for calculations). These concepts can be taught without a heavy excursion into the underlying mathematics or quantum mechanics of each of the theories. Likewise, we want students to recognize and have a qualitative understanding of the use and role of basis sets, one of the key decisions a computational chemist makes when running a calculation.
• Applications of computational chemistry to chemical systems: in this section, students should learn different types of calculations that are common in computational chemistry, such as calculation of single point energies, vibrational frequencies, and potential energy scans. Students can (and should) also learn how computational chemistry can be used to study reactions, such as the oxidation of nitrogen monoxide (NO) to form nitrogen dioxide. For the longer session and/or more advanced students, topics such as transition state determinations (activation energy) and excited state chemistry (UV-Vis and emission spectroscopy) might be discussed.

So how might this program work in a typical classroom? There are multiple approaches:

• Teacher-led: in this scenario, the classroom chemistry teacher would serve as the content organizer and presenter. A typical scenario might be a 20-25 minute presentation by the instructor, followed by a 45-50 minute computational lab activity. Example lab activities can be found on the North Carolina High School Computational Chemistry server. [It should be noted that this server is dedicated to pre-college students and teachers in the state of North Carolina, but there is another server, located at the Shodor Education Foundation, that is a mirror to the North Carolina School of Science and Mathematics (NCSSM) server in Durham, and is available to a national audience.] Each day would serve as a stand-alone unit, and while there is a natural progression of topics, especially in the first part of the course, the topics are chosen and structured to allow for flexibility. For example, a knowledgeable instructor might decide not to spend any time on methods such as molecular mechanics, ab initio, or semi-empirical, but focus solely on the DFT methods used by most computational chemists. Likewise, instructors could change the order of the topics listed or eliminate them entirely in favor of some other topic.
• Student-directed: individual students or, preferably, small groups of students could organize themselves into a “short course study group” and leverage existing online materials. For example, a course in computational chemistry is offered as a full-semester offering at NCSSM. In support of this course, there are a series of podcasts available. Most of these podcasts are approximately 20 minutes long. Students doing individual study, small group study, or students working in conjunction with the classroom teacher could use these podcasts.
• External instructor-led: if your school is near a university, especially one of the larger ones, it is likely that there will be a computational chemist on the faculty. Many universities welcome the opportunity to provide outreach to schools, and the likelihood of getting a computational chemist to come in and teach this short class might be worth investigating. As with an experienced teacher-led program, the external instructor could use his or her expertise to develop their own scope and sequence, modify the ones shown in the tables below, or follow this program as developed.

The most challenging part of this program is, without a doubt, the lab activities that accompany each topic or unit. The two controlling issues are access to computational chemistry computer resources (software and hardware), and time.

There are a number of places where you might look to get access to computational chemistry software packages. All of the lab materials that have been developed for computational chemistry students at NCSSM are based on the Gaussian software (versions ’03, ’09, and/or ’16). Gaussian, like most other computational chemistry software packages, is prohibitively expensive for most high school programs, especially for a short course! Some options are as follows:

• University access: some universities might be willing to provide short-term access to their computing resources (i.e., access to the appropriate software programs and disk storage resources) for a program like this. There is likely, however, a long lead time to getting such arrangements set up, and also some work required to help students learn how to log into and use these remote resources.
• Use existing online resources: there are a number of existing Web-based resources that might be available. One is the server housed and maintained by the Shodor Education Foundation. This machine provides an easy-to-use interface, WebMO, that allows students to build molecules, prepare input files, run those files, and view the results. WebMO is not the chemistry software, but rather the interface that allows users to build molecules and submit them to one of several chemistry packages, such as Gaussian16 or MOPAC. The learning curve on WebMO is very short, well within the time limitations of a short course. The developers of the WebMO interface have a demo server that can run very small jobs (up to five minutes of CPU time, good for many of the types of jobs students might want to run).

The issues related to time are based on run times for most computational calculations. Even for relatively small molecules using basic mathematical methods, run times can sometimes be hours, depending on the computer resources available. The Shodor and NCSSM machines, for example, both use a “first in first out” queuing system, so if there are lots of jobs being submitted on any given day, it may take 24 hours or more for your job to complete and deliver results. The ideal situation is for the student to build his or her own molecule(s), set up the calculation, and run the job — all of which takes time, depending on the size of the molecule and what is being computed.

Needless to say, in a short course like this, waiting for longer jobs to complete might be impractical. A simple (but less than ideal) solution for this is to have students use tools like WebMO to view results of completed jobs (available from a repository of files run by NCSSM science faculty).

For example, students might want to study the fluorescence properties of nanowires. These computations take a long time, even with high-performance computing (supercomputing) resources, and there isn’t much to be learned in each student submitting a job. The interesting and educational part lies in the analysis of the results. For a series of structurally-related nanowires, which is the best one for fluorescence at a specific wavelength? Students can either look at the raw output data and/or upload the output files to WebMO for visualization of results.

By using this approach, students can learn the foundations of the topic such as absorption and emission spectroscopy, or learn about a sample system such as nanowires. The approach lets them view and analyze existing data to make some statements about how computational chemistry has helped them to do this type of science.

The lab, Find the Best Bond Angle and Bond Length of Water, is a good starting point for teachers considering introducing computational chemistry to their students. We are asking the student to study the molecular structure of a basic molecule, water. In introductory chemistry, we want students to understand that molecules have a structure that is determined by the types of atoms, the bond types (single, double, etc.), the bond lengths, angles, and, for larger molecules, dihedral angles. We have them learn that the bond angle of water is typically about 104.5 degrees. We can use computational chemistry to investigate the degree to which this is a valid bond angle.

What we typically do not teach students is that the structure of the molecule influences the energy of the molecule, and that the most stable version of the molecule is the one that has the lowest energy value. With this lab, students can perform a potential energy scan, or PES. This calculation determines the energy of the molecule as a function of the bond length and the bond angle, starting at some value for both and running the model for a number of steps at a user-determined interval. The data generated is the bond lengths, bond angles, and energy for each iteration. The student can then use this data to prepare a 3D representation of the PES. In our classes, we use Mathematica, but students can easily use Excel to create a plot of the energy scan. We also ask our students to do a PES run three times, each time “zooming in” on a closer approximation of the bond length and the bond energy.

This is the lab that I use with my beginning chemistry students and my introductory computational science students. It requires them to build the molecule, understand how to configure the interface, and modify the code generated by the interface. The first example is “scripted,” then I ask them to decide their own values for two more runs, based on the results of the first run.

So, you are intrigued – what’s next? Over the course of the 2017-2018 school year, members of the computational chemistry staff at NCSSM have been establishing a series of podcasts, lab activities with supporting data files, and other resources that will be publically available to AP chemistry teachers for use in their programs. The framework for this short course can be found here. It is anticipated that this resource will be well-stocked with appropriate materials for the 2019 school year, but materials are currently available for the 2018 school year. The author would welcome the opportunity to work with some number of teachers directly on activities and projects for the 2018 school year.

References

1. Sorensen, E. Chemist applies Google software to webs of the molecular world. https://sciencedaily.com. Feb. 13, 2012.

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