Integrating Computational Chemistry into the Physical Chemistry

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Integrating Computational Chemistry into the Physical Chemistry Curriculum Lewis E. Johnson and Thomas Engel* Department of Chemistry, University of Washington, Seattle, Washington 98195, United States

bS Supporting Information ABSTRACT: Relatively few undergraduate physical chemistry programs integrate molecular modeling into their quantum mechanics curriculum owing to concerns about limited access to computational facilities, the cost of software, and concerns about increasing the course material. However, modeling exercises can be integrated into an undergraduate course at a nontrivial level with minor modifications to the lecture curriculum and software that is inexpensively available to individual students. The modified curriculum was tested over a two-year period, and student reception of the new curriculum was assessed by means of end-of course surveys. Students found the added computational material to be useful and not overly difficult. KEYWORDS: Upper-Division Undergraduate, Physical Chemistry, ComputerBased Learning, Molecular Modeling, Quantum Chemistry

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he undergraduate physical chemistry curriculum is traditionally constructed around the topics of thermodynamics, quantum mechanics and spectroscopy, kinetics and transport, and statistical thermodynamics. For the most part, the training that students obtain in a standard physical chemistry course is good preparation for later professional activity. In studying thermodynamics, students learn how to calculate values for state functions at conditions differing from the standard state, how to calculate activities for components in a nonideal solution, and how to calculate the concentration of various components in an equilibrium mixture of reactive gases. In studying kinetics, students learn how to determine reaction mechanisms, how to predict the change in concentration of species with time, and how to extract activation energies from experimental data. In studying transport phenomena, students learn how to calculate diffusion rates, the rate of charge transport in ionic solutions, and rates of sedimentation and centrifugation. In studying statistical thermodynamics, students learn how to calculate thermodynamic state functions from molecular level properties. In studying spectroscopy, students learn how to obtain molecular information from the widely used techniques of vibrational, electronic, and NMR spectroscopy. Quantum mechanics is the one area of physical chemistry in which the material that the students learn is often not closely related to their later professional activity. Undergraduate quantum chemistry courses typically focus on basic theory, including particle and wave behavior, and solving the Schr€odinger equations for a few simple systems that can be evaluated analytically. These topics are appropriate for such a course because undergraduate physical chemistry is often a student’s first exposure to the material at a nontrivial level. However, it is deeply unsatisfying to both instructors and students to move from a quantitative model for the hydrogen atom and the H2þ molecule to a purely Copyright r 2011 American Chemical Society and Division of Chemical Education, Inc.

qualitative model for any other atom or molecule. For the vast majority of chemistry graduates, molecular modeling software will be their primary tool in applying their knowledge of quantum mechanics to real-world problems. Although still a rapidly growing field, computational molecular modeling has been used in undergraduate education for over two decades, paralleling the rise of modern desktop PCs with graphical interfaces. Early experiments and curricula focused on classical molecular mechanics and dynamics,1,2 as well as semiempirical electronic structure models.3 Schusterman and Schusterman4 discussed use of ab initio electron density surfaces in general and organic chemistry over a decade ago. Since then, several approaches to incorporating computational quantum mechanics into undergraduate coursework have been developed, including required chemical computation courses5 and comprehensive undergraduate curricula.6-8 The integration of modeling into the general, organic, and inorganic chemistry curricula has continued to increase. A few recent (since 2007) pedagogical applications for quantum mechanical modeling in coursework include calculating the inversion potential of ammonia,9 analysis of the stereospecificity of the Cope rearrangement,10 heats of formation of high explosives,11 π backbonding in carbonyl complexes,12 and UV-vis spectra of azulene derivatives.13 However, computational chemistry is less often covered in physical chemistry core coursework. Instead, computational quantum mechanics is often placed in a separate upper-division computational modeling course.14 Although a few schools use modeling exercises in their physical chemistry classes, it is neither common nor has it received significant attention in the literature. Why is molecular modeling software only rarely integrated into the physical chemistry curriculum? In our view, there are Published: February 28, 2011 569

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several perceived reasons that have made instructors reluctant to do so: Limited classroom time: Most textbooks already have more material than can be covered in a single course. If molecular modeling is added to a course, what material should be cut? Logistics: Chemistry departments at larger universities generally do not have enough computers with appropriate software accessible at convenient times for entire lecture sections of students due to the cost of hardware, software, and computational lab staffing. Laboratory implementation may be possible at colleges and universities with smaller class sizes. Limited time to invest in software training: Some lecture or discussion time will need to be dedicated to instructing students on the basics of operating modeling software. Furthermore, instructor time will be needed for troubleshooting software problems. We tested these hypotheses while teaching quantum mechanics and spectroscopy to 75 students, with students having individual access to modeling software. We used Spartan Student Physical Chemistry Edition,15 currently Spartan Student Edition,16 together with Engel and Reid’s textbook Physical Chemistry17 or Engel’s textbook Quantum Chemistry and Spectroscopy.18 Spartan, which has been used in the educational setting since its release,3 comes with a large number of tutorials and exercises, has an inexpensive individually licensed student version, and is well documented for teaching use.19,20 Currently, over 600 educational institutions possess site licenses to various editions of the software. Although our exercises were developed for use with Spartan, they can be adapted for use with other modeling packages such as Gaussian21 or GAMESS,22 using graphical front-ends such as WebMO,23 Avogadro,24 Ghemical,25 or Molden.26 Students in the course were provided an option to download GAMESS and Ghemical for free and some instructions in using GAMESS and Ghemical (in addition to those for Spartan) were provided during the first year the curriculum was tested. Depending on the licensing for the software in question, it could be run in a client-server arrangement or on students’ own computers. Some examples of exercises (mostly for organic or inorganic chemistry) written for use with Gaussian are provided on the Gaussian, Inc. education page.27 No department computers were reserved for the course, nor were any new software purchased by the department, although an older version of Spartan was available on a few machines in a computer lab. Because this university operates on a quarter system, a physical chemistry instructor has a total of 27 50-min lecture meetings to present new material, two of which are used for midterm examinations. The instructor also conducts one weekly tutorial, which is optional for students and focuses on problem solving. Typically, two homework problems from the textbook are assigned at each lecture, due at the following lecture, to encourage the students to practice the skills taught in lecture in a timely fashion. An online message board was also available to the students for discussing course concepts, homework, and computational exercises with each other and with the teaching assistants.

’ TRAINING STUDENTS TO USE COMPUTATIONAL CHEMISTRY SOFTWARE Instruction in use of the software consisted of three main components: (i) a single demonstration lecture showing how to

build a few simple molecules and submit geometry optimization calculations using the Spartan interface, (ii) homework assignments with detailed instructions (including needed commands), and (iii) lectures from the computational chemistry chapter in the Engel and Reid textbook.17 The demonstration lecture was delivered shortly before the first computational assignment and focused almost entirely on the practical issues of setting up calculations and reading output data. The detailed instructions for three of the problems described in the next section are included as Supporting Information. Some of the theoretical methods used within the modeling software, including basic many-electron electronic structure theory, were discussed in lectures near the end of the course. Such a course structure results in the software being used as a “black box” for the first few exercises, which is difficult to address owing to the large amount of background material needed to understand the Hartree-Fock method. The problem is somewhat mitigated by the computational details revealed later in the course and by focusing background material in the earlier assignments on concepts instead of methods. The teaching assistants provided supplemental instruction and technical support for students working on computational assignments during their office hours, as well as moderating an online message board for collaboration on assignments.

’ COMPUTATIONAL CHEMISTRY PROBLEMS Computational problems were assigned during four portions of the course: applications of the particle in a box, the harmonic oscillator and vibrational spectroscopy, many-electron atoms, and diatomic and polyatomic molecules. Multiple problems were assigned during the molecular quantum mechanics portion of the course. The first two homework assignments were tutorial exercises from Wavefunction’s Molecular Modeling in Physical Chemistry28 on how to use the Spartan interface. In the first assigned problem, students carried out a Spartan tutorial28 in which they calculated the equilibrium geometry of acetonitrile. This tutorial acquainted them with the model kit used to enter molecular geometry in the necessary input parameters (model, basis set, charge, multiplicity) required for a calculation. It also trained the student to read the output produced by the calculation. In the second assigned problem, students carried out another Spartan tutorial in which they compared the total energy of SF4 in the square planar and see-saw geometries and learned how to obtain values for atomic charges. These tutorials provide an excellent background for carrying out calculations, and very few questions about the software arose in the course after the tutorials were completed. In the third assigned problem, students calculated the HOMO-LUMO gap of butadiene, hexatriene, and octatetreane as a function of length using density functional theory (B3LYP/ 6-31G* functional and basis combination) and compared the trend in the band gap energy to that predicted by modeling the system as a particle in a one-dimensional box. Students also compared their butadiene result to an experimental UV-vis spectrum of butadiene and to TD-DFT calculations run by the instructors for the other molecules. The problem illustrated that the simple one-dimensional box model predicts the trends correctly, but does not give quantitative values for the energy gap. In the fourth assigned problem, students calculated the vibrational spectrum of several simple diatomic molecules (HF, 570

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HCl, CO, and NaCl). Students also examined isotope effects on vibrational spectra by repeating the HCl calculation using DCl, and calculated the bond dissociation energy, De, for HCl. All of the calculations used a B3LYP/6-311þG* functional-basis combination, which resulted in vibrational frequencies within 5% of experimental values. Students also calculated force constants from vibrational frequencies and related them to bond strength. In the fifth assigned problem, students calculated atomic properties of many-electron systems, demonstrating the concepts of electron correlation, spin multiplicity, and electronegativity, as well as Koopman’s theorem. Students compared the total electronic energy of a helium atom calculated with HF/6-311þG*, which does not include electron correlation, with a calculation on the same system using second-order Møller-Plesset perturbation theory (MP2), which does include correlation. They then repeated the Hartree-Fock calculation on Heþ, demonstrating that the Hartree-Fock method yields the exact (hydrogen-like) energy for a single-electron system. The remainder of the exercise involved using MP2/6-311þG* calculations to calculate the HOMO and LUMO energy for C and O in their most stable spin state, and use those orbital energies to calculate the Mulliken electronegativity of the atoms. Students also performed calculations on both anions and cations, using the energies to predict whether CO dissociates into ions or neutral radicals. This problem shows students that quantitative calculations can be carried out easily on systems that are not amenable to simple models. In the sixth assigned problem, students calculated the electronic structure of diatomic and polyatomic molecules. Students constructed qualitative molecular orbital (MO) diagrams for B2 and C2 based on the discussion in Engel and Reid textbook17 and then compared the MOs that they predicted with MOs generated by HF/3-21G calculations. The exercise also included an optional problem involving comparing B3LYP/6-31G* calculated MOs of benzene with predictions from H€uckel theory, as well as estimating the values of the H€uckel parameters R and β by solving a system of linear equations using MO energy values. This problem illustrates both the utility and limitations of simple models for real molecules. During the final weeks of the course, additional problems demonstrating applications of molecular modeling were assigned from the computational chapter of the Engel and Reid textbook.17 These problems typically involved more complex systems than the earlier conceptual exercises. No written homework covering computational methods themselves was assigned, though written questions on modeling methods, theory, and interpretation of software output were included in the final examination.

Figure 1. Interest in and difficulty of QM topics in 2008 class.

Figure 2. Difficulty of learning how to use Spartan.

to their careers as chemists. We first asked for input on both the difficulty level and the level of student interest in the major topics presented in the course. The results are shown in Figure 1. The variations among topics was small, and interest was negatively correlated with difficulty (R2 = 0.67, p < 0.01). We interpreted the computational chemistry category to encompass all computational material covered in the class. The perceived student difficulty of learning to use the Spartan software is shown in Figure 2. Only 16% of the students had a difficult time in learning the software. A teaching assistant was available for two office hours a week, as well as by e-mail and on the course message board, but was asked very few questions after students had completed the two tutorials introducing them to the software. Prior computational experience was not likely an important factor, as only three students in the class had any previous experience with molecular modeling software. Very few students skipped the assignments entirely (“did not use” on the figure). Figure 3 shows the perceived difficulty of the computational chemistry chapter in the Engel and Reid textbook,17 which in the view of the authors is written at a significantly higher mathematical level than the rest of the textbook. Students seemed to share this view. However, the material can be presented at a significantly lower level of mathematical rigor in lecture. Despite the perceived increase in difficulty, there was no statistically significant (p = 0.19,

’ STUDENT EVALUATION Student feedback regarding the inclusion of computational chemistry in the curriculum was solicited using an online survey administered during the week before the final exam. Students who submitted a survey received extra credit on the final exam, and 69 out of 75 (92%) of students from the 2008 class responded to the survey. Only the 2008 results were used in the following discussion, as the curriculum was more mature during the second year of testing. However, the 2007 results generally closely tracked the 2008 results. Data were analyzed using Microsoft Excel with the Data Analysis ToolPak, and error values are given as the standard error of the mean. The survey was intended to assess student interest in the material, difficulty learning it, and perceived utility of the material 571

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to have computational facilities for students to integrate computational chemistry in a physical chemistry course. On demand student access was achieved using student versions of commercial software (e.g., Spartan Student Edition) or software that is free or open source or free for academic use. Finally, adding computational problems did not cause significant disruption to the physical chemistry curriculum. Instructions on using the software were presented in a single lecture, and basic computational electronic structure theory such as the Hartree-Fock method and electron correlation were summarized in two to three lectures. The assigned computational homework replaced pencil-and-paper problems on a one-to-one basis. The only topic that was left out of the previous conventional course to accommodate the new material was quantum numbers for manyelectron atoms and atomic terms.

Figure 3. Difficulty of computational chapter in Engel/Reid relative to other chapters.

’ ASSOCIATED CONTENT

bS

Supporting Information Detailed instructions for three of the problems. This material is available via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

Figure 4. Utility of computational exercises.

one-tailed t test) increase in time spent on the computational assignments (2.7 ( 0.3 h) versus ordinary homework assignments 2.5 ( 0.4 h. The response of students when asked how useful the computational problems were in helping them understand the course material is shown in Figure 4. Nearly half of the students found the problems useful and only 15% felt that solving the problems was not useful to their understanding of quantum chemistry. Students were also given an option to respond freely regarding what quantum mechanics-related topic they expected would be most useful to them in later professional activity. Although fewer students responded to this question than the other questions, 40 students provided an answer. The topics most frequently mentioned in descending order were spectroscopy, chemical bonding, basic principles and simple models, and computational chemistry.

’ ACKNOWLEDGMENT The authors thank Philip Reid (UW), Warren Hehre (Wavefunction, Inc), Sean Ohlinger (Wavefunction, Inc), and Fred Grieman (Pomona College) for useful discussion, Wenkel Liang for TAing the 2008 course, and the students in Prof. Engel’s 2007 and 2008 Chem 455 courses for their feedback on the curriculum. ’ REFERENCES (1) Rosenfeld, S. Molecular Modeling as an Integral Part of an Advanced Lab Course. J. Chem. Educ. 1990, 68 (6), 488–489. (2) Dugas, H. Teaching Molecular Modeling. J. Chem. Educ. 1992, 69 (7), 533–535. (3) Casanova, J. Computer-Based Modeling in the Curriculum. J. Chem. Educ. 1993, 70 (11), 904–909. (4) Schusterman, G. P.; Schusterman, A. J. Teaching Chemistry with Electron Density Models. J. Chem. Educ. 1997, 74 (7), 771–776. (5) Kantardjieff, K. A.; Hardinger, S. A.; Willis, W. V. Introducing Chemical Computation Early in the Undergraduate Chemistry Curriculum. J. Chem. Educ. 1999, 76 (5), 694–697. (6) Palsek, R. A.; Zoellner, R. W. Molecular Modeling and Computational Chemistry at Humboldt State University. J. Chem. Educ. 2002, 79 (10), 1192–1195. (7) Martin, N. H. Integration of Computational Chemistry into the Chemistry Curriculum. J. Chem. Educ. 1998, 75 (2), 241–243. (8) Feller, S. E.; Dallinger, R. F.; McKinney, P. C. A Program of Computational Chemistry Exercises for the First-Semester General Chemistry Course. J. Chem. Educ. 2004, 81 (2), 283–287. (9) Halpern, A. M.; Ramachandran, B. R.; E., D. G. The Inversion Potential of Ammonia: An Intrinsic Reaction Coordinate Calculation for Student Investigation. J. Chem. Educ. 2007, 84 (6), 1067–1072. (10) Glish, L.; Hanks, T. W. Computational Analysis of Stereospecificity in the Cope Rearrangement. J. Chem. Educ. 2007, 84 (12), 2001–2003.

’ CONCLUSIONS Students did not find learning how to operate the software unreasonably difficult, particularly when tutorial exercises were provided early in the course. However, it was necessary to provide step-by-step instructions for setting up the calculations in each problem for standalone computational homework assignments. By the time that students were assigned textbook problems in the computational chemistry chapter, they were sufficiently comfortable with the software that detailed instructions were no longer necessary. It was not necessary for the chemistry department 572

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