In the Classroom
A Computational-Modeling Course for Undergraduate Students in Chemical Technology
W
Rita K. Hessley College of Applied Science, University of Cincinnati, Cincinnati, OH 45206;
[email protected] This Journal has published manuscripts recently that describe an array of applications and insightful ways to integrate several commercially available PC-based molecular modeling software packages into classroom and laboratory instruction (1). Several other articles have appeared recently in this Journal that describe methodologies with which broader integration of computational methods, including modeling, into the chemistry curriculum has been achieved at both the undergraduate and graduate levels (2). PC-based software technology makes it possible to illustrate fairly rapidly the dynamic nature of molecules in ways drawings and handheld models cannot. It provides a visual context for many of the abstract concepts that lie at the heart of chemistry, such as electron distribution, atomic and ionic sizes, bond motions, and molecular orbitals. Formulating a visual image for abstract concepts in chemistry has been shown to make it easier for students to grasp and retain their meaning and significance, to comprehend more fully the meaning of terms, and to more easily make connections among related concepts (3). Moreover, even at an introductory level, to make sense of and apply computed data to draw conclusions and answer questions proposed about a structure using modeling software requires minds-on engagement, not merely hands-on manipulation. Connected to development of chemical concepts, molecular modeling has the potential to stretch students’ critical reasoning skills and to help them hone their chemical intuition. The UC College of Applied Science five-year baccalaureate program leading to the degree Bachelor of Science in Chemical Technology is laboratory-intensive. Most courses have six hours weekly of the laboratory component, and coop work experience in the chemical industry is required. The program requires two quarters of calculus and statistics, but neither physical chemistry nor mathematics beyond Calculus II are required. Students complete their program of study with a capstone senior project. This is a yearlong process carried out in consultation with an industrial or faculty mentor and includes identifying and investigating a hypothesis-driven problem and the written and oral presentation of the experimental results. In addition to modeling as a learning aid, the decision to include a stand-alone course in molecular modeling into the chemical technology curriculum was motivated by our view of the link between the increased prominence modeling has in industry and the quality of our curriculum. Our graduates are employed by a variety of chemical industries where they become involved in experimental design, data acquisition, and data reduction associated with the R&D activities of those industries. Our program stresses instruction and experience in the use, applications, and limitations of other modern laboratory instrumentation and methodologies
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for chemical analysis. It seemed important that we also expose our students to the language associated with molecular modeling and to the rudiments of modeling. A goal was to have them realize that chemistry being done in the “computer-information age” is still thoroughly grounded in the scientific method: it involves observation, questioning, hypothesis formation, and testing. Perhaps the best feature molecular modeling has to offer toward this end is that it explicitly links theory with the practice of chemistry at the bench. While a command of quantum chemistry and its application to modeling will likely be beyond the scope of our students’ future work without additional education, we believe some experience with molecular modeling will add to our graduates’ value as members of a research team. Finally, it was also our hope that exposure to molecular modeling at an introductory level would prompt at least a few of our students to include molecular modeling in their senior capstone research project. Course Design and Context In designing this particular course the proposition we made was that students’ lack of mathematical background ought not reduce the use of molecular modeling to blackbox, “video-game” manipulation. In addition to using modeling to support instruction elsewhere in the curriculum, principally in organic chemistry, this course was seen as a useful, and versatile, addition to the curriculum that could be modified almost without limit according to the background and interests of students who enroll. The course was designed for students who had already completed a full year of organic chemistry. The course, called Introduction to Molecular Modeling, did not merely re-teach topics covered in sophomore organic chemistry; rather, it explored the ways modeling software can deal with a variety of structures and how it can be used to propose answers to multifarious questions. Current news and research using modeling were also discussed in class and explored in some student activities. Our class terms are 10 weeks. This was a three-credit course that met for 75 minutes twice each week. In addition to four quarters of our first-year chemistry sequence and a full year of organic chemistry, students had completed at least two quarters of a three-term sequence in chemical instrumentation and two chemistry electives, but no students had completed biochemistry, instrumental analysis, or molecular spectroscopy. Nine students enrolled and seven students completed the course. The software used was PC SpartanPlus2.0 (4).1 No specific text was required. Students were expected to have access to a textbook for first-year chemistry and one for organic chemistry. Several textbooks, reference books, the Tutorial and User’s Guide and glossary published by Wavefunction, Inc. (5) were available in the classroom. No exams
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In the Classroom
were given. Quizzes were used to assess students’ facility with the software and with using the data, but not for grade determination. The course grade was based on a weighted contribution among class participation, graded homework, and a mastery project portfolio (see the Supplemental MaterialW for more details). All in-class work was done collaboratively. Some exercises were divided so that each team contributed part of the data, while on other occasions each team carried out the same computations and data were compared.2 Pedagogy The course was handled entirely in an interactive, guided-discovery format, with no formal lecture. Students began using the software during the first class meeting. To avoid merely telling them “how to do” things and “what to look at”, parts of the tutorial that accompanies the software (5) were rewritten as worksheets to prompt exploration of the software. Class work and homework wove together three principal threads: 1. Early use of simple exercises about which students believed they knew the right answers. These were chosen intentionally to allay anxiety students had about their ability to understand how to use the software and how to “make sense” of the information it produced.
2. More complex and difficult assignments in which students carried out prescribed computations involving unfamiliar structures and answered questions about the molecules. These were selected to permit students to practice the reasoning skills they would need to complete the mastery portfolio. 3. Illustration and discussion of some examples of modeling applications from the current news. These were chosen to show that some of the same type of computations and vocabulary the students were using are integral to analyses being done on more complex and sophisticated problems and to stress that underlying these real-world problems are the same fundamental chemical principles they have studied.
Over time, as our students begin to use modeling software in earlier courses, this course is expected to evolve so that there will be more opportunity to deal in greater detail with theoretical features of the software and to permit students more opportunity to select the appropriate level of theory. For this initial course, however, all the computations were prescriptive. Because our goals were to bolster reasoning skills and enhancing students’ chemical intuition, the main emphases were that students learn two “habits”: (a) looking at their data to assess whether it “made sense” in so
Table 1. A Selection of Some Representative Structures Used for Modeling and Analysisa Representative Structure(s)
Topic or Consideration
Comments
Several random selections of atoms and bonds, rings, and functional groups
Exploration of the software: the menus, how to build unusual structures, manipulating structures, and observing the minimize (5) function
Students ended the first two sessions with correct structures for actual molecules that they needed to complete homework assignments; Their data contributed to the next class discussion
H2O, NH3, CH4, CH3X
Correlation of computed geometry to expected (VSEPR) geometry, bond polarity,3 and electron orbital space
Structures familiar to the students; Use of constrained (5) angles to illustrate how computed energy is indicative of stability.4
H⫺H, H⫺F, Li⫺H, HC⬅C−Na+, HC⬅C−Li+
Bond polarity as revealed by electron density and electrostatic potential maps5
__
SF4, O3 (cyclic or acyclic?), azide ion*
Determination of most stable geometry6 for "unknown" molecules
Local minima are uncovered in proposed SF4 geometries7; Modeling structures that have resonance contributors8
Nitrogen-bases
Using multiple-stage computations; Using heat of reaction to assess relative basicity; Electrostatic maps to reveal nucleophilic centers
Applying computations of heat of reaction to rank the basicity a molecule for which experimental data are not be available; Gas-phase vs condensed-phase (aq) basicity
Ciprofloxacin
Current news: the antidote for anthrax and a N-base
The structure was featured on the ACS Web site; The instructor illustrated the electrostatic potential map; The discussion centered around the relative basicity of the N atoms since the drug is administered as the hydrochloride salt
Benzophenone, benzhydrol, benzoic acid, heptane, ethyl acetate*
AM1 and 3-21G* molecular dipole moment computations
Using computational data to predict TLC elution behavior based on relative polarity9
Al4Li−
Current research: metallic aromatic structures (7a, 7b, 9)
Atomic charges; MO displays; Delocalized π electrons10
a The problems marked with an * were developed by the author; all others were adapted from materials published by Wavefunction, Inc. (5, 6) or used from other sources cited.
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far as the structure was built properly and that the specified computation was submitted and (b) to reflect on “how to” make sense of the data and use it to draw conclusions about the structure. However, it was also considered important for students to “see” that data are not automatically correct or meaningful just because they are returned by a computer in response to some input. Thus, some exercises did include segments designed to illustrate some of the limitations or pitfalls associated with this particular software. A few representative examples of structures investigated are shown in Table 1. The course culminated in the mastery project portfolio. The portfolio consisted of 10 problems selected by each student from a set of 30 problems. Most of the problems were adapted from commercially available workbooks (6). Each problem identified the level of theory and basis set(s) to be used. Students submitted a disc with all structures and the relevant computational setup for each problem; data were submitted in formal tables or graphs, as appropriate, and all answers to questions associated with each structure were presented in a formal written document.
The instructor’s assessment focused on three areas: • Students’ preparedness with fundamental chemistry principles from prior course work • How the format worked • The impact of minimizing quantum mechanics and details about the theories used in modeling
Overall, the class recalled their first-year chemistry and much of their organic chemistry; little class time was needed reviewing subject matter from prior courses. Some topics addressed in this course did reveal that earlier courses had not included sufficient emphasis on concepts important to modeling. In particular, students’ ability to use computed data to deal with reaction thermodynamics or to interpret electrophilic and nucleophilic character, topics typically included in an organic chemistry course, did require additional instructional time before the related modeling exercises could be carried out meaningfully. Responses given to questions accompanying some portfolio problems concerning molecular orbitals and the significance of differences in orbital energies reflects the lack of emphasis on MO theory in the organic chemistry course and also reflects the fact that these students had not yet taken a course dealing with molecular spectroscopy. In spite of not yet having taken biochemistry, exercises involving zwitterion structure or hydrogen-bonding between N-base pairs were readily grasped based solely on their recollection of organic chemistry. However, further consideration of the α helix or β sheet were not pursued, nor was the construction of a Rachmandarian plot illustrated, topics that could be beneficial components of a course for students at a different point in their program. With regard to modeling itself, the meaning of isosurfaces (5, 6) seemed to remain obscure to most of the class even at its culmination. This is a topic that would be developed more fully with greater emphasis on the workings of the various computational methods. Journal of Chemical Education
We believe that a broadly focused molecular modeling course for students not grounded in advanced mathematics or in physical chemistry need not be superficial and “black box”. Just as others have shown that this technology can enhance learning even in beginning courses in chemistry, students can benefit in substantial ways from a stand-alone course such as this one. By being broadly focused, this course was successful in bringing students’ prior chemistry knowledge to bear on PC-based modeling activities. The author believes the course work did extend and expand students’ knowledge and their chemical intuition. It permitted each student to explore topics of individual interest. As a “computational appreciation” course a stand-alone course such as the one we describe here can serve genuine learning goals in the discipline. Such a course can be meaningful, yet within the grasp of mid-level students. As the use of modeling is increasingly incorporated into a chemistry curriculum this course will be able to accommodate a wider array of topics and a greater depth of theory. Notes
Assessment
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1. Five copies of the software were purchased for use with five desktop computers maintained by the department for our students. Costs prohibited acquisition of more computers or more software packages, and requiring students to purchase the software was not considered a viable option. The desktop computers use a Pentium II processor running Windows 2000. They have 128 MB RAM and 1 GB disk space. Each computer also has graphing and word processing software installed. Students were required to have their own data storage disks (one zip disk proved sufficient) so that they could use any computer at any time. While some features of other commercially available modeling software might vary from those of this version of PCSpartan, to our knowledge there is nothing about the format and problems used in this course that could not be used with other PC modeling software. 2. While it was not explicitly documented, it did become evident that all members of the class worked independently as well as with in collaboration with their classmates. 3. PCSpartan-Plus provides the dipole moment and the symmetry element of structures. In our experience with the software the AM1 dipole moment does not agree with experimental values but can be used to make some comparisons. However the molecular dipole vector is nearly always ambiguous in its location and orientation. Dipole moment values obtained at 3-21G* are generally much closer to available experimental data. With regard to the computed point group, our students had not been exposed to symmetry elements and operations. A brief presentation of some features of symmetry operations was given but the emphasis was that the point group is a characteristic descriptor of molecular structure often documented in the literature or in reference texts. Whenever a problem referred to the point group, students were required to confirm that their computations produced the same information. 4. Since ∆Hf values obtained from semi-empirical computations with this version of Spartan software cannot be compared directly to experimental values, the deviations between computed energy values and experimental values were pointed out at the outset of the course. However, trends in these data for a set of similar structures can be used to draw accurate conclusions about relative stability. Similarly, this software does not reproduce observed val-
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In the Classroom ues for vibrational energy (IR). However, by using a reference bond, computed values for the energy of a particular vibration as a function of structure can be adjusted easily to produce excellent agreement between computed and observed IR signals (the author’s unpublished data) so that correct conclusions about structure and IR can be made readily. 5. Visual displays of electron density and electrostatic potential maps (5, 6) are obtained for this set of structures using semiempirical (AM1) computation. The exercise was extended to the halogens to illustrate increasing molecular size as revealed in the electron density. The AM1 basis set in this software does not handle iodine. However, because a computation for iodine can be done using semi-empirical methods, the opportunity arose to discuss the necessity to reflect critically on the data output. Iodine can be handled with the PM3 basis set for semi-empirical computations or by using higher-level theory (HF, 3-21G*). 6. For modeling SF4 the class did not have the tutorial (6a) that specifies using a high level of theory for determining the equilibrium geometry and that specifies the known structure. Instead, students proposed, constructed, and computed the equilibrium geometry for all possible “starting” structures this software provides for in the expert builder (square pyramidal and trigonal bipyramidal with the lone pair electrons alternatively axial and equatorial), and students used both semi-empirical (AM1) and Hartree-Fock (321G* and 6-31G*) computations. When the square pyramidal geometry with the lone pair (LP) of electrons in an equatorial position is used as the initial structure, the equilibrium geometry found is one that has reverted to the (accepted) “see-saw” structure. However, when the LP is initially in the axial (“mast”) position of the square pyramid frame, a higher energy—“local minimum”—is computed that maintains this geometry. Starting with the LP axial in the trigonal bipyramidal frame results in a structure that displays the correct (accepted) geometry but that has a higher total energy than is computed for the “correct” structure starting with the square pyramidal frame and LP electrons equatorial. The HOMO for this structure does, however, illustrate that the LP electrons are associated predominately with the S atom, as predicted. Without requiring a detailed presentation of basis sets, this example segued to pointing out that the ab initio calculation used by the Hartree–Fock methods includes consideration of d orbital functions that might be expected to give more accurate computations for this model than semi-empirical theory. A semi-empirical computation does produce the correct geometry, a reasonable HOMO, (high electron density centered at the S atom) and sensible positive atomic charge for S (6a), showing that, in this case, there is little obvious advantage to using a higher level of computation. Nevertheless, since little time is required for the higherlevel computation on this small molecule, using the higher level does support the reliability of the lower-level data. 7. In our experience the potentially misleading effect of finding local minima was particularly noticeable when comparing the electrophilic character of the acidic H atom in carboxylic acids (6). Results varied erratically and proved to be especially confusing if the structures were not constructed in a consistent manner (see diagram below). The lowest energy is obtained from the structure on the left below at AM1 but not at 3-21G*. O
O H
vs
O
O H
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8. Ozone provided an interesting set of results relative to the level of theory used for the computation. The reference (6a) specified HF 6-31G*. Our students did not have this information, nor were they told whether the structure is cyclic or acyclic. They were directed to build and carry out the computations for both structures using several levels of theory and basis sets. Only a few minutes are required to obtain the equilibrium geometry using AM1, PM3, HF 3-21G*, and HF 6-32G*. Heat of formation computed using semi-empirical AM1 and PM3 indicate the acyclic structure is more stable (AM1: ∼37 kcal兾mol and PM3: ∼57 kcal兾mol ) than the cyclic isomer (AM1: 111 kcal兾mol and PM3: 75 kcal兾mol). However, in our hands, the ab initio computation with the 3-21G* basis set indicates that the cyclic isomer is more stable, but, of course, has a zero dipole moment (᎑223.06 au and 0 D vs ᎑222.98 au and 0.518 D for the acyclic isomer). The still larger 6-31G* basis set (per ref 6 ) shows that the acyclic structure has the lower total energy (᎑224.26 au and 0.826 D vs ᎑224.24 au and 0 D). These discrepancies provide an example of the necessity to avoid an uncritical reliance on “the computer” (or on just ∆Hf, which students seem to think is especially important). It permits reinforcing the notion that using a computer does not override the need to practice “good science”, that is, bringing empirical knowledge or data from alternative measurements (e.g., bond lengths, bond angles, dipole moment) to bear on a computed value. The acyclic structure of ozone and the structure of the azide ion also illustrate how the modeling software deals with resonance structures. Of course, any aromatic structure, including aromatic ions, provides a ready illustration of resonance as well. 9. We observed that the ab initio computation leads to a different order of molecular polarity for the three aromatic compounds than is obtained using the semi-empirical method. The data nevertheless permit meaningful discussion about how a solvent could be found to separate the three compounds. 10. Examples of current topics involving computational methods were taken from Chem. Eng. News (7, 8). Not all of the topics cited were explored using the modeling software; some were simply brought to the attention of the class as relevant examples of how molecular modeling is being used. The structure suggested by the formula Al4Li− is within the grasp of students to model. The Chem. Eng. News reports for structures of this type (7a) are appropriate for college students and, while the original article in Science (9) deals with complexity beyond this course, the MO images provided there will be familiar. Building these particular structures is trivial using this software. The literature describing the modeling of these structures (9) provides data derived from density functional computations, a capability our software does not have. However, these students had learned that a semi-empirical computation involving metals atoms requires the PM3 basis set. Using that basis set the bond distance found between the Al atoms differ by less than about 0.02 Å, and the Al-Li distance differs by ∼0.2 Å compared to those reported (9). While beginning students are prepared to do little more than compare the visual images for MO’s, doing so made it apparent that PM3 computations give visually different results than those reported (7, 9). The more surprising result, however, is that PM3 produces positive values for Al atomic charges (electrostatic and Mulliken) and a negative charge for the lithium ion. Students can be challenged to reflect on the logic of that result and to consider whether a different level of theory needs to be applied. Carrying out the computation using HF 3-21G* results in more sensible atomic charge data, and MO’s that are visually identical to those
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In the Classroom published (9). While parts of the original article are beyond the scope of this course, this structure can serve to show novice users that fundamental concepts with which they are familiar (relative electronegativity and delocalization of π electrons) are precisely those being brought to bear on more sophisticated research. W
Supplemental Material
Course goals and objectives, descriptions of the first meeting, computational methods, and the mastery portfolio, and the instructor’s assessment are available in this issue of JCE Online.
3. 4. 5.
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