Article Cite This: J. Chem. Educ. XXXX, XXX, XXX−XXX
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Empirically Corrected Electronic Structure Calculations Applied to the Enthalpy of Combustion Physical Chemistry Laboratory James W. Mazzuca,* Alexis R. Downing, and Christopher Potter Chemistry Department, Alma College, Alma, Michigan 48801, United States
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S Supporting Information *
ABSTRACT: A method for using electronic structure calculations to predict the standard molar enthalpy of combustion for hydrocarbons is presented. In this approach, simple geometry optimizations can be used to accurately compute the enthalpy of combustion within 3% of the experimental value using Hartree−Fock, MP2, or virtually any functional in density functional theory calculations. This approach keeps the electronic structure calculations conceptually simple and computationally cheap, making this method accessible for a teaching lab with only minimal computational resources. This method is especially applicable to the bomb calorimeter experiment that typically appears in the physical chemistry teaching laboratory, and we provide an example of how our electronic structure calculations can be integrated into the laboratory curriculum. KEYWORDS: Upper-Division Undergraduate, Physical Chemistry, Computer-Based Learning, Calorimetry/Thermochemistry, Computational Chemistry, Molecular Modeling, Thermodynamics, Theoretical Chemistry
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INTRODUCTION The combustion of hydrocarbons is a popular topic among educators when discussing exothermic reactions in the undergraduate curriculum. An introduction to thermodynamics typically begins at the general chemistry level for first-year undergraduates, and this topic is revisited extensively in their organic chemistry courses. When students eventually enroll in physical chemistry, the underlying principles of combustion reactions are examined at a fundamental level. These principles are reinforced often using an oxygen bomb calorimeter in the physical chemistry teaching laboratory.1 This experiment has been modified in a variety of ways over the years to examine the combustion properties of fuels2,3 and biological compounds4 and to use enthalpy of combustion measurements to compute other properties such as resonance stabilization5 and ring strain.6 Here, we present an extension of the traditional bomb calorimeter experiment in which we emphasize the use of electronic structure methods and symbolic mathematical software to gain a deeper understanding of the process of combustion. We recognize that the calculation of an accurate standard enthalpy of formation, and therefore, the standard enthalpy of combustion, ΔcH⊖ m , for any particular hydrocarbon is quite difficult from an electronic structure perspective7−11 and may therefore be prohibitively expensive in the typical teaching laboratory setting. Additionally, the conceptual complexity of these calculations may not be appropriate for an undergraduate physical chemistry course on chemical thermodynamics.12 To address this problem, we have © XXXX American Chemical Society and Division of Chemical Education, Inc.
computed empirical correction factors that can be used directly in the teaching laboratory to improve the accuracy of first-principles enthalpy of combustion calculations. Students can use these correction factors to obtain accurate ΔcH⊖ m predictions from straightforward geometry optimizations of single molecules. We demonstrate that this approach is viable for a test set of organic molecules across seven different electronic structure methods. Once calculated, these empirical correction factors can be used in addition to just standard geometry optimization calculations to accurately predict ΔcH⊖ m for other organic compounds. This creates an opportunity to employ computational chemistry tools in a way that is feasible on standard computers and suitable for an undergraduate chemical thermodynamics course. This paper is organized in the following way. First, we present the overall organization of a bomb calorimeter experiment that includes the computational resources outlined above. Following this discussion, we describe how electronic structure calculations are directly used to compute ΔcH⊖ m (298.15 K) using only geometry optimization calculations. The last portion of this paper describes how the empirical correction factors were computed, and we demonstrate their effectiveness on a small test set of organic compounds. These correction factors can be used as written Received: January 9, 2019 Revised: March 27, 2019
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DOI: 10.1021/acs.jchemed.9b00019 J. Chem. Educ. XXXX, XXX, XXX−XXX
Journal of Chemical Education
Article
to improve ΔcH⊖ m (298.15 K) calculations for other organic compounds, or new corrective factors can be generated for other electronic structure theory methods using the approach presented in this work.
that can be used to repeat calculations for different data sets. Students first find an equation for ΔcH⊖ m (298.15 K) that involves all properties that were physically measured and then import this equation into Maple in a way that they can easily differentiate the function with respect to all measurements to propagate the error for their calculated ΔcH⊖ m (298.15 K). Students are encouraged to leave space at the beginning of the worksheet to define the value of measured variables and reexecute the worksheet to quickly determine the propagation of error for each trial. This time is also used by students to ask for input or clarifying remarks about the experiment before they finish writing their report over the next couple of weeks. An example Maple worksheet that calculates the calorimeter constant as well as the molar enthalpy of combustion, and can be used to propagate the error for a single trial for naphthalene can be found in the Supporting Information. An outline for the written lab report can also be seen in the Supporting Information. When the reports are graded, large emphasis is put on the introduction as well as the results and discussion section. The introduction is of particular importance and contains the motivation for the study as well as all theoretical groundwork and relevant equations. The results and discussion section is where students show that they can manipulate the data and connect the results to the theory discussed in the introduction. This section is where a student demonstrates that they understand the physical significance of their laboratory measurements and calculations.
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FORMAT OF TEACHING LABORATORY The physical chemistry sequence at Alma College consists of two courses: CHM 331 Chemical Thermodynamics and CHM 332 Quantum Chemistry. This represents a fairly typical division of content, and these courses may be taken in either order. It should be noted that statistical thermodynamics content is covered in CHM 331, so it may be advantageous for students to enroll in CHM 332 first for this reason, although it is not required. The sample syllabi for these courses can be found in the Supporting Information. The laboratory portion currently meets once a week for 3 h, and a formal lab report written in the style of The Journal of Physical Chemistry is the required outcome for each experiment. A typical experiment takes 2−3 weeks to perform and usually involves one meeting in which the students collect and analyze data from a physical system. The next one or two meetings involve performing electronic structure calculations and other high-level data analysis that typically involves tools such as Maple mathematical software13 and Microsoft Excel. In the enthalpy of combusion experiment, for which the laboratory manual can be found in the Supporting Information, the first week is spent performing electronic structure calculations using Spartan Student.14,15 Using the standard molar internal energy, U⊖ m (0 K), calculated at the MP2/6311+G** level of theory for gas-phase reactant and product molecules, students can compute the standard enthalpy of combustion, ΔcH⊖ m , at 298.15 K for any hydrocarbon of interest. To connect directly to lecture content, and to avoid empirical bias, the equipartition theorem16 is used to determine heat capacities for each species, and these heat ⊖ capacities are used to convert ΔcU⊖ m (0 K) to ΔcHm (298.15 K). A Maple worksheet is typically used to perform these calculations, and an example of such a worksheet can be found in the Supporting Information. When the computational chemistry aspect of the experiment was first tested, the students performed B3LYP/6-31G* calculations rather than MP2/6-311+G**, and we typically observed ∼30% error in the calculated ΔcH⊖ m (298.15 K). We have found that MP2 calculations, using the approach outlined above, produce an average error of ∼2% for both benzoic acid and naphthalene. This initial observation is what lead to the investigation described in the next section. In the second week of the experiment, the students use an oxygen bomb calorimeter to experimentally determine the enthalpy of combustion of naphthalene against a benzoic acid standard. This part of the experiment represents the traditional physical chemistry enthalpy of combustion experiment, and we have observed that when done properly, the experiment typically produces an error of
