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Making theoretical chemistry useful to practicing chemists as researchers and educators
Miorelli, Jonathan T.
Miorelli, Jonathan T.
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2016
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Abstract
Chemistry is concerned with understanding and predicting the interactions and properties of matter. A valuable tool towards this goal is Density Functional Theory, which asserts that all ground-state properties can be determined using the charge density alone. Conceptual Density Functional Theory (CDFT) has given rigorous definitions for a variety of chemical concepts such as electronegativity and chemical hardness, though use of these definitions often requires knowledge of the system beyond just the ground-state charge density. Applied Density Functional Theory (ADFT) seeks to extract these same chemical properties from computed or experimental charge densities alone. ADFT also seeks to be "applied" by making theses charge-density analyses accessible and useful to practicing chemists. The first section of the thesis shows how ADFT is able to address problems currently present within the theoretical community. Researchers are developing conceptually based models linking the structure and dynamics of molecular charge density to properties. Key among these has been the discovery and description of the bond path and bond critical point from the Quantum Theory of Atoms in Molecules (QTAIM). The discovery of bond paths in systems not considered to be chemically bound – e.g. a H-H bond between adjacent hydrogens in a di-benzene complex and He-C bonds in the He + adamantane inclusion complex – seemed to pose a considerable challenge to analyzing bonding via topological analysis of the charge density. Using extensions to QTAIM developed by the Molecular Theory Group one can use a molecule’s ridges to define a natural simplex over the charge density. The resulting simplicial complex can be represented at various levels by its 0, 1, and 2-skeleton (dependent sets of points, lines, and surfaces). The geometry of these n-skeletons retains critical information regarding the structure and stability of molecular systems while greatly simplifying charge density analysis. Via the geometry of these n-skeletons one can uncover the fingerprints of instability and metastability in the systems mentioned above: the di-benzene complex and He + adamantane inclusion complex. The second section of the thesis investigates how "nearsighted" the charge density is and the significance of this nearsightedness. As has been demonstrated by Kohn and others, the charge density is "nearsighted" in that beyond some distance R from a test point, r0, any change to the external potential will only result in a small change in the change density at r0 ( Δρ(r0, R)). Two crucial questions are how large is R for a given system and how small of changes at r0 are small enough to be considered insignificant? To address this problem organic functional groups are used as a model of how much the charge density can change while still retaining a characteristic chemistry. The calculations presented below demonstrate that for halogen substitution on oxygen-containing functional groups the overall magnitudes of Δρ(r0, R) are all below 0.05-0.06 a.u. for the magnitude of charge at a bond CP and 0.3 a.u. for the curvatures at a bond CP. The effective radius beyond which halogen substitution no longer had a noticeable effect was on the order of two carbon bond-lengths (~3 Å). Values for Δρ are shown to be robust across a variety of DFT functionals and provide a framework for the transfer of the functional group concept other disciplines, such as metallurgy. The final section demonstrates how the concepts of ADFT can be adapted in a way that allows students to make use of the charge density. For instance, the chemical bond concept is the foundation of the molecular sciences in general and ADFT specifically. As such, helping students gain a clear physical representation of chemical bonding is necessary for the progress of ADFT. Bond Explorer, an activity that utilizes the 3D plotting functionality of Mathematica, is intended to provide a clear physical picture of electron sharing among atoms – i.e. a physical picture of the chemical bond. The activity was designed in accordance with the best practices of scientific teaching with a focus on active learning and peer-instruction. Through the course of the activity, students visualize the 3D charge density using both fog and contour plots. Students then go on to describe the density differences that characterize various bonding types, i.e. covalent, polar-covalent, and ionic. The activity involves independent work at home prior to class to provide exposure to the material prior to the in-class portion of the activity. In-class, a short review lecture is followed up by group work where students identify key similarities and differences in the charge density corresponding to various bond types. The in-class portion of the activity involves students working on concept-focused open-ended questions in small groups, to better encourage peer-instruction. Analysis of exam scores from the fall 2015 CHGN 121 revealed that students who participated in the activity performed better on the first two exams following participation in the activity (t-test at 95% confidence). A short quiz focused on Bond Explorer was administered before and after students participated in the activity in the summer 2016 section of CHGN 121 showed that students did perform better on the quantitative portion of the quiz (Wilcoxon signed-rank test at 90% confidence). Analysis of the qualitative portion of the quiz revealed possible misconceptions about bonding that will be addressed in further versions of Bond Explorer.
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