Combining Research in Theoretical Chemistry and Chemistry Education

Abstract

This dissertation is a combination of work in theoretical vibrational spectroscopy and chemical education. The research in the former focuses on studies of molecules that exhibit large amplitude motions. One such system is water clusters, which serve as intermediates between a single water molecule and bulk water. The addition of water molecules introduces hydrogen bonding, a strong intermolecular interaction that is an ongoing topic of study. An effective method for studying systems that undergo large amplitude motions is diffusion Monte Carlo (DMC), a method that can be used to obtain the ground state vibrational wave function and zero-point energy for an arbitrary system. The research in the latter part of this work includes developing and utilizing a rubric to classify the cognitive effort required by a student to solve multiple-choice general chemistry problems. To begin, the diffusion Monte Carlo algorithm will be reviewed as well as extensions to guided DMC and the evaluation of excited states and molecular properties. The approach has been shown to require increasingly large ensembles when intra- and intermolecular vibrations are weakly coupled. Our group recently proposed a guided variant of diffusion Monte Carlo to address these challenges for water clusters, (H$_2$O)$_n$. An extension of this approach is then applied to more strongly bound molecular ions, specifically CH$_5^+$ and H$^+$(H$_2$O$)_{n=1-4}$. For the protonated water systems, this work shows that the guided DMC approach that was developed for studies of (H$_2$O)$_n$ can be used to describe the OH stretches and HOH bends in the solvating water molecules, as well as the free OH stretches in the hydronium core. For the hydrogen bonded OH stretches in the H$_3$O$^+$ core of H$^+$(H$_2$O)$_n$ and the CH stretches in CH$_5^+$, adaptive guiding functions based on the instantaneous structure of the ion of interest were developed. Using these guiding functions, converged zero-point energies and ground state wave functions are obtained using ensemble sizes that are as small as 10\% the size that is needed to obtain similar accuracy from unguided calculations. The isomerization pathway between the energetically low-lying Zundel and Eigen isomers of the protonated water hexamer is then investigated using high-level \textit{ab initio} calculations including a proper treatment of zero point corrections. On the basis of these calculations, the Zundel-Eigen isomerization was found to proceed through a stable intermediate isomer, which consists of a four-membered ring with two single acceptor water molecules. The inclusion of vibrational zero-point energy is shown to be important for accurately establishing the relative energies of the three relevant isomers involved in the Zundel-Eigen isomerization. {Diffusion Monte Carlo calculations including anharmonic vibrational effects show that all three isomers of H$^+$(H$_2$O$)_{6}$ and D$^+$(D$_2$O$)_{6}$ have well-defined structures.} The energetic ordering of the three isomers changes upon deuteration. Implications of these results for the vibrational spectra of H$^+$(H$_2$O$)_{6}$ and D$^+$(D$_2$O$)_{6}$ are also discussed. Further exploring the spectra of H$^+$(H$_2$O$)_{6}$, a spectral map is created using relationships between vibrationally averaged hydrogen-bonded OH and OD distances and the frequencies and intensities associated with those vibrations. This allows spectral features to be predicted using vibrationally averaged distances obtained from DMC calculations. This spectral mapping method is compared against scaled harmonic and vibrational perturbation theory, as well as experiment. It is calibrated using smaller protonated water clusters which shows better agreement to experiment for vibrational modes with large anharmonicities. The spectral map is then used with four isomers of H$^+$(H$_2$O$)_{6}$ and D$^+$(D$_2$O$)_{6}$ to compare the spectral features to experiment. Finally, Marzano's taxonomy was used as a basis for developing a rubric that specifically assessed the cognitive level of general chemistry multiple choice questions. The rubric was then applied to a bank of multiple-choice questions, which came from four University of Washington chemistry instructors who, though teaching a common syllabus from a common textbook, had idiosyncratic approaches to the material and how they presented it in class. An Inter-Rater Reliability of 92\% for at least two out of three coders was obtained. This work shows that the cognitive level of most questions was quite low and that a solid majority of all questions were classified as ``execution of a learned algorithm,” which is consistent with trends noted in the literature on chemistry assessments.