Thesis (M.S.) -- Central Connecticut State University, 2006. / Thesis advisor: S. Louise Gould. "... in partial fulfillment of the requirements for the degree of Master of Science in Secondary Mathematics Education." Includes bibliographical references (leaves 28-30). Also available via the World Wide Web.

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 104-111). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 104-111). Also available on the Internet.

The primary focus of this dissertation is the advancement of the correlation consistent composite approach (ccCA) methodology from its original formulation to the current implementation. Although for large main group test sets which contained both first- (Li-Ne) and second-row (Na-Ar) species ccCA produced chemical accuracy (generally estimated as a deviation of ~1 kcal mol-1 from reliable experiment), the second-row species were smaller in molecular size in comparison to their corresponding first-row species. Previous theoretical work has shown that the accuracy for theoretical calculations involving second-row species (specifically sulfur-containing species) are more basis set dependent than first-row species. Therefore, an analysis of the accuracy of ccCA for sulfur-containing species is warranted. The ccCA methodology is used to evaluate both enthalpies of formation and bond dissociation energies of sulfur-containing species as well as examine isomerization energies for three sets of sulfur-containing isomers. During the testing of ccCA for sulfur-containing species two observations were made which led to further investigations. First, there is no agreement between different theoretical methodologies on the lowest energetic isomer between SNO and NSO. In fact, G3 and G3B3 which differ only by the geometry of the single-point calculations do not agree on the lowest isomer. For this reason, larger, more complete theoretical treatments of SNO and NSO are investigated. Second, for open-shell sulfur-containing systems the accuracy of the ccCA methodology begins to degrade when spin-contamination becomes non-negligible. Therefore, we investigate the accuracy of the ccCA methodology when spin-contamination is removed from the wavefunction. Finally, the ccCA methodology is utilized in a multilayer ONIOM approach as the high level of theory in conjunction with density functional theory as the low level for the C-H bond dissociation energies of anthracene and fluorene analogues.

The energy of a graph began with German physicist, Erich H¨uckel’s 1931 paper, Quantenttheoretische Beitr¨age zum Benzolproblem. His work developed a method for computing the binding energy of the π-electrons for a certain class of organic molecules. The vertices of the graph represented the carbon atoms while the single edge between each pair of distinct vertices represented the hydrogen bonds between the carbon atoms. In turn, the chemical graphs were represented by an n × n matrix used in solving Schr¨odinger’s eigenvalue/eigenvector equation. The sum of the absolute values of these graph eigenvalues represented the total π-electron energy. The criteria for constructing these chemical graphs and the chemical interpretations of all the quantities involved made up the H¨uckel Molecular Orbital theory or HMO theory. In this paper, we will show how the chemical interpretation of H¨uckel’s graph energy evolved to a mathematical interpretation of graph energy that Ivan Gutman provided for us in his famous 1978 definition of the energy of a graph. Next, we will present Charles Coulson’s 1940 theorem that expresses the energy of a graph as a contour integral and prove some of its corollaries. These corollaries allow us to order the energies of acyclic and bipartite graphs by the coefficients of their characteristic polynomial. Following Coulson’s theorem and its corollaries we will look at McClelland’s first theorem on the bounds for the energy of a graph. In the corollaries that follow McClelland’s 1971 theorem, we will prove the corollaries that show a direct variation between the energy of a graph and the number of its vertices and edges. Finally, we will see how this relationship led to Gutman’s conjecture that the complete graph on n vertices has maximal energy. Although this was disproved by Chris Godsil in 1981, we will provide an independent counterexample with the help of the software, Maple 13

Lee Ho-Lam. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 71-72). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgements --- p.iii / Table of Contents --- p.iv / List of Tables --- p.vi / List of Figures --- p.vii / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Gaussian´ؤ3 Method --- p.1 / Chapter 1.2 --- "The G2++, a Modified Gaussian-2 Method" --- p.2 / Chapter 1.3 --- Density Functional Theory (DFT) --- p.2 / Chapter 1.4 --- Calculation of Thermodynamical Data --- p.3 / Chapter 1.5 --- Remark on the Location of Equilibrium and Transition Structures --- p.3 / Chapter 1.6 --- Natural Bond Orbital (NBO) Analysis --- p.3 / Chapter 1.7 --- Scope of the Thesis --- p.4 / Chapter 1.8 --- References --- p.4 / Chapter Chapter 2 --- Structures and Energetics of C3H6S+´Ø Isomers: A Gaussian-3 ab initio Study --- p.6 / Chapter 2.1 --- Introduction --- p.7 / Chapter 2.2 --- Methods of Calculation --- p.8 / Chapter 2.3 --- Results and Discussion --- p.8 / Chapter 2.4 --- Conclusion --- p.21 / Chapter 2.5 --- Publication Note --- p.21 / Chapter 2.6 --- References --- p.22 / Chapter Chapter 3 --- A Gaussian-3 Study of the C3H6S Isomers and the Dissociation Channels of Diradical ´ØCH2CH2SCH2´Ø and Its Radical Cation ´ØCH2CH2SCH2+ --- p.24 / Chapter 3.1 --- Introduction --- p.24 / Chapter 3.2 --- Methods of Calculation --- p.25 / Chapter 3.3 --- Results and Discussion --- p.26 / Chapter 3.3.1 --- Structures and Energetics of C3H6S Isomers --- p.26 / Chapter 3.3.2 --- Dissociation Channels of ´ØCH2CH2SCH2´Ø and ´ØCH2CH2SCH2+ --- p.34 / Chapter 3.4 --- Conclusion --- p.40 / Chapter 3.5 --- Publication Note --- p.41 / Chapter 3.6 --- References --- p.41 / Chapter Chapter 4 --- Computational Study on the Electrocyclic Reactions of [16]Annulene --- p.43 / Chapter 4.1 --- Introduction --- p.43 / Chapter 4.2 --- Methods of Calculation --- p.45 / Chapter 4.3 --- Results and Discussion --- p.45 / Chapter 4.3.1 --- Reaction (1) --- p.49 / Chapter 4.3.2 --- Reaction (2) --- p.50 / Chapter 4.3.3 --- Reaction (3) --- p.52 / Chapter 4.3.4 --- Overall Reaction --- p.53 / Chapter 4.4 --- Conclusion --- p.54 / Chapter 4.5 --- Publication Note --- p.55 / Chapter 4.6 --- References --- p.55 / Chapter Chapter 5 --- Computational Study on the Structures and Stabilities of Some Hypothetical Silicon Nanotubes --- p.57 / Chapter 5.1 --- Introduction --- p.57 / Chapter 5.2 --- Model Design and Methods of Calculation --- p.59 / Chapter 5.3 --- Results and Discussion --- p.59 / Chapter 5.3.1 --- "Armchair (n,n) SiNTs" --- p.60 / Chapter 5.3.2 --- "Zigzag (n,0) SiNTs" --- p.61 / Chapter 5.3.3 --- "Chiral (n,m) SiNTs" --- p.65 / Chapter 5.3.4 --- Stabilities of SiNTs at Elevated Temperature --- p.69 / Chapter 5.4 --- Conclusion --- p.70 / Chapter 5.5 --- References --- p.71 / Chapter Chapter 6 --- Conclusion --- p.73 / Appendix A --- p.74 / Appendix B --- p.76 / Appendix C --- p.77

Density functional theory has been used in combination with the correlation consistent and polarization consistent basis sets to investigate the structures and energetics for a series of first-row closed shell and several second-row molecules of potential importance in atmospheric chemistry. The impact of basis set choice upon molecular description has been examined, and irregular convergence of molecular properties with respect to increasing basis set size for several functionals and molecules has been observed. The possible reasons and solutions for this unexpected behavior including the effect of contraction and uncontraction, of the basis set diffuse sp basis functions, basis set superposition error (BSSE) and core-valence sets also have been examined.

Quantum chemistry methodologies can be used to address a wide variety of chemical problems. Key to the success of quantum chemistry methodologies, however, is the selection of suitable methodologies for specific problems of interest, which often requires significant assessment. To gauge a number of methodologies, the utility of density functionals (BLYP, B97D, TPSS, M06L, PBE0, B3LYP, M06, and TPSSh) in predicting reaction energetics was examined for model studies of C-O bond activation of methoxyethane and methanol. These species provide excellent representative examples of lignin degradation via C-O bond cleavage. PBE0, which performed better than other considered DFT functionals, was used to investigate late 3d (Fe, Co, and Ni), 4d (Ru, Rh, and Pd), and 5d (Re, Os, and Ir) transition metal atom mediated Cβ -O bond activation of the β–O–4 linkage of lignin. Additionally, the impact of the choice of DFT functionals, basis sets, implicit solvation models, and layered quantum chemical methods (i.e., ONIOM, Our Own N-layered Integrated molecular Orbital and molecular Mechanics) was investigated for the prediction of pKa for a set of Ni-group metal hydrides (M = Ni, Pd, and Pt) in acetonitrile. These investigations have provided insight about the utility of a number of theoretical methods in the computation of thermodynamic properties of transition metal hydrides in solution. As single reference wavefunction methods commonly perform poorly in describing molecular systems that involve bond-breaking and forming or electronic near-degeneracies and are typically best described with computationally costly multireference wavefunction-based methods, it is imperative to a priori analyze the multireference character for molecular systems so that the proper methodology choice is applied. In this work, diagnostic criteria for assessing the multireference character of 4d transition metal-containing molecules was investigated. Four diagnostics were considered in this work, including the weight of the leading configuration of the CASSCF wavefunction, C02; T1, the Frobenius norm of the coupled cluster amplitude vector related to single excitations and D1, the matrix norm of the coupled cluster amplitude vector arising from coupled cluster calculations; and the percent total atomization energy, %TAE. This work demonstrated the need to have different diagnostic criteria for 4d molecules than for main group molecules.

Computational chemistry lies at the intersection of chemistry, physics, mathematics, and computer science, and can be used to explain the behavior of atoms and molecules, as well as to augment experiment. In this work, computational chemistry methods are used to predict structural and energetic properties of small molecules, i.e. molecules with less than 60 atoms. Different aspects of computational chemistry are examined in this work. The importance of examining the converged orbitals obtained in an electronic structure calculation is explained. The ability to more completely describe the orbital space through the extrapolation of energies obtained at increasing quality of basis set is investigated with the use of the Sapporo-nZP-2012 family of basis set. The correlation consistent Composite Approach (ccCA) is utilized to compute the enthalpies of formation of a set of molecules and the accuracy is compared with the target method, CCSD(T,FC1)/aug-cc-pCV∞Z-DK. Both methodologies are able to produce computed enthalpies of formation that are typically within 1 kcal mol-1 of reliable experiment. This demonstrates that ccCA can be used instead of much more computationally intensive methods (in terms of memory, processors, and time required for a calculation) with the expectation of similar accuracy yet at a reduced computational cost. The enthalpies of formation for systems containing s-block elements have been computed using the multireference variant of ccCA (MR-ccCA), which is designed specifically for systems that require an explicit treatment of nondynamical correlation. Density functional theory (DFT) has been used for the prediction of the structural properties of a set of lanthanide trihalide molecules as well as the reaction energetics for the rearrangement of diphosphine ligands around a triosmium cluster.

Advances in computing capabilities have facilitated the application of quantum mechanical methods to increasingly larger and more complex chemical systems, including weakly interacting and biologically relevant species. One such ab initio-based composite methodology, the correlation consistent composite approach (ccCA), has been shown to be reliable for the prediction of enthalpies of formation and reaction energies of main group species in the gas phase to within 1 kcal mol-1, on average, of well-established experiment, without dependence on experimental parameterization or empirical corrections. In this collection of work, ccCA has been utilized to determine the proton affinities of deoxyribonucleosides within an ONIOM framework (ONIOM-ccCA) and to predict accurate enthalpies of formation for organophosphorus compounds. Despite the complexity of these systems, ccCA is shown to result in enthalpies of formation to within ~2 kcal mol-1 of experiment and predict reliable reaction energies for systems with little to no experimental data. New applications for the ccCA method have also been introduced, expanding the utility of ccCA to solvated systems and complexes with significant noncovalent interactions. By incorporating the SMD solvation model into the ccCA formulation, the Solv-ccCA method is able to predict the pKa values of nitrogen systems to within 0.7 pKa unit (less than 1.0 kcal mol-1), overall. A hydrogen bonding constant has also been developed for use with weakly interacting dimers and small cluster compounds, resulting in ccCA interaction energies for water clusters and dimers of the S66 set to within 1.0 kcal mol-1 of well-established theoretical values.