published_or_final_version / abstract / Mechanical Engineering / Master / Master of Philosophy

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, in fulfillment of the requirements for the degree of Doctor of Philosophy, April 2013. / Density functional theory (DFT) and time dependent-DFT (TD-DFT) was applied to investigate the geometric and electronic properties of cobalamin (Cbl) models. Model compounds of the type, [B–(Co(III)(L)4–X)–Y]n+ were used, where B and Y were comprised of the alpha (α) and β axial ligands, (L)4 represented the equatorial ligand(s) and X was either hydrogen or a substituent of electron donating or withdrawing character, quantified by the Hammett constant (σp), at C10 of the corrin. All calculations were conducted in the gas phase or implicit solvent medium at the BP86/6-31+G(d,p) level of theory. High-resolution crystal structures of B12, extracted from the Cambridge Crystal Structural Database (CCSD), were used as the source of initial coordinates. DFT was used to explore the trans influence of the lower (α) axial ligand, the cis influence of various equatorial ligands and the cis influence of a substituted corrin ring at the C10 position on the Gibbs free energy (ΔG) and bond dissociation energies (BDEs) of the Co(III)–Cβ bond. Other geometric parameters such as ring distortion, axial bond lengths, equatorial bond lengths and partial charges on the Co metal centre, donor atom of the upper and lower axial ligands as well as the N-donor atoms of the macrocyclic ring are documented and discussed. The use of a broad range of alpha (α) ligands in the cobalamin models from charged and neutral N-donor ligands (NH3, NH2–, NH2–, NH2F, NHF–, NF2–, NH2CH3, NHCH3, NH(CH3)2, N(CH3)3), to naturally occurring amino acids or realistic models of their metal-coordinating side chains (methanethiol, dimethylsulfide, cysteine, methanethiolate, glycine, p-aminopyridine, imidazole, histidine, acetate, 2-propanol, serine and tyrosine), provided significant information on the trans influence of these ligands on the BDE of the Co(III)–C bond (upper axial ligand). The ligands NH3, NH2–, NH2–, NH2F, NHF–, NF2–, NH2CH3, NHCH3, were used to explore electronic effects while NH3, NH2CH3, NH(CH3)2, and N(CH3)3 were used to investigate steric effects. The naturally occurring amino acids or their models focused primarily on exploring why nature chooses an N-donor ligand such as histidine or imidazole instead of an S-donor or O-donor ligand that is also readily available from protein side chains. As the basicity of the α ligand increased in the series NH2F < NH3 < CH3NH2 < (CH3)2NH < (CH3)3N < NHF– < NHCH3– < NH2– < NF2– < NH2–(as assessed by the proton affinities) a normal trans influence was observed between the axial ligands. While the Co(III)–C bond was observed to increase in length, the Co(III)–Nα bond length decreased. The weakening of the Co(III)–C bond was paralleled by the decrease in the Co(III)–C BDE. On the other hand, as the steric bulk of the α ligand (NH3, NH2CH3, NH(CH3)2, and N(CH3)3) increased (assessed by the molar volume and Tolman cone angle), an inverse trans influence (in other words, simultaneous lengthening or shortening) between the upper and lower axial bonds was observed. The Co(III)–C bond showed a marginal increase in length while the Co(III)–Nα bond length steadily increased as the molar volume of the α ligand increased. Interestingly, the large difference in the Co–Nα bond length from the 5-coordinate to the 6-coordinate complex (later referred to as ΔCo–Nα(5c-6c)), paralleled the decrease of the Co(III)–C BDEs. It also became evident from calculations with the amino acids posing as α ligands that the nature of the α ligand (assessed by the absolute chemical hardness (η) of the ligand, with the greater the η value the harder the ligand) plays a major role in the labilisation of the organometallic bond. As the η of the α ligand increased, the Co(III)–C BDE increased. The trans influence of the α ligands resulted in the strengthening (hard ligand) and weakening (soft ligand) of the Co(III)–C bond, as was affirmed by the electron density at the bond critical point (bcp) of the Co(III)–C bond. The N-donor ligands (described as having an intermediate character as the η- values were between the hard and soft ligands) were found to be catalytically suitable (31.89 – 32.45 kcal mol -1), rather than the soft and hard donor ligands. The trans influence of the latter two ligands on the upper axial bond revealed a weakly and strongly bound alkyl group to the Co metal centre, giving Co(III)–C BDEs values of 29.39–32.27 kcal mol-1and 32.54–34.96 kcal mol-1, respectively. In addition to the corrin macrocycle, other equatorial ligands like cobaloxime, corrole, porphyrin, methylcobalt(III) pentaamine, [14-ane]N4, [15-ane]N4 and [16-ane]N4 were used in calculations to explore the cis influence on the labilisation of the Co(III)–C bond. These ligands included saturated and unsaturated cyclic rings. The results showed that the flexibility of the ring increased as the size of the equatorial ligand increased and thus affected the displacement of the Co(III) metal centre from the defined mean plane. This subsequently affected the strength of the organometallic bond, which paralleled the BDEs. The hydrogen atom at C10 of the corrin ring was substituted by electron donating (CH3, OH and NH2) or –withdrawing groups (NO, NO2, CN, COOH and Br) and the cis influence of these groups on the organometallic bond was investigated. A normal trans influence between the axial ligands was observed. As the electron density from the substitutents increased towards the ring, the Co(III)–C bond strengthened and the Co(III)–Nα bond weakened. The increased electron density from the C10 substituents influenced the contraction of the Co–Nα bond length. The greater difference in contraction of the Co–Nα bond length from the 5-coordinate to the 6-coordinate complex (ΔCo–Nα(5c-6c)) resulted in lower Co(III)–C BDEs. The TD-DFT method was used to generate both the absorption and circular dichroism (CD) spectra where the vertical electronic excited states of Co(III) cobalamin species that differ with respect to their upper axial ligand, including FCbl, ClCbl, BrCbl,SeCNCbl and CH3Cbl were calculated. The cis influence for each of the species was analysed within the framework of TD-DFT to assign the major spectral features, in other words, the α/β, D/E and γ bands in the predicted UV-visible spectra. These studies reveal that the “typical” and “atypical” absorption exhibit a high degree of σ-donation from the β-ligand to the Co(III) metal centre and the subsequent destabilisation of the corresponding d-orbitals of Co. Furthermore, as the donor ability of the β ligand increased, the contributions from the antibonding d z2 orbital to the HOMO increased, leading to a strong Co(III)–Nα σ-antibonding interaction, which is consistent with the observed lengthening of the same bond from FCbl, ClCbl, BrCbl, SeCNCbl to CH3Cbl.

Chiu Lai Fan. / Thesis submitted in: December 2004. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves [74-77]). / Abstracts in English and Chinese. / ABSTRACT (ENGLISH) --- p.iii / ABSTRACT (CHINESE) --- p.v / ACKNOWLEDGMENTS --- p.vi / TABLE OF CONTENTS --- p.vii / LIST OF FIGURES --- p.ix / LIST OF TABLES --- p.xi / LIST OF SYMBOLS --- p.xiii / Chapter CHAPTER ONE --- INTRODUCTION AND BACKGROUND --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- The nature of hydrogen bonding interactions --- p.2 / Chapter 1.3 --- Evidences of hydrogen bonding interactions --- p.4 / Chapter 1.4 --- Three-centered hydrogen bond --- p.4 / Chapter 1.4.1 --- Literature review of three-centered H-bonds --- p.6 / Chapter 1.4.2 --- Review of three-centered H-bonds characterization --- p.8 / Chapter 1.5 --- Cooperative effect --- p.12 / Chapter 1.6 --- Scope of thesis --- p.13 / Chapter CHAPTER TWO --- THEORY AND METHODOLOGY --- p.15 / Chapter 2.1 --- Introduction --- p.15 / Chapter 2.2 --- Theory --- p.16 / Chapter 2.2.1 --- Density Functional Theory (DFT) --- p.16 / Chapter 2.2.2 --- Natural Bonding Orbital Theory (NBO) --- p.19 / Chapter 2.2.3 --- Spin-Spin coupling constants --- p.22 / Chapter 2.2.4 --- Wiberg Bond Index --- p.24 / Chapter 2.3 --- Methodology --- p.25 / Chapter CHAPTER THREE --- RESULTS AND DISCUSSION --- p.32 / Chapter 3.1 --- The nature of three-centered hydrogen bond interaction --- p.32 / Chapter 3.1.1 --- Geometries --- p.32 / Chapter 3.1.2 --- Natural bond orbital analysis - Donor-acceptor interactions --- p.41 / Chapter 3.1.3 --- Spin-Spin coupling across the hydrogen bonds --- p.46 / Chapter 3.1.4 --- Wiberg bond index --- p.51 / Chapter 3.1.5 --- Proton transfer -Hydrogen bond strengths on the effect of remote proton transfer --- p.53 / Chapter 3.1.6 --- Cooperactive character in hydrogen bonding clusters --- p.65 / Chapter CHAPTER FOUR --- CONCLUSING REMARKS --- p.71 / REFERENCES / APPENDIX

Lee, Shun Hang = 密度泛函理論計算的壓力修正 / 李信恆. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (p. 67-69). / Abstracts in English and Chinese. / Lee, Shun Hang = Mi du fan han li lun ji suan de ya li xiu zheng / Li Xinheng. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Theoretical backgrounds --- p.4 / Chapter 2.1 --- Density Functional Theory --- p.4 / Chapter 2.2 --- Pseudopotential approximation --- p.6 / Chapter 2.3 --- Car-Parrinello Molecular Dynamics --- p.8 / Chapter 3 --- Simulation details --- p.10 / Chapter 3.1 --- Simulation overview --- p.10 / Chapter 3.2 --- Electronic minimization --- p.11 / Chapter 3.2.1 --- The need and setting of electronic minimization --- p.11 / Chapter 3.2.2 --- Results and convergence of electronic minimization --- p.13 / Chapter 3.3 --- Atomic minimization --- p.13 / Chapter 3.4 --- CPMD runs and parameter settings --- p.14 / Chapter 3.4.1 --- The NVE ensemble --- p.14 / Chapter 3.4.2 --- The NVT ensemble --- p.14 / Chapter 3.5 --- Taking the average --- p.20 / Chapter 3.6 --- Check for valid stress tensors and pressure --- p.22 / Chapter 3.7 --- Check for the structure --- p.24 / Chapter 3.7.1 --- The need for structure checks --- p.24 / Chapter 3.7.2 --- Methods to check the structures --- p.24 / Chapter 4 --- Pressure Correction --- p.30 / Chapter 4.1 --- Theoretical Basis for the Correction --- p.30 / Chapter 4.2 --- CPMD Calculation Results --- p.32 / Chapter 4.2.1 --- E(V) at different T --- p.34 / Chapter 4.2.2 --- Results of stress tensor checks --- p.35 / Chapter 4.2.3 --- The EOS's found in this study --- p.38 / Chapter 4.2.4 --- Comparisons with others´ة work --- p.39 / Chapter 4.2.5 --- Difference between LDA and GGA results --- p.42 / Chapter 5 --- Magnesium Silicate (MgSiO3) --- p.45 / Chapter 5.1 --- Simulations for MgSiO3 perovskite --- p.47 / Chapter 5.1.1 --- Simulation parameters and various check --- p.47 / Chapter 5.1.2 --- Results for MgSiO3 perovskite --- p.50 / Chapter 5.2 --- Simulations for MgSiO3 post-perovskite --- p.53 / Chapter 5.2.1 --- Simulation parameters and various check --- p.53 / Chapter 5.2.2 --- Results of MgSiO3 post-perovskite --- p.55 / Chapter 6 --- Discussions --- p.58 / Chapter 6.1 --- Other thermodynamic quantities --- p.58 / Chapter 6.2 --- Asymptotic behaviour of ΔP(V) --- p.59 / Chapter 6.3 --- Applications to the exact XC functional --- p.60 / Chapter 7 --- Conclusion --- p.61 / Chapter 8 --- Appendix --- p.62 / Chapter 8.1 --- Efficient method to perform electronic minimization --- p.62 / Chapter 8.2 --- Efficient method to perform atomic minimization --- p.63 / Chapter 8.3 --- Other related settings --- p.64 / Chapter 8.4 --- Typical input files for CPMD calculations using Quantum-Espresso --- p.65 / Bibliography --- p.67

Immersion energies for an impurity in a homogeneous electron gas with a uniform positive background charge density have been calculated numerically using density functional theory. The numerical aspects of this problem are very demanding and have not been properly discussed in previous work. The numerical problems are related to approximations of infinity and continuity, and they have been corrected using physics based on the Friedel sum rule and Friedel oscillations. The numerical precision is tested extensively. Immersion energies are obtained for non-spin-polarized systems, and are compared with published data. Numerical results, such as phase shifts, density of states, dielectric constants, and compressibilities, are obtained and compared with analytical theories. Immersion energies for excited systems are obtained by varying the number of electrons in the bound states of an impurity. The model is extended to spin-polarized systems and is tested in detail for a carbon impurity. The spin-coupling with an external magnetic field is considered mainly for a hydrogen impurity. These new results show very interesting behavior at low densities. / Graduation date: 2005

Immersion energies of atoms in a jellium environment were calculated using density functional theory and the Kohn-Sham (KS) equations. It was found that the KS scheme does not destroy an existing axial symmetry of the electron structure of the impurity atom. The definition of phase shifts was extended to those problems and it was shown that they are m-dependent. A suitable cut-off for the l-values was found in the partial wave analysis of the scattered states. The Kohn-Sham equations were solved numerically on a computer. Results for H and Fe were analyzed. The results for H are in reasonable agreement with previously reported data. Differences are possibly due to a difference in the choice for the cut-off of the l-values. / Graduation date: 1999

Thesis (M. Phil.)--University of Hong Kong, 2008. / Title proper from title frame. Also available in printed format.

Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Document formatted into pages; contains xxi, 298 p.; also includes graphics. Includes bibliographical references (p. 280-298).

Thesis (Ph.D.)--Brown University, 2005. / Vita. Thesis advisor: Jimmie D. Doll. Includes bibliographical references (leaves 159-170). Also available online.

Thesis (Ph. D.)--University of Oregon, 2000. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 159-176). Also available for download via the World Wide Web; free to University of Oregon users. Address:http://wwwlib.umi.com/cr/uoregon/fullcit?p9963443.