PART I. Fundamental Theory.- The Relativistic Kepler Problem and Gödel's Paradox.- "The Dirac Electron: Spin, Zitterbewegung, the Compton Wavelength, and the Kinetic Foundation of Rest Mass".- Molecular Parity Violation and Chirality: the Asymmetry of Life and the Symmetry Violations of Physics.- PART II. Molecular Processes.- Application of Density Matrix Method to Ultrafast Processes.- Quantum Master Equation Study of Electromagnetically Induced Transparency in Dipole-Coupled Dimer Models.- Laser-Induced Electronic and Nuclear Coherent Motions in Chiral Aromatic Molecules.- Simulation of Nuclear Dynamics of C60: from Vibrational Excitation by Near-IR Femtosecond Laser Pulses to Subsequent Nanosecond Rearrangement and Fragmentation.- Systematics and Prediction in Franck-Condon Factors.- Electron Momentum Distribution and Atomic Collisions.- Ab initio Path Integral Molecular Dynamics: Simulations of F2H- and F2H+.- Relativistic Energy Approach to Cooperative Electron -Nuclear Processes: NEET Effect.- Advanced Relativistic Energy Approach to Radiative Decay Processes in Multielectron Atoms and Multicharged Ions.- PART III. Molecular Structure.- "Solving the Schrödinger Equation for the Hydrogen Molecular Ion in a Magnetic Field using the Free-Complement Method".- Description of Core Ionized and Excited States by Density Functional Theory and Time-Dependent Density Functional Theory.- Intermolecular Potentials of the Carbon Tetrachloride and Trifluoromethane Dimers Calculated with Density Functional Theory.- Ab-initio study of the Potential Energy Surface and Stability of the Li2+(X2Σg+) Alkali Dimer in Interaction with the Xenon Atom.- Validation of Quantum Chemical Calculations for Sulfonamide Geometrical Parameters.- Approximate Spin Projection for Geometry Optimization of Biradical Systems - Case Studies of Through-Space and Through-Bond Systems.- PART IV. Molecular Properties.- DFT Calculations of the Hetero-Junction Effect for Precious Metal Cluster Catalysts.- Luminescence Wavelengths and Energy Level Structure of Binuclear Copper Complexes and Related Metal Complexes.- Valence XPS, IR, and Solution 13C NMR Spectral Analysis of Representative Polymers by Quantum Chemical Calculations.- PART V. Condensed Matter.- Quantum Decoherence at the Femtosecond Level in Liquids and Solids Observed in Neutron Compton Scattering.- Variational Path Integral Molecular Dynamics Study of Small Para-Hydrogen Clusters.- Origin of Antiferromagnetism in Molecular and Periodic Systems in the Original KohnSham Local Density Approximation.- Calculation of Magnetic Properties and Spectroscopic Parameters of Manganese Clusters with Density Functional Theory.- Density Functional Study of Manganese Complexes: Protonation Effects on Geometry and Magnetism.- Depth Profile Assignments of nm and mm Orders by Quantum Chemical Calculations for Chitosan Films Modified by Kr+ Beam Bombardment.- PART VI. Biosystems.- Color Tuning in Human Cone Visual Pigments: the Role of the Protein Environment.- Free Energy of Cell-Penetrating Peptide through Lipid Bilayer Membrane: Coarse-Grained Model Simulation.- Density Functional Study of the Origin of the Strongly Delocalized Electronic Structure of the CuA Site in Cytochrome c Oxidase.- The Potentials of the Atoms around Mg2+ in the H-ras GTP and GDP Complexes.- Molecular Dynamics Study of Glutathione S-Transferase: Structure and Binding Character of Glutathione.- Designing the Binding Surface of Proteins to Construct Nano-Fibers.