This dissertation is comprised of seven chapters: Chapter 1 provides the theoretical background of ab initio methods and density functional theory, which are relevant to the computational methodologies presented in the following chapters. Chapter 2 examines the anharmonicity associated with weakly bound metal cation dihydrogen complexes using the vibrational self-consistent field (VSCF) method and characterizes the interaction between a hydrogen molecule and a metal cation. Chapter 3 illustrates a study of molecular hydrogen clustering around the lithium cation and their accompanied vibrational anharmonicity employing VSCF. Chapter 4 provides a qualitative interpretation of solvent-induced shifts of amides and simulated electronic absorption spectra using the combined time-dependent density functional theory/effective fragment potential method (TDDFT/EFP). Chapter 5 elucidates an excited-state solvent assisted quadruple hydrogen atom transfer reaction of a coumarin derivative using micro solvated quantum mechanical (QM) water and macro solvated EFP water. Chapter 6 presents a dispersion correction to the QM-EFP1 interaction energy. Finally, a general conclusion of this dissertation work and prospective future direction are presented in Chapter 7.