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.