Free energy simulations have been widely employed to compute the thermodynamic properties of many important biochemical processes. In the first part of this dissertation, two important biochemical processes, protonation/deprotonation of acid in solution and solvation of small organic molecules, are investigated using free energy simulations. Accurate computation of the pKa value of a compound in solution is important and challenging. To efficiently simulate the free energy change associated with the protonation/deprotonation processes in solution, a new method of mixing Hamiltonian, implemented as an approach using a fractional protonin the hybrid quantum mechanics/molecular mechanics (QM/MM) scheme, is developed. This method is a combination of a large class of λ-coupled free-energy simulation methods and the linear combination of atomic potential approach. Theoretical and technical details of this method, along with the calculation results of the pKa value of methanol and methanethiol molecules in aqueous solution, are discussed. The simulation results show satisfactory agreement with experimental data. Though the QM/MM method is one of the most useful methods in the modeling of biochemical processes, little attention has been paid to the accuracy of QM/MM methods as an integrated unit. Therefore, the solvation free energies of a set of small organic molecules are simulated as an assessment of ab initio QM/MM methods. It shows that the solvation free energy from QM/MM simulations can vary over a broad range depending on the level of QM theory / basis sets employed. Diffuse functions tend to over-stabilize the solute molecules in aqueous solution. The deviations pose a pressing challenge to the future development of new generation of MM force fields and QM/MM methods if consistency with QM methods becomes a natural requirement. In the second part of the dissertation, the dynamic and energetic properties of two molten globule (MG) protein molecules, α-lactalbumin(α-LA) and monomeric chorismate mutase (mCM) are investigated using molecular dynamics simulations. The exploring of the molecular mechanism of protein folding is a never-settled battle while the properties of MG states and their roles in protein folding become an important question. The MGs show increased side chain flexibility while maintain comparable side-chain coupling compared to the native state, which partially explains the preserving of native-like overall conformation. The enhanced sampling method, temperature-accelerated molecular dynamics (TAMD), is used for the study of the hydrophobic interactions inside both biomolecules. The results suggest that these hydrophobic cores could overcome energy barriers and repack into new conformation states with even lower energies. The repacking of the hydrophobic cores in MGs might be served as a criterion for recognizing the MGs in large class of biomolecules. / published_or_final_version / Chemistry / Doctoral / Doctor of Philosophy