Although molecular dynamics (MD) simulations have been applied frequently to study flexible molecules, the sampling of conformational states separated by barriers is limited due to currently possible simulation time scales. Replica-exchange (Rex)MD simulations that allow for exchanges between simulations performed at different temperatures (T-RexMD) can achieve improved conformational sampling. However, in the case of T-RexMD the computational demand grows rapidly with system size. A Hamiltonian RexMD method that specifically enhances coupled dihedral angle transitions has been developed. The method employs added biasing potentials as replica parameters that destabilize available dihedral substates and was applied to study coupled dihedral transitions in nucleic acid molecules. The biasing potentials can be either fixed at the beginning of the simulation or optimized during an equilibration phase. The method was extensively tested and compared to conventional MD simulations and T-RexMD simulations on an adenine dinucleotide system and on a DNA abasic site. The biasing potential RexMD method showed improved sampling of conformational substates compared to conventional MD simulations similar to T-RexMD simulations but at a fraction of the computational demand. It is well suited to study systematically the fine structure and dynamics of large nucleic acids under realistic conditions including explicit solvent and ions and can be easily extended to other types of molecules.