In this thesis, a method is presented for the determination of tunnel splittings of the rotational quantum states of methyl groups in the condensed-phase. The rotational quantum states are obtained via direct diagonalization of the corresponding Hamiltonian in one and two dimensions. The rotational potential and the methylmethyl coupling strength are obtained quantitatively via quantum chemical calculations of the corresponding potential energy surface within the framework of density functional theory combined with the nudged elastic band method. Experimentally, a large tunnel splitting can be exploited for enforcing the exclusive population of the lowest rotational quantum state of the methyl groups of a macroscopic sample at low temperatures. This well-defined population, in turn, can be transferred to the proton spin state, yielding a large spin hyperpolarization beyond the Boltzmann level, which results in a signal amplification in NMR spectroscopy by several orders of magnitude.