Organic semiconductors have the potential to create flexible, transparent electronic devices. Unfortunately, these materials suffer from low mobilities because atomic vibrations, known as phonons, localize charge carriers. In order to improve mobility in these materials, it is essential to understand which types of phonons are present and how they affect charge transport. Inelastic neutron scattering (INS) can measure these motions directly, but the results cannot be interpreted without computing the phonon modes from an experimental structure. These calculations typically rely on density functional theory (DFT) which is highly accurate but computationally costly. This limits calculations to highly-ordered small molecules. To try and push past these limits, we used six different computational methods to compute the phonon modes ranging from DFT to molecular dynamics (MD) and machine learning (ML). We find that while nothing can compete with DFT, density functional tight binding (DFTB) and DFTB with a machine learning component produce decent results at a fraction of the cost. Then, we apply INS along with our optimized DFT-based method to a metal-organic framework (MOF) system. These MOFs are known to have defects that play an important role in their catalytic activity, but characterizing these defects remains an ongoing challenge. By measuring the phonons with INS and simulating them with DFT, we are able to identify peaks that correspond to defects in the MOF. By using a variety of structures, we are able to identify the structure of the MOF along with the types of defects present. Finally, we develop a novel workflow, ElPh, which allows us to couple our phonon calculations to the electronic structure in small-molecule organic semiconductors. This allows us to understand how all of the phonons work together to limit charge mobility. In addition, we developed a novel analysis technique that shows how each atom limits charge transport. This novel approach allows us to discover design rules for the first time--making meaningful progress toward designing new, high-performance materials.