Hydrogen-bonded systems often exhibit very broad and unusually shaped features in their vibrational spectra. The origin of these features is oftentimes unclear. Consequently, computational methods are frequently used to model these features in order to better understand their origin. However, reproducing these features with computational methods is often quite challenging. Many methods have been developed each of which has its own advantages and disadvantages. The research presented in this thesis focuses on the development and application of new computational methods to reproduce the multi-hump (broad peak) vibrational features found in many hydrogen-bonded dimers. These methods utilize density functional theory to calculate the potential energy surface and a quantum variational approach to calculate vibrational spectra from these surfaces. One of the methods developed involves adiabatically separating lower frequency vibrational modes, which modulate the hydrogen bond length, from higher frequency modes that contribute to the structure. Another method that was developed uses a classical molecular dynamics simulation, in place of low-frequency modes, to more accurately sample configurations. The results of the calculations performed with these methods indicate that the broadness of these multi-hump features originate from low-frequency modes modulating the hydrogen bond length, while the multi-hump lineshape is derived from strong Fermi resonances between the OH stretch and the OH bending modes.