Terahertz (THz) vibrational spectroscopy is a promising tool for the nondestructive and potentially noninvasive characterization of historical objects, which can provide information on the materials used for their production as well as identify and monitor their chemical degradation. Copper sulfate (CuSO4) has drawn interest due to its inclusion in the preparation of iron gall inks found in historical artwork and documents. Copper sulfate rapidly forms hydrates which contribute to the formulation of these ink species and may influence their corrosive nature. In this study, copper sulfate has been studied using a combination of THz time-domain spectroscopy, powder X-ray diffraction (PXRD), and solid-state density functional theory (DFT) in order to better understand the spectral absorbances in the THz region. The results have revealed that the THz spectrum of commercially available "anhydrous" copper sulfate results from the presence of not only the anhydrous form but also the monohydrate (CuSO4.H2O) and trihydrate (CuSO4.3H(2)O) forms. Complete assignment of the experimental spectrum was achieved through a comparison of density functionals and extensive investigation of the influence of basis set polarization functions on the bonding interactions, lattice parameters, and low-frequency motions in these crystalline solids.