Crystals of nitric acid hydrates have been studied theoretically by means of a recently developed ab initio method (SIESTA). Using as input data the X-ray structures of crystals of nitric acid monohydrate (NAM), dihydrate (NAD), and trihydrate (NAT), the atomic geometry within each unit cell has been refined. The calculated geometrical structure of these atmospherically relevant systems allows the study of further physicochemical properties. In this article, their vibrational normal modes have also been evaluated. These have been used to propose the assignment of the observed spectra of the hydrate crystals, with good overall agreement between experiment and calculation. This is the first time that this type of calculation has been carried out for NAD, whose recently observed two phases (I and II) have been studied here.