The adsorption of a series of atoms and small molecules and radicals (H, C, N, O, NH, OH, H₂O, CH₃ , and NH₃) on hexagonal crystalline and amorphous ice clusters were obtained via classical molecular dynamics and electronic structure methods. The geometry and binding energies were calculated using a QMHigh:QMLow hybrid method on model clusters. Several combination of basis sets, density functionals and semi-empirical methods were compared and tested against previous works. More accurate binding energies were also refined via single point Coupled Cluster calculations. Most species, except carbon atom, physisorb on the surface, leading to rather small binding energies. The carbon atom forms a COH₂ molecule and in some cases leads to the formation of a COH-H₃O⁺ complex. Amorphous ices are characterized by slightly stronger binding energies than the crystalline phase. A major result of this work is to also access the dispersion of the binding energies since a variety of adsorption sites is explored. The interaction energies thus obtained may serve to feed or refine astrochemical models. The present methodology could be easily extended to other types of surfaces and larger adsorbates.