Previous experimental and computational investigations show that the copper binding in the prion protein that is involved in a number of neurodegenerative diseases is complicated and the exact binding structures remain to be determined. To facilitate structural investigation in this field, we report a quantum chemical investigation of structural, EPR superhyperfine, and NMR hyperfine properties of various copper complexes of the octarepeat domain, which has several copies of highly conserved amino acid sequence of PHGGGWGQ, The predicted metal ligand bond lengths of the X-ray structure of CuHGGGW, involving the central five residues in this domain, from the best method examined here, have a mean absolute deviation (MAD) of 0.030 angstrom, basically the same as found with experimental errors of various metal complexes. Prior controversial results regarding water coordination were resolved here with a more extensive computational investigation on 10 models with various water molecules and sequences (both HGGGW and PHGGGWGQ), which are consistent with the experimental reports. Experimental EPR superhyperfine constants are accurately reproduced with a MAD of 0.95 MHz. Results here suggest that the NMR hyperfine shifts which can be readily measured in NMR experiments and accurately predicted in quantum chemical calculations can provide more extensive and more sensitive structural probes than those from the current EPR studies. These results will be helpful for future experimental and computational investigations of the copper binding structures of the prion protein as well as other related systems.