We report the results of density functional theory (DFT) studies on the formation of the complex H1--Cu2+-H1- consisting of two deprotonated hydroxypyridone ligands (H1-) and a Cu2+ ion. We compare the total energies of three possible structures with different symmetries and show that the structure with plane reflection symmetry has the lowest energy. The electronic structure of the periodic extended DNA-like double helix consisting of stacked H1--Cu2+-H1- units is then calculated within the density functional method, and the double helix is found to be an insulating ferromagnet.