In order to investigate an origin of structural stability of a copper ion containing artificial DNA, we evaluated the stacking energy between [H-Cu2+-H] (H: hydroxypyridone) dimer by means of density functional theory (DFT) with an Anderson-Langreth-Lindqvist van der Waals (vdW) functional. The calculated distance between the copper ions is about 3.6 angstrom, which agrees well with the experimental data. Evaluated stacking energy is about 8-10 kcal/mol, which is slightly smaller than that of two base pairs in a natural B-DNA. This tendency does not change in [H-2H(+)-H], which does not contain copper ions. These results indicate that the vdW interaction dominates the inter-base-pair interaction over spin-spin interaction, in contrast to a conjecture by an experimental group. According to the results by the open-shell DFT, antiferromagnetic (singlet) and ferromagnetic (triplet) states are almost degenerated when the two bases are vertically located and both bases have a planar structure as found in the B-DNA.