The applicability of density functional theory (DFT) to van der Waals (vdW) calculations are investigated by using the long-range exchange correction scheme and the Andersson-Langreth-Lundqvist vdW functional. By calculating bond energy potentials of rare-gas dimers, it was found that the present scheme gives much more accurate potentials for all dimers than conventional sophisticated DFT methods do. We therefore confirmed that vdW bonds are constructed under the balance of long-range exchange and vdW correlation interactions, although neither of these interactions are usually contained in pure exchange-correlation functionals. It was also found that calculated vdW potentials are obviously affected by functional forms for rapidly varying densities. Especially in vdW calculations, we must employ a correlation functional that satisfies the fundamental condition for rapidly varying density.