Application of the generalized-gradient approximation to rare-gas dimers

By performing numerically precise calculations on the ${\mathrm{He}}_2,$ ${\mathrm{Ne}}_2,$ ${\mathrm{Ar}}_2,$ ${\mathrm{Kr}}_2,$ HeNe, HeAr, HeKr, NeAr, NeKr, and ArKr diatomic molecules we have determined the capacity of three popular approximations to density-functional theory to accurately describe bonding in these rare-gas systems. The local-density approximation, the Perdew-Wang 1991 generalized-gradient approximation, and the Perdew-Burke-Ernzerhof generalized-gradient approximation are utilized in the calculation of equilibrium bond lengths, atomization energies, and anharmonic and harmonic vibrational frequencies. We also use the density-functional-based determination of atomic polarizabilities and ionization potentials to obtain the coefficients for the long-range ${(1/r}^6)$ attraction. Our calculations suggest that the interaction from the overlap of atomic densities is the primary binding mechanism in these systems at short range but that the long-range ${1/r}^6$ attraction could also contribute to the total binding energy.