Test of a nonempirical density functional: Short-range part of the van der Waals interaction in rare-gas dimers

It is known that the nonempirical generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) provides a much more realistic description of the short-range part of the van der Waals (vdW) interaction than does the local spin density (LSD) approximation. In the present work, the ability of the higher-level nonempirical meta-GGA of Tao, Perdew, Staroverov, and Scuseria (TPSS) to describe vdW interaction is tested self-consistently in ten rare-gas dimers with Z< or =36. The one-parameter hybrid version (TPSSh) of the TPSS exchange-correlation functional is also included in this test. Calculations show that both TPSS and TPSSh functionals correctly yield vdW bonds in these dimers and significantly improve the prediction of bond lengths, binding energies, and harmonic vibrational frequencies over LSD. The rather close agreement of TPSS with PBE for these dimers confirms a principle of the TPSS construction: preservation of the PBE large-gradient behavior. More importantly, it suggests that TPSS can serve as a platform on which to construct a still-higher level of nonempirical functionals. Compared with the PBE GGA, TPSS, and TPSSh yield a slightly weaker binding. As for normally bonded molecules, TPSSh yields the most accurate vibrational frequencies. The typically too-long bond lengths and too-small binding energies of TPSS meta-GGA suggest the need for some long-range vdW interaction correction even in this class of systems. The effect of basis-set superposition error on the calculated properties of these vdW systems is investigated. We also show that the relatively strong anharmonic effects in the rare-gas dimers are described remarkably well by the Morse potential.