Density-functional study of lanthanum, ytterbium, and lutetium dimers

La-2, Yb-2, and Lu-2 have been studied by use of the density-functional methods B3LYP, BLYP, B3PW91, BHLYP, BP86, B3P86, MPW1PW91, and PBE1PBE. In these density-functional methods, the exchange functional is from either Becke's three-parameter HF-DFT hybrid exchange functional (B3), pure DFT exchange functional of 1988 (B), a modification of the half-and-half HF/DFT hybrid method (BH), Perdew-Wang 1991 (PW91), or Barone's modified PW91 (MPW1), while the correlation functional is from either Lee, Yang, and Parr (LYP), Perdew-Wang 1991 (PW91), or Perdew 86 (P86). PBE1PBE is the generalized-gradient-approximation exchange-correlation functional of Perdew, Burke, and Ernzerhof. For La-2, the calculated bond distance is in reasonable agreement with the experiment, but the calculated vibrational frequency is underestimated significantly compared with the experiment. Only BP86 and B3P86 have the best performance in reproducing the experimental dissociation energy for La-2. For the van der Waals dimer Yb-2, three functionals, B3LYP, BLYP, and BHLYP have excellent performance in reproducing the spectroscopic constants compared with both the experiment and previous theoretical studies.