Accurately solving the electronic Schrodinger equation of atoms and molecules by extrapolating to the basis set limit.: I.: The helium dimer (He2)

A new formula, E-L-E proportional to(L+3/4)(-3), to extrapolate energies, E-L (that arise when the basis set is truncated at a finite angular momentum quantum number, L) to the limit, E, is derived and applied to the computation of the pair potential of He. Large basis sets up to d-aug-cc-pV5Z and -6Z are used, and in addition, a new cc-pV7Z set is presented. The full-CI is approximated using the multireference averaged coupled-pair functional (MR-ACPF) with 121 references. The calculated molecular constants of He-2 are in excellent agreement with those recently obtained with r(12)-MR-ACPF [R. J. Gdanitz, Mol. Phys. 96, 1423 (1999)], but they agree only fairly with the complete-CI estimate of van Mourik and Dunning [J. Chem. Phys. 111, 9248 (1999)]. The potential of Komasa [J. Chem. Phys. 110, 7909 (1999)] which has been calculated with the exponentially correlated Gaussians method does not give a bound state. The sensitivity of the molecular constants < R > and D-0 to errors of the interaction potential at different distances is estimated by perturbing the potential by Gaussian functions. The region of 5 less than or similar to R/a(0)less than or similar to 9 is found to be most sensitive. From this analysis, doubts arise that recent calculations (including the present one) are accurate enough to allow the molecular constants to be determined to better than approximate to 10%. (C) 2000 American Institute of Physics. [S0021-9606(00)30137-4].