Convergence of symmetry-adapted perturbation theory for the interaction between helium atoms and between a hydrogen molecule and a helium atom

Convergence properties of perturbation expansions for the interaction energy are investigated by performing high-order calculations for the interaction between helium atoms and between a hydrogen molecule and a helium atom. It is shown that for small intermonomer distances the standard Rayleigh-Schrödinger (polarization) expansion converges to a Pauli forbidden state of the dimer. At large separations the exchange component of the interaction energy is not recovered in a practically low order and an apparent convergence to the Coulomb part of the interaction energy is observed. The symmetrized Rayleigh-Schrödinger (SRS) theory provides in low order very accurate values of both the Coulomb and the exchange parts of the interaction energy for the physical, Pauli allowed state. In the region of the van der Waals minimum already the second-order treatment reproduces the full configuration interaction (FCI) energy with an error of a few percent. In very high orders the convergence of the SRS theory becomes extremely slow and the series appears to converge to a nonphysical limit very close to the exact interaction energy. The symmetry-adaptation characteristic of the Hirschfelder-Silbey (HS) theory is shown to correct this pathological behavior although the improved convergence is observed only in very high orders, so from the practical point of view the HS theory is not superior to the SRS approach. The HS series converges to the FCI interaction energy only if the latter is corrected for the basis set superposition error using the full counterpoise correction of Boys and Bernardi. © 1997 Academic Press Inc.