On the Performance of Bond Functions and Basis Set Extrapolation Techniques in High-Accuracy Calculations of Interatomic Potentials. A Helium Dimer Study

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Abstract
Helium dimer interaction energies, Eint, obtained recently using the Gaussian geminal implementation of the coupled cluster doubles (CCD) and singles and doubles (CCSD) theory, were employed to evaluate the performance of conventional orbital calculations applying the correlation-consistent polarized valence X-tuple zeta (cc-pVXZ) bases, with X ranging from 4 to 7, and very large sets of bond functions. We found that while the bond functions improve dramatically the convergence of the doubles and triples contribution to the interaction energy, these functions are inefficient or even counterproductive in predicting the effect of the single excitations and the small contribution beyond the CCSD(T) (CCSD model with noniterative account of triple excitations) level of electronic structure theory. We also found that bond functions are very effective in extrapolation techniques. Using simple two-point extrapolations based on the single-power laws X-2 and X-3 for the basis set truncation error, the Gaussian geminal CCSD result for Eint, equal to -9.150 ± 0.001 K at the equilibrium interatomic distance of R = 5.6 bohr, could be reproduced with an error of 2-3 mK. Linear extrapolation of the functional dependence of the CCSD energy on the value of the second-order Møller-Plesset energy and the use of the known accurate value of the latter leads to an even smaller error. Using these extrapolation techniques with basis sets up to doubly augmented septuple-zeta quality and containing large sets of bond functions, we estimated the contribution of triple excitations within the CCSD(T) model to be -1.535 ± 0.002 K, with the error bars reflecting the spread of extrapolated results. The contribution beyond the CCSD(T) model, estimated from full configuration interaction (FCI) calculations with up to 255 orbitals, amounts to -0.323 ± 0.005 K. Combining the Gaussian geminal value of the CCSD energy with the orbital estimations of the CCSD(T) and FCI contributions, we found that Eint = -11.008 ± 0.008 K. This value is consistent with recent high-level orbital computations (van Mourik T., Dunning T. H.: J. Chem. Phys. 1999, 111, 9246; Klopper W.: J. Chem. Phys. 2001, 115, 761) but has substantially tighter error bounds. It differs somewhat, however, from the value of -10.98 ± 0.02 K obtained recently from the "exact" quantum Monte Carlo calculations (Anderson J. B.: J. Chem. Phys. 2001, 115, 4546).