On one-electron basis set extrapolation of atomic and molecular correlation energies

Abstract

It is well known that the convergence of correlation energies in atomic and molecular calculations is relatively slow and that calculations aimed at high accuracy must explicitly make corrections for this. In this work we consider 1e ⁻ basis set extrapolation as a means of obtaining high accuracy. The correlation consistent basis sets of Dunning et al. have provided a convenient platform for extrapolation, with the independent variable being X = D, T, Q, 5, … . There has been much debate in the literature about the functional form to use for the extrapolation, with contention between the ‘theoretically justified’ (X + 1)⁻³ form and empirical forms based on exponentials or variable powers. We will dissect the theoretical justification of the (X + 1)⁻³ form by considering MP2 calculations on He and Ne as a function of the maximum angular momentum (⪙) in the basis using basis sets having converged radial extent. Calculations with ⪙ up to 14 were carried out for Ne. It is shown that while the asymptotic form of (⪙ + 1)⁻³ is clearly reached, higher order terms are very important in the range of ⪙ normally used in molecular calculations. We also use similar analysis techniques for an open shell atom and a small molecule. The functional form for the dependence of molecular properties with ⪙ is complex and it is safer to extrapolate fitting parameters than energies.

Keywords:

• extrapolation
• one-electron basis sets
• correlation energies