Accurate extrapolation of electron correlation energies from small basis sets

A new two-point scheme is proposed for the extrapolation of electron correlation energies obtained with small basis sets. Using the series of correlation-consistent polarized valence basis sets, cc-pVXZ, the basis set truncation error is expressed as EX X+i−. The angular momentum offset i captures differences in effective rates of convergence previously observed for first-row molecules. It is based on simple electron counts and tends to values close to 0 for hydrogen-rich compounds and values closer to 1 for pure first-row compounds containing several electronegative atoms. The formula is motivated theoretically by the structure of correlation-consistent basis sets which include basis functions up to angular momentum L=X−1 for hydrogen and helium and up to L=X for first-row atoms. It contains three parameters which are calibrated against a large set of 105 reference molecules H, C, N, O, F for extrapolations of MP2 and CCSD valence-shell correlation energies from double- and triple-zeta DT and triple- and quadruple-zeta TQ basis sets. The new model is shown to be three to five times more accurate than previous two-point schemes using a single parameter, and TQ extrapolations are found to reproduce a small set of available R12 reference data better than even 56 extrapolations using the conventional asymptotic limit formula EXX−3. Applications to a small selection of boron compounds and to neon show very satisfactory results as well. Limitations of the model are discussed. © 2007 American Institute of Physics. DOI: 10.1063/1.2768359 I