Assessment of basis sets for F12 explicitly-correlated molecular electronic-structure methods

Abstract

One-electron basis sets for F12 explicitly-correlated molecular electronic-structure methods are assessed by analysing the accuracy of Hartree–Fock energies and valence-only second-order correlation energies of a test set of 106 small molecules containing the atoms H, C, N, O and F. For these molecules, near Hartree–Fock-limit energies and benchmark second-order correlation energies (accurate to within 99.95% of the basis-set limit) are provided. Absolute energies are analysed as well as the Hartree–Fock and second-order correlation contributions to the atomisation energies of the molecules. Standard basis sets such as the Karlsruhe def2-TZVPP and def2-QZVPP sets and the augmented correlation-consistent polarised valence X-tuple zeta (aug-cc-p VXZ, X = D, T, Q, 5) sets are compared with the specialised cc-pVXZ-F12 (X = D, T, Q) sets that were recently optimised by Peterson and co-workers [J. Chem. Phys. 128, 084102 (2008)] for use in F12 theory. The results obtained from F12 explicitly-correlated molecular electronic-structure calculations are compared with those that are obtained by standard electronic-structure calculations followed by basis-set extrapolation based on the X ⁻³ convergence behaviour of the aug-cc-pVXZ basis sets. The most important conclusions are that the cc-pVXZ-F12 sets are the preferred basis sets for F12 theory and that the X ⁻³ extrapolation from the aug-cc-pVQZ and aug-cc-pV5Z is slightly more accurate than F12 theory in the cc-pVTZ-F12 basis but less accurate than F12 theory in the cc-pVQZ-F12 basis.

Keywords:

• basis sets
• explicitly-correlated wave functions
• F12 methods
• atomisation energies

Acknowledgements

This research was supported by the Deutsche Forschungsgemeinschaft (DFG) in the framework of the Schwerpunktprogramm ‘First Principles Methods’ (SPP 1145, grant No. KL 721/2-3). F.A.B. gratefully acknowledges support by the Fonds der Chemischen Industrie through a Chemiefonds stipend. D.P.T. gratefully acknowledges support by the DFG through grant No. TE 644/1-1.