Nuclear magnetic resonance shieldings of water clusters: is it possible to reach the complete basis set limit by extrapolation?

Abstract

We have explored the possibility of using extrapolation techniques to estimate the complete basis set limit of nuclear shieldings of small water clusters. Several density functionals (Becke-Lee-Yang-Parr (BLYP), Perdew-Burke-Ernzerhof (PBE), OPTX-Perdew-Burke-Ernzerhof (OPBE), Swart-Solà-Bickelhaupt functional with Grimme's Dispersion included (SSB-D) and wavefunction methods (Hartree–Fock, Møller-Plesser perturbation theory for electron correlation up to second order (MP2) and coupled cluster) were used in combination with Dunning's (augmented) correlation-consistent and Jensen's polarisation-consistent basis sets. Although density functionals show larger nuclear shieldings than coupled cluster methods for these water clusters, differences in chemical shifts are much smaller. A new extrapolation scheme based on a Gaussian exponential function is shown to achieve better results for reaching the basis set limiting values, but the exponential needed for it cannot be obtained a priori with good confidence. This renders a two-point extrapolation for prediction of the basis set limiting value impossible.

Keywords:

• complete basis set extrapolation
• density functional theory
• coupled cluster methods
• nuclear magnetic resonance
• water clusters

Acknowledgements

The following organisations are thanked for financial support: the Ministerio de Ciencia e Innovación (MICINN, project numbers CTQ2011-23156/BQU and CTQ2011-25086/BQU), and the DIUE of the Generalitat de Catalunya (project numbers 2009SGR637, 2009SGR528, and the Xarxa de Referència en Química Teòrica i Computacional). Financial support from MICINN (Ministry of Science and Innovation, Spain) and the FEDER fund (European Fund for Regional Development) was provided by grant UNGI08-4E-003. Excellent service by the Centre de Supercomputació de Catalunya (CESCA) is gratefully acknowledged. Support for the research of M. Solà was received through the ICREA Academia 2009 prize for excellence in research funded by the DIUE of the Generalitat de Catalunya.

Notes

^aCorrelation part, defined as σ _post-HF – σ _HF.

^aCorrelation part, defined as σ _post-HF – σ _HF.

^aLowest value obtained with any basis set, see Tables 1 and 2; ^bMean absolute deviation between input and fit (see text); ^cValues obtained by fitting to pcS-n with n = 1–3.

^aLowest value obtained with any basis set, see Tables 1 and 2; ^bMean absolute deviation between input and fit (see text).

^aLowest value obtained with any basis set; ^bObtained using Equation (2), see Table 3; ^cObtained using Equation (5).

^aIn parentheses the post-HF correlation contribution to it; ^bCBS limit from Equation (6).

^aIn parentheses the post-HF correlation contribution to it; ^bCBS limit from Equation (6).