Inversion levels of H₃O⁺ as a probe for the basis set convergence in traditional and explicitly correlated coupled-cluster calculations

Abstract

The strong dependence of the symmetrical part of the full six-dimensional potential energy surface on the inversion levels and splittings of H₃O⁺ is exploited in examining the convergence of correlated electronic structure calculations with respect to the atomic basis set size. Results with standard coupled-cluster calculations employing correlation consistent basis sets are compared to the values obtained with explicitly correlated coupled-cluster calculations in the R12 approach, which includes the interelectronic coordinate in the electronic wave function. A Taylor-type series expansion of the potential energy function and a kinetic energy operator, which is exact within the Born–Oppenheimer approximation, are used to solve the six-dimensional vibrational problem variationally. This permits one to extend the comparison to spectroscopic observables. Approaching the accuracy of explicitly correlated methods in standard calculations is only possible with large basis sets combined with the basis set extrapolation technique. However, caution should be taken. Extrapolation may behave improperly for the Hartree–Fock energy and the use of augmented basis sets may slow down the convergence.

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Notes on contributors

Lauri Halonen *

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