The performance of Dunning, Jensen, and Karlsruhe basis sets on computing relative energies and geometries

ABSTRACT

In an effort to assist researchers in choosing basis sets for quantum mechanical modeling of molecules (i.e. balancing calculation cost versus desired accuracy), we present a systematic study on the accuracy of computed conformational relative energies and their geometries in comparison to MP2/CBS and MP2/AV5Z data, respectively. In order to do so, we introduce a new nomenclature to unambiguously indicate how a CBS extrapolation was computed. Nineteen minima and transition states of buta-1,3-diene, propan-2-ol and the water dimer were optimized using 45 different basis sets. Specifically, this includes one Pople (i.e. 6-31G(d)), 8 Dunning (i.e. VXZ and AVXZ, X = 2–5), 25 Jensen (i.e. pc-n, pcseg-n, aug-pcseg-n, pcSseg-n, and aug-pcSseg-n, n = 0–4), and 9 Karlsruhe (e.g. def2-SV(P), def2-QZVPPD) basis sets. The molecules were chosen to represent both common and electronically diverse molecular systems. In comparison to MP2/CBS relative energies computed using the largest Jensen basis sets (i.e. n = 2,3,4), the use of smaller sizes (n = 0,1,2 and n = 1,2,3) provides results that are within 0.11–0.24 and 0.09–0.16 kcal$\cdot$mol${ }^{-1}$. To practically guide researchers in their basis set choice, an equation is introduced that ranks basis sets based on a user-defined balance between their accuracy and calculation cost. Furthermore, we explain why the aug-pcseg-2, def2-TZVPPD and def2-TZVP basis sets are very suitable choices to balance speed and accuracy.

KEYWORDS:

• Basis set
• complete basis set limit
• water dimer
• propan-2-ol
• mp2

Acknowledgments

We would like to thank Rudolf Berrendorf and Javed Razzaq for their continuous development and support of the university’s high performance computing cluster, and we highly value the feedback given by anonymous reviewers for improving the manuscript. We would also like to acknowledge the tremendous and inspiring contributions of Florian Müller-Plathe who acted as a trend-setter for a broad number of topics within the soft matter field and to whom we dedicate this work. Computer hardware was supported by the Federal Ministry for Education and Research and by the Ministry for Innovation, Science, Research, and Technology of the state Northrhine-Westfalia (research grant 13FH156IN6).

Supplementary material

Supplemental data for this article can be accessed on the publisher’s website.