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

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.