Optimal basis sets for CBS extrapolation of the correlation energy: oV x Z and oV(x+d)Z

Abstract

We seek correlation consistent double- and triple-zeta basis sets that perform optimally for extrapolating the correlation energy to the one-electron complete basis set limit. Since the methods used are approximate, the novel basis sets become method specific in the sense of performing best for the chosen level of theory. Such basis sets are also shown to perform accurately for tensorial properties and do not significantly alter the Hartree-Fock energy. Quantitatively, the extrapolated correlation energies from (oVdZ, oVtZ) outperform typically by three- to fivefold those obtained from traditional ansatzes with similar flexibility, thus being (VtZ, VqZ) type or even better. They may even outperform explicitly correlated ones. Not surprisingly, the outperformance in relative energies (e.g., atomization and dissociation energies, and ionization potential) is somewhat downscaled, albeit consistently better than with traditional basis sets. As a case study, we also consider the polarizability of p-nitroaniline, a sizeable system for which complete basis set (CBS)(oVdZ, oVtZ) calculations are shown to outperform equally expensive CBS(VdZ, VtZ) results.

Optimal diffuse augmented atomic basis sets for extrapolation of the correlation energy

“…In fact, the CCSD(T) differences in the odd columns are systematically slightly smaller than in the even, as one might hope from a physically motivated scheme (the AV X Z basis approaches faster the CBS limit). The opposite occurs for MP2, which tends to approach even faster, possibly slightly overestimating, the CBS values …”

“…Table presents the exponents obtained as described above (see also elsewhere). Although further exponents could have been optimized, we focused on the single exponent case as its simplicity best illustrates the capability of the method.…”

“…Using the above idea, we reported oV x Z ( x 1 = d , t ) basis sets for coupled cluster (CC) and Møller‐Plesset correlated methods. The results at the CBS/oV( d , t )Z level of extrapolation have been shown to significantly outperform the ones obtained from the original Dunning V X Z basis sets at the same hierarchical level for absolute correlation and total energies (a total of about 150 molecular systems have been considered a test set for the statistics), atomization energies (106 systems), ionization potentials (18 systems), and polarizabilities (7 systems). Moreover, the novel oV x Z basis sets have often shown deviations similar to higher‐level CBS/V( t , q )Z calculations for both absolute and atomization energies, which can only be viewed as a promising outcome.…”

“…All the above basis sets have in common being hierarchized, a key asset that allows us to extrapolate to the complete basis set limit (CBS) the energy (as well as any property that is relatable to the energy; the list is by no means complete, with the reader referred to recent articles from which others may be obtained through cross‐referencing) and hence estimate the basis set incompleteness error. Of course, there is a need for a reliable CBS extrapolation scheme, and here, we have chosen the one utilized in the first article of this series …”

“…As in the first article of this series, the electronic structure calculations performed here use single‐reference Møller‐Plesset perturbation theory (MP2) and the couple‐cluster singles and doubles method, both without (CCSD) and with inclusion of iterative triple excitations [CCSD(T)]. As the calculated energies are approximate, the new basis sets will further become method‐dependent.…”