Gaussian-type functions for the 3d Rydberg and 3d correlation orbitals in B to Ne and Al to Ar

Abstract

Gaussian-type basis sets for the 3d Rydberg orbitals and 3d correlation orbitals are developed for the first- and second-row main group elements. The numbers of the Gaussian-type functions (GTFs) used for the 3d orbitals are 1–3 for the former elements and 1–4 for the latter elements. The 3d Rydberg orbitals for the first-row main group elements are close to the hydrogen (H) 3d orbitals, but those of the second-row main group elements are very different from H 3d except for Al. A two d or three d GTF set suffices to model the first-row main group elements, but at least four d GTFs are necessary for the second-row main group elements. The Rydberg GTF orbitals, consisting of three GTFs, are converted into correlating orbitals by introducing a single scaling factor. The correlation energies (CEs) calculated using these correlating orbitals cover 99.4–100% of those calculated using Dunning's three primitive GTFs for the first-row main group elements, and 94.9–99.7% of the CEs of Woon and Dunning's d's for the second-row main group elements. The resulting correlating 3d orbitals were tested by picking out F2 and Cl2, yielding spectroscopic constants close to or more accurate than those calculated by Dunning's 3d orbitals and Woon and Dunning's 3d orbitals.