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

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.