Comparative performance of different hyperbolic cosine functions and generalized B functions basis sets for atomic systems

Ertürk M., Coşkun M.

PHYSICA SCRIPTA, vol.97, no.7, pp.1-11, 2022 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 97 Issue: 7
  • Publication Date: 2022
  • Doi Number: 10.1088/1402-4896/ac7588
  • Journal Name: PHYSICA SCRIPTA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Chemical Abstracts Core, Compendex, INSPEC, zbMATH
  • Page Numbers: pp.1-11
  • Çanakkale Onsekiz Mart University Affiliated: Yes


Recently, we reported a new set of Bessel type functions, which include the radial part of generalized Bessel functions ${r}^{n-1}{e}^{-\zeta \,{r}^{\mu }}$ for LCAO calculations of atomic systems. In this study, to achieve further improvement of the performance of generalized Bessel type basis sets in the Hartree–Fock-Roothaan calculations, different hyperbolic cosine functions inserted into the radial part of those generalized Bessel functions. For this purpose, three different generalized hyperbolic cosine functions have been used to construct the generalized Bessel type hyperbolic cosine basis sets. The accuracies of generalized Bessel type hyperbolic cosine functions within the minimal basis sets approach are compared to show their superiority to conventional approaches those in the literature. The performance of the presented basis functions is also compared to the numerical Hartree–Fock results. Our virial ratios are in good agreement to within 8-digits of the −2. It is shown that the results obtained by the new basis sets surpass the quality and accuracy of existing Bessel type basis sets.