https://doi.org/10.1140/epjd/s10053-025-01092-w
Research - Atoms, Molecules, Ions, and Clusters
Reassessing Gaussian-type orbital and B-spline basis functions for accurate calculations of atomic properties: application to 
Cs
Department of Physics, Guru Nanak Dev University, 143005, Amritsar, Punjab, India
Received:
25
August
2025
Accepted:
6
November
2025
Published online:
17
November
2025
The choice of basis functions plays a vital role in performing accurate calculations of atomic properties. An alternative to the commonly used Gaussian-type orbitals (GTOs) is the use of B-spline functions, which offer a highly flexible and efficient basis for representing atomic wave functions. The accuracy of an atomic property depends on the quality of the chosen basis functions used to construct single-particle wave functions. This work aims at revisiting the behavior of GTOs and B-spline functions to use them optimally in different atomic calculations so that it can help reduce computational cost. In this context, we analyze the magnetic-dipole hyperfine constants (
) for a number of atomic states in Cs. We first analyze results obtained using GTOs and B-splines, which are often used in the literature, followed by redefining them to improve efficiency in the calculation of atomic properties. Our comparative study reveals that an adaptive distribution of GTOs delivers the best results for low- and intermediate-lying states, whereas a kinetically balanced B-spline basis becomes more reliable for high-lying states, especially when a large number of basis functions are employed.
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
