Guseinov, Israfil IsaSahin, E.Erturk, M.2025-01-272025-01-2720140026-89761362-3028https://doi.org/10.1080/00268976.2013.795665https://hdl.handle.net/20.500.12428/22940The complete orthonormal sets of psi((alpha)*())-exponential type orbitals (psi((alpha)*())-ETOs) in LCAO approximation are investigated for the determination of the optimal values of integer (- < 2) and non-integer * (- < * < 3) by minimising the total energies in atomic calculations. The Hartree-Fock-Roothaan calculations with the use of different values of indices and * are performed within the framework of the minimal basis sets approximation for the ground states of neutral atoms. It is found for non-integer values of * that the efficiency of psi((alpha)*())-ETOs in total energy calculations, electron density, and its derivative and cusp ratio at the nuclei is much better than the other integer values of . It should be noted that the Coulomb-Sturmian and Lambda ETOs are special classes of (())-ETOs for = 1 and = 0, respectively. The performance of psi((alpha)*())-ETOs in atomic energy calculations is also compared to those obtained by using other ETOs such as Slater and B functions. The optimal non-integer values of * are also determined for each atom examined in this work. It is shown that the notably improvement in the efficiency of psi((alpha)*())-ETOs can be obtained by the use of non-integer * values.eninfo:eu-repo/semantics/closedAccessexponential type orbitalelectron densityelectronic structure calculationArticle1121354010.1080/00268976.2013.795665Q3WOS:0003284714000042-s2.0-84890799196Q2