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Exponential type orbital with hyperbolic cosine basis functions, proposed recently for Hartree–Fock–Roothaan calculations of neutral atoms, are studied in detail for the calculations of isoelectronic series of atoms from Be to Ne. Calculations are performed for the neutral and the first 20 cationic members of the isoelectronic series of each atom in its ground state. Three of the most popular exponential type orbitals (Slater type functions, B functions and  ψ   ( α )  functions with  α  = 2) are combined with modified hyperbolic cosine function cosh( βr  +  γ ) to improve the basis function quality within the minimal basis sets framework. Performances of the basis functions are compared with each other by using the same number of variational parameters in them. The obtained results are also compared with numerical Hartree–Fock and extended Slater type basis set results. The presented accuracy of the minimal basis descriptions of atomic systems supports the usage of these unconventional basis functions in electronic structure and property calculations.

Exponential type orbitals with hyperbolic cosine function basis sets for isoelectronic series of the atoms Be to Ne