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Unified formulae for augmented near orthonormalized STO-kG (1s, …, 4f) basis sets via atomic orbital energy fit with graphical representations to use in molecular structure calculations Kristyan, Sandor Ab initio calculations Computational chemistry Unified STO-kG basis sets Molecular structure calculations STO-kG(3d and 4f) basis functions Recursive formulae for overlap molecular integrals STO-kG type (linear combination of k Gaussians) basis functions for 1s to 4f Hydrogen-like orbitals by ‘energy fit’ are reported as simple functions of the atomic number Z and quantum numbers to utilize in molecular electronic structure calculations. We analyze how they reproduce the one-electron atomic wave function shapes and energy values (-Z2/(2n2)) as an obvious primary claim along with reproducing the nodes exactly. The literature STO-kG yields a huge number of tables for different atoms in the periodic table; in contrast, our sets contain Z as a parameter yielding a compact list. A ‘variation-like’ property is also discussed for excited states (2s and up). The optimizations have been done by using least squares fits via the Lagrange multiplier method for energy with a constraint for normalization. All these STO-kG basis functions are normalized exactly to one in our tables. The general problem of STO-kG(3 and 4du^2) and STO-kG(4fu^3 and 4fuv^2) basis functions among the six technical 3duv as well as the ten technical 4f used in practice is commented on. In relation and comparison, the Gaussian package STO-kG basis set is commented on. Atlanta Publishing House LLC 2025-12-31 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion application/pdf https://www.eurjchem.com/index.php/eurjchem/article/view/2711 10.5155/eurjchem.16.4.382-394.2711 European Journal of Chemistry; Vol. 16 No. 4 (2025): December 2025; 382-394 2153-2257 2153-2249 eng https://www.eurjchem.com/index.php/eurjchem/article/view/2711/2985 Copyright (c) 2025 Sandor Kristyan https://creativecommons.org/licenses/by-nc/4.0