Unified Formulae For Augmented Near Orthonormalized STO-mG Basis Sets Via Atomic Orbital Energy Fit To Use In Molecular Structure Calculations

STO-mG type basis functions for 1s to 4f Hydrogen-like orbitals by “energy fit” are reported as simple functions of running parameter atomic number Z and quantum numbers to utilize the basis set from these functions in molecular electronic structure and energy calculations. We mimic the accurate solution of Slater-type atomic orbitals (STO, here called ASTO) as close as possible (in shape and orbital energy) with a linear combination of m Gaussian functions; the use of Gaussians is vital for the analytical evaluation of molecular integrals. We analyze how they reproduce the one-electron atomic wave function shapes and energy values (-Z2/(2n2)) as an obvious primary claim, as well as we compare it to the literature. The direct wave function (shape) fit to the exp(-Z r/n) part of Hydrogen-like orbitals with a linear combination of Gaussians, Sum[i=1]mAiexp(-ai r2), is the basic way to create STO-mG basis sets in literature, yielding a huge number of tables for different atoms, that is, listed separately for different atomic numbers Z in the periodic table.