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

Abstract

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 4d_u^2) and STO-kG(4f_u^3 and 4f_uv^2) basis functions among the six technical 3d_uv 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.