An improvement on - exponential type orbitals for atoms in standard convention

Abstract

The complete orthonormal sets of -exponential type orbitals (-ETOs) in LCAO approximation are investigated for the determination of the optimal values of integer α (− ∞ < α ⩽ 2) and non-integer α* (− ∞ < α* < 3) by minimising the total energies in atomic calculations. The Hartree–Fock–Roothaan calculations with the use of different values of indices α and α* 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 α* that the efficiency of -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 α. It should be noted that the Coulomb–Sturmian and Lambda ETOs are special classes of ψ(α)-ETOs for α = 1 and α = 0, respectively. The performance of -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 α* are also determined for each atom examined in this work. It is shown that the notably improvement in the efficiency of -ETOs can be obtained by the use of non-integer α* values.