Chapter 8 - Further Improvements on ψ(α*)—ETOs with Hyperbolic Cosine Functions and Their Effectiveness in Atomic Calculations

Abstract

Abstract In the last few years, exponential type orbitals became very important in electronic structure calculations of atoms and molecules. In this work, improvements on effectiveness of the ψ ( α ∗ ) -exponential type orbitals ( ψ ( α ∗ ) -ETOs) ( - ∞ α ∗ 3 ) containing different hyperbolic cosine functions are presented for the ground states of neutral atoms and their ions. The Hartree–Fock–Roothaan energies within the minimal basis set framework for some atoms up to Z = 18 and their ions are listed and compared with the results obtained with other exponential type orbitals such as conventional double-zeta Slater, noninteger-n Slater with different hyperbolic cosine basis sets and numerical Hartree–Fock values. The accuracy of ψ ( α ∗ ) -ETOs is greatly improved for all atomic systems studied. The optimal noninteger values of α ∗ are determined for each atomic system examined in this work.