Construction of complex STO-NG basis sets by the method of least squares and their applications

Electronic resonance state energies and photoionization cross sections of atoms and molecules are calculated with the complex basis function method by using mixture of appropriate complex basis functions representing one-electron continuum orbitals and the usual real basis functions for the remaining bound state orbitals. The choice of complex basis functions has long been a central difficulty in such calculations. To address this challenge, we constructed complex Slater-type orbital represented by N-term Gaussian-type orbitals (cSTO-NG) basis sets using the method of least squares. Three expansion schemes are tested: (1) expansion in complex Gaussian-type orbitals, (2) expansion in real Gaussian-type orbitals, and (3) expansion in even-tempered real Gaussian-type orbitals. By extending the Shavitt–Karplus integral transform expression to cSTO functions, we have established a mathematical foundation for these expansions. To demonstrate the efficacy of this approach, we have applied these basis sets to the calculation of the lowest Feshbach resonance of H₂ and the photoionization cross section of the He atom including autoionization features due to doubly excited states. These calculations produce acceptably accurate results compared with past calculations and experimental data in all cases examined here.