Efficient recursive Gaussian integral calculation of anion photodetachment cross sections

Photodetachment cross sections (PDCSs) are key parameters for quantitatively characterizing the generation and annihilation of anions, with transition moment integrals being the critical component in their theoretical calculation. This work introduces an efficient method for calculating transition moments within the plane wave approximation, based on the analytical expressions of the recursive Cartesian two-center Gaussian integral. This method effectively bypasses the convergence issues commonly associated with traditional plane wave expansion techniques. By incorporating the random orientation of gas-phase molecular anions, the total PDCSs can be derived. For molecules with low anisotropy wavefunctions, the integration is further simplified to three orthogonal directions, dramatically reducing computational costs. Benchmark tests on a variety of atomic and molecular anions (H-, Li-, C-, O-, F-, S-, Cl-, OH-, NH2-, CN-, and C2H-) show excellent agreement with previous experimental measurements and high-level theoretical results. Furthermore, the method's superior computational efficiency is demonstrated through applications to larger systems, such as benzyl anion, glycine anion, and water tetramer anion. The proposed method holds significant potential for advancing the field of vacuum ultraviolet photochemistry.