Simulation of Negative Ion Photoelectron Spectroscopy Using a Nuclear Ensemble Approach: Implications from a Nuclear Vibration Effect.

The negative ion photoelectron spectroscopy (NIPES) has been proven to be a powerful technique to reveal the electronic structures and spectroscopic properties of various cluster anions/radicals with very high precision. However, direct comparisons of the theoretical NIPES with experimental measurements remain challenging. Particularly the nuclear vibration effect and the ionization probability are typically ignored in reproducing NIPES. In this work, the NIPES of three representative anions (NaS5-, P2N3-, and HCPN3-) with significantly different spectral features were simulated by combining the nuclear ensemble approach (NEA) and Dyson orbitals (DOs). Overall, the simulated NIPES are in good agreement with the experimentally determined ones, confirming the robustness of such a strategy. The analysis of frontier molecular orbitals (MOs) and DOs further suggests the similar mixed characters for the first ionized doublet (D0) and adjacent D1 states of NaS5- with distributions on the side sulfur atoms. And the D0 of P2N3* is confirmed as the lowest energy σ radical state; however, the D0 of HCPN3* should possess a mixture of π and σ electrons by taking into account the nuclear vibration effect. Next, the broader vibrational distribution and stronger main vibration modes of P2N3- and HCPN3- explain why the nuclear vibration possesses a more pronounced influence in reproducing their NIPES while it has little effect on NaS5-. Last, the limitations based on the double-harmonic approximation model and density of state method were also discussed, highlighting that the ionization probability and orbital relaxation effect during the ionization process should be reasonably considered.