Ab initio study on the low-lying excited states of gas-phase PH+ cation including spin–orbit coupling

Abstract

Ab initio calculations have been performed on the low-lying excited and ground states of PH+. The potential energy curves (PECs) of the Λ–S states were calculated with multi-reference configuration interaction (MRCI) method along with the basis sets at 5-ξ level. In order to improve the PECs, the Davidson(+Q) correction and the Scalar relativistic effect are included. The corresponding spectroscopic constants were determined and good agreements with the available measurement were found. The interactions of the A2Δ–4Π and 12Σ+–4Π by the spin–orbit coupling (SOC) effect were well described by the spin–orbit matrix elements. The SOC effect makes the original 8 Λ–S states split into 15Ω states. The Ω=1/2 state generated from the X2Π state is confirmed to the ground Ω state. And the SOC splitting for the X2Π is calculated to be 294cm−1. The SOC effect has large effect on the PECs of the A2Δ and 12Σ+ states, leading to much more shallow potential wells as well as potential barriers. The analysis of the wavefunction for the Ω states shows that the strong spin–orbit interaction exists near the crossing points of the PECs for the Λ–S states. The transition dipole moments (TDMs) of transitions A2Δ–X2Π and 12Σ−–X2Π are evaluated with the MRCI wavefunction. Based on the TDMs along with the calculated Franck–Condon factors, the radiative lifetimes for the selected vibrational levels of A2Δ and 12Σ− states are predicted at the microseconds (μs). Good agreement with the measurement shows that the lowest vibrational level for A2Δ state is almost uninfluenced by the perturbation via the SOC effect.