Formation of diphosphorus (P₂⁺) and phosphorus mononitride (PN⁺) cations by radiative association

¹ Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China
² Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Universidade de São Paulo, Rua do Matão 1226, 05508-090, São Paulo, SP, Brazil
³ Instituto de Geociências e Ciências Exatas, Universidade Estadual Paulista, Av. 24A, 13506-900 Rio Claro, SP, Brazil

^★ Corresponding author: yanbing@jlu.edu.cn

Received: 23 December 2024
Accepted: 25 September 2025

Abstract

We estimated radiative association rate coefficients for P(⁴S) atoms and P⁺(³P) ions interacting with P(⁴S) and N(⁴S) atoms to form P₂⁺ and PN⁺ cations, respectively. The required potential energy curves of P₂⁺ and PN⁺ and the transition dipole moments coupling the states of interest were obtained using the multi-reference configuration interaction approach with a Davidson correction (MRCI+Q). The rate coefficients were obtained from the cross-sections, which were computed using a quantum mechanical method. The maximum rate constant values we predict are 3.13×10⁻¹⁹ cm³ s⁻¹ at 10 K for the PN⁺ cation and 1.66×10⁻¹⁶ cm³ s⁻¹ at 3500→6000 K for the P₂⁺ cation. For the convenience of astrochemical applications, the thermal rate constants were fitted to the standard equation, k(T) = A(T/300)^α e^β/T.