Analytical potential energy function for the electronic states ²П_1/2 and ²П_3/2 of O₂^x(x=+1, --1)

The splitting of potential energy levels for ground state X²\Pi_g of O₂^x(x=+1, -1) under spin--orbit coupling (SOC) has been calculated by using the spin--orbit (SO) multi-configuration quasi-degenerate perturbation theory (SO-MCQDPT). Their Murrell--Sorbie (M--S) potential functions are gained, and then the spectroscopic constants for electronic states ²\Pi_1/2 and ²\Pi_3/2are derived from the M--S function. The vertical excitation energies for O₂^x(x=+1, -1) are \nu O₂⁺¹ (²\Pi_3/2 → X²\Pi_1/2)=195.652cm^-1, and \nu O₂^-1(²\Pi_1/2 → X²\Pi_3/2 )=182.568cm^-1, respectively. All the spectroscopic data for electronic states ²\Pi_1/2 and ²\Pi_3/2 are given for the first time.