C, D, and E Electronic States of the SO2+ Ion Studied Using Multiconfiguration Second-Order Perturbation Theory

Abstract

For exploring the C, D, and E states of the SO2+ ion, eight excited states of SO2+, 22A1, 32A1, 22B2, 32B2, 12B1, 22B1, 32B1, and 22A2, have been studied using the complete active-space self-consistent field (CASSCF) and multiconfiguration second-order perturbation theory (CASPT2) methods in conjunction with two contracted atomic natural orbital basis sets, S[6s4p3d1f]/O[5s3p2d1f] (ANO-L) and S[4s3p2d]/O[3s2p1d] (ANO-S) (the 12A1, 12B2, and 12A2 states were previously studied and assigned to the X, A, and B states, respectively). Equilibrium geometries and the v1 and v2 vibrational frequencies for the eight excited states were predicted at the CASSCF/ANO-L level. For the eight states, the CASPT2/ANO-L adiabatic excitation energy (T0) and vertical excitation energy (Tv) values were calculated using the CASSCF/ANO-L geometries, and the CASPT2/ANO-L relative energy (Tv‘) values to X2A1 were calculated at the SO2 molecular geometry. The CASPT2/ANO-L T0 ordering is: 12B1, 22B1, 22A2, 22A1, 32A1, 22B2, 32B2, and 32B1 (in increasing order of energy), and five of these states have shake-up ionization character. We assign the observed C, D, and E states of SO2+ to 12B1, 22A1, and 22B2, respectively, and the three calculated states have primary ionization character at the molecular geometry. The CASPT2/ANO-L T0 values and the CASSCF/ANO-L v1 and v2 values for 12B1 and 22A1 are in good agreement with the experimental T0, v1, and v2 values for the C and D states, respectively. The CASPT2/ANO-L T0 value and the CASSCF/ANO-L v1 and v2 values for 22B2 are in reasonable agreement with the experimental T0, v1, and v2 values for the E state, respectively. For preliminarily exploring the potential energy surfaces (PESs), potential energy curves (PECs) of the eight excited states, as functions of the OSO bond angle, were calculated at the CASPT2/ANO-S level, and then in the CASSCF/ANO-L PESs of 12B1 and 22A1 we found other minimum energy geometries which have lower CASPT2/ANO-L energies than the “equilibrium geometries” of the respective states. However, these geometries are far away from the Franck−Condon regions for the ground-state molecule and ion. For preliminarily exploring dissociation processes of SO2+, a Jacobi coordinate system (Cs symmetry) was adopted and dissociation potential energy curves (DPECs) for the 1-62A‘ and 1-52A‘ ‘ states were calculated at the CASPT2/ANO-S level. The calculations indicate that the 12A‘, 22A‘, 32A‘, 12A‘ ‘, 22A‘ ‘, and 32A‘ ‘ DPECs converge to the first dissociation limit [SO+ (X2Π) + O (3Pg)]. By considering the correlation relations of the Cs states with the C2v states and our assignments for the C, D, and E states, we conclude that, among the C, D, and E states, only two directly correlate to the first dissociation limit.