Ab initio mixed polarizabilities responsible for the Raman-forbidden <i>ν</i> 2 transition in carbon dioxide molecule

The vibrational parity of a centrosymmetric molecule can be broken in the Raman spectra when the electric-dipole (E1) virtual transitions are accompanied by the electric-quadrupole (E2) or magnetic-dipole (M1) ones. To assess the intensity of the not yet detected ν2 CO2 Raman band, accurate ab initio values of the mixed E1-E2 (Â) and E1-M1 (Ĝ) polarizabilities of a bent CO2 molecule are presently obtained using the DALTON program suite. The previous SCF results of Amos, Buckingham, and Williams [Mol. Phys. 39, 819 (1980)] for the Â-tensor components are substantially refined by employing the extended basis sets and accounting for the electron correlation (up to CCSD). By using the SOPPA approach, the derivatives of Ĝ are obtained for the first time. The results are processed to derive the rank-r irreducible spherical tensors (IST), Xκ(r), which vary in space as the Wigner functions Dκm(r) whose subscript κ determines the dependence on the bent-molecule plane orientation relative to the symmetry axis. As a result, four ISTs (A1 (1), A1 (2), A1 (3), and A3 (3)) fully determine the ν2 E1-E2 intensity whereas tensors G1 (1) and G1 (2) do the same for the magnetic channel. Using the thus derived properties, the integrated ν2 band intensities are calculated for the first time and, like our recent assessments for the ν3 band [Kouzov et al., Opt. Spectrosc. 133, 581 (2025)], show the leading role of the E1-M1 terms. The results could be helpful for detection of this novel parity-changing Raman process.