Effective Hamiltonians for calculation of rotational energy levels and relative intensities in open-shell clusters containing O2 (3Σg-) and a closed–shell molecule

We introduce two effective Hamiltonians that are suitable for analysis and fitting IR and MW high resolution spectra in non-planar or planar O₂-closed-shell complexes, where the closed-shell moiety is a diatom or a triatomic molecule of any symmetry. These new Hamiltonians differ in our choice for the direction of quantization of the projection of the electron-spin angular momentum. For both electron-spin coupling schemes, the total rotation-spin-tunneling Hamiltonians include tunneling, electron-spin–spin coupling, electron-spin-rotation interaction, and centrifugal distortion forces. In addition, we introduce the appropriate molecular symmetry treatment for an O₂ (${}^3{\Sigma }_g^{-}$)-XY₂ (e.g., O₂-SO₂ and O₂-H₂O) dimer in which the monomers exhibit permeation-inversion tunneling motion. Non-vanishing matrix elements of the total Hamiltonians and expectation values of six quantum numbers are evaluated in the appropriate basis set $\left(S,P_s;P,J,M_J\right)$. Diagonalization of the total Hamiltonian matrix provides the energy levels while the eigenfunctions are used to transform expectation values of the quantum numbers into the eigenfunctions basis and for calculation of relative intensities of the allowed transitions. The reported Hamiltonians were successfully applied for fitting the observed IR and FTMW spectra of the O₂-DF and O₂-SO₂ complexes, respectively.