Two codes for calculation of the rotation-spin-tunneling energy levels in the microwave and the infrared spectra of O2 (Σg-3)-XY2 open-shell complexes

Abstract

We developed new FORTRAN codes that employ two different Hamiltonians [Wafaa M. Fawzy, J. Mol. Spectrosc., 397, 111,822, 2023] for calculation of energy levels and relative intensities of rotational transitions in an asymmetric or a symmetric top weakly-bonded open-shell dimer. The type of complexes of interest consist of a polyatomic/diatomic closed-shell molecule and the O₂ diradical in its ground electronic state, where the monomers experience rotation-tunneling motion. The programs set up the Hamiltonian matrix considering pure rotation, quartic and sextic centrifugal distortion terms, electron-spin electron-spin coupling, R-dependence of electron-spin constants, electron-spin-rotation interaction, a symmetry treatment for rotation-tunneling of the monomers, and dependence of the rotational constants on the rotation-tunneling state. Numerical diagonalization of the total Hamiltonian matrix in the molecular basis set provides the eigenvalues and the eigenfunctions. The eigenfunctions are used to transform expectation values of the parity, five quantum numbers (<P>, <K>, <N>, <P_s>, <Σ>), and the electric dipole moment matrix elements from the Hamiltonian basis set to the eigenfunctions basis of the complex. Calculations showed that goodness of the quantum numbers depends on geometry and relative values of the electron–spin electron–spin coupling constants, the rotational parameters, the tunneling splitting. We used the Hellman–Feynman theory for calculation of derivatives of the eigenvalues with respect to molecular parameters, which significantly reduces the computer time for the non-linear least squares fits of transitions. The FORTRAN suites of computer programs were tested and validated by fitting the high resolution IR and MW spectra of the O₂–DF and the O₂-SO₂ dimers, respectively, with standard deviations within accuracy of the frequency measurement. However, the codes should be suitable for spectral analysis of any O₂ -XY₂ or O₂ -XY cluster, where XY₂ and XY represent a closed-shell non-linear triatomic molecule of C₂v symmetry (e.g. H₂O) and a diatomic entity (e.g. CO), respectively. The FORTRAN source programs, input and output files for spectral fits of the MW spectrum of O₂-SO₂ are discussed. In addition, zipped files of the suites of programs, the input and output files for fitting the MW spectrum of O₂-SO₂ and the IR spectrum of O₂ -DF, respectively, are provided as supplements that can be downloaded.