The rotation-vibration structure of the SO$_2$ $\mathrm{\tilde{C}}^1\mathrm{B}_2$ state explained by a new internal coordinate force field

A new quartic force field for the SO$_2$ $\tilde{\text{C}}$$^1$B$_2$ state has been derived, based on high resolution data from S$^{16}$O$_2$ and S$^{18}$O$_2$. Included are eight $b_2$ symmetry vibrational levels of S$^{16}$O$_2$ reported in the first paper of this series [G. B. Park, $\textit{et al.}$, J. Chem. Phys. $\textbf{144}$, 144311 (2016)]. Many of the experimental observables not included in the fit, such as the Franck-Condon intensities and the Coriolis-perturbed effective $C$ rotational constants of highly anharmonic $\tilde{\text{C}}$ state vibrational levels, are well reproduced using our force field. Because the two stretching modes of the $\tilde{\text{C}}$ state are strongly coupled via Fermi-133 interaction, the vibrational structure of the $\tilde{\text{C}}$ state is analyzed in a Fermi-system basis set, constructed explicitly in this work via $\textit{partial}$ $\textit{diagonalization}$ of the vibrational Hamiltonian. The physical significance of the Fermi-system basis is discussed in terms of semiclassical dynamics, based on study of Fermi-resonance systems by Kellman and coworkers [M. E. Kellman and L. Xiao, J. Chem. Phys. $\textbf{93}$, 5821 (1990)]. By diagonalizing the vibrational Hamiltonian in the Fermi-system basis, the vibrational characters of all vibrational levels can be determined unambiguously. It is shown that the bending mode cannot be treated separately from the coupled stretching modes, particularly at vibrational energies of more than 2000 cm$^{-1}$. Based on our force field, the structure of the Coriolis interactions in the $\tilde{\text{C}}$ state of SO$_2$ is also discussed. We identify the origin of the alternating patterns in the effective $C$ rotational constants of levels in the vibrational progressions of the symmetry-breaking mode, $\nu_\beta$ (which correlates with the antisymmetric stretching mode in our assignment scheme).