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 (${}^3{\mathrm{\Sigma }}_g^{-}$)-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.

我们引入了两种有效的哈密顿量，适用于分析和拟合非平面或平面 O ₂ -闭壳配合物中的红外和MW高分辨率光谱，其中闭壳部分是任何对称性的硅藻或三原子分子。这些新的哈密顿量在我们对电子自旋角动量投影的量化方向的选择上有所不同。对于两种电子-自旋耦合方案，总的旋转-自旋-隧道哈密顿量包括隧道、电子-自旋-自旋耦合、电子-自旋-旋转相互作用和离心畸变力。此外，我们还介绍了 O ₂ (${}^3{\mathrm{\Sigma }}_G^{-}$)-XY ₂ (例如O ₂ -SO ₂和O ₂ -H ₂ O)二聚体，其中单体表现出渗透反转隧道运动。在适当的基组中评估总哈密顿量的非零矩阵元素和六个量子数的期望值$\left|S,{磷}_s;磷,J,{\mathrm{中号}}_J\right.〉$。总哈密顿矩阵的对角化提供了能级，而本征函数用于将量子数的期望值转换为本征函数基础并用于计算允许跃迁的相对强度。报道的哈密顿量成功地应用于分别拟合观察到的O ₂ -DF 和O ₂ -SO ₂配合物的IR 和FTMW 光谱。