山西大学激光光谱研究所

_{A new and concise method to obtain the eigenvalues and eigenfunctions of a two-dimensional rotational–torsional Hamiltonian with correct boundary conditions is proposed for oriented AXn1–BYn2 type molecules. The corresponding eigenfunctions are not only eigenfunctions of the Hamiltonian but also common eigenfunctions of several symmetry operators. Numerical calculations for the lowest 1000 rotational–torsional eigenstates of BF2BCl2 demonstrate the advantages and applicability of our method.}

_{we propose a new and concise method to investigate the rotational–torsional eigenstates of oriented AXn1–BYn2 type molecules. Due to boundary conditions, the eigenstates of a rotational–torsional Hamiltonian are not the direct products of the rotational and torsional eigenstates even when there are no couplings. After considering correct boundary conditions, we obtain the final expression of the eigenstates. Two mathematically different but physically equivalent representations of the eigenstates are provided. With this efficient method, we have performed numerical calculations for the lowest 1000 rotational–torsional eigenstates of BF2BCl2. The corresponding results agree well with those obtained by much more time-consuming brute-force calculations using the conventional representation . In addition, our method automatically distinguishes degenerate or near-degenerate eigenstates due to the definition of quantum numbers with clear physical meanings. In contrast, the results of the brute-force calculations by conventional methods may mix up degenerate or near-degenerate eigenstates, leading to difficulties for further applications. The efficient method developed in this work can be used to calculate the corresponding eigenenergies and eigenfunctions of the other AXn1–BYn2 type of molecules. As an outlook, these eigenfunctions can be used for efficient manipulations of rotational–torsional dynamics of such molecules with intense laser pulses.}

Article link：https://doi.org/10.1063/5.0254560