Department of Chemistry, Carleton University, Ottawa, Ontario K1S5B6, Canada.
Phys Chem Chem Phys. 2018 May 7;20(17):12312-12322. doi: 10.1039/c8cp01394b. Epub 2018 Apr 24.
We derive general expansion formulas in vibrational coordinates for all bimodal Jahn-Teller and pseudo-Jahn-Teller Hamiltonians in tetragonal symmetry. Symmetry information of all the vibronic Hamiltonian matrix elements is fully carried by up to only 4 eigenvalues of symmetry operators. This problem-to-eigenvalue reduction enables us to handle thousands of vibronic problems in one work. The derived bimodal formulas can be easily extended to cover problems with one or more than two vibrational modes. They lay a solid foundation for future vibronic coupling studies of tetragonal systems. More importantly, the efficient derivation can be applied to handle (pseudo-)Jahn-Teller Hamiltonians for all problems with one principal symmetry axis.
我们推导出了在四方对称下所有双模态 Jahn-Teller 和赝 Jahn-Teller 哈密顿量的振动坐标中的通用展开公式。所有振子哈密顿量矩阵元的对称信息完全由最多 4 个对称算符的本征值携带。这个问题到本征值的简化使得我们能够在一次计算中处理数千个振子问题。所推导的双模态公式可以很容易地扩展到覆盖一个或多个振动模式的问题。它们为未来四方体系的振子耦合研究奠定了坚实的基础。更重要的是，这种高效的推导方法可以应用于处理具有一个主要对称轴的所有（赝）Jahn-Teller 哈密顿量。
