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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.

General formalism for vibronic Hamiltonians in tetragonal symmetry and beyond