Calculated torsion-vibration energy levels in the crude adiabatic approximation [Eqs. (4) and (5)], in the adiabatic limit [Eqs. (4) and (9)], and for a fully coupled solution of the model Hamiltonian. The doubly degenerate levels have symmetry in and the singly degenerate levels are and with the levels indicated (#). Correlation lines between the three stacks of levels connect levels of the same symmetry and the same or similar vibrational character. Labels on either side indicate the nominal torsion-vibration character of the levels. Labels on the left are best for the ground torsional state of each CH stretch fundamental where each vibration is split into and states by torsional tunneling. Labels on the right are most appropriate for the highest levels where torsional tunneling becomes free internal rotation and and coalesce into the degenerate vibration .
Scaling behavior of nonadiabatic (IVR) matrix elements. Points represent the torsion-vibration coupling matrix elements at each coupling order, averaged over the indicated range of torsional states. The lines are linear fits, which give the indicated values of the scaling parameter, .
The scaling behavior of the coefficients of two adiabatic torsional wave functions of the vibration. In one case, the largest contribution is from the torsional angular momentum, (solid squares), and in the other from (solid circles). The lines serve as a guide to the eye to highlight the trend of the solid points. For comparison, two torsional functions of the ground vibrational ground state are also represented, one with (open squares), and the other with (open circles).
Labeling schemes for adiabatic basis states and fully coupled eigenstates.
Mixing of selected pairs of adiabatic basis.
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