Abstract
Spectra of high-symmetry molecules contain fine and superfine level cluster structure related to J-tunneling between hills and valleys on rovibronic energy surfaces (RES). Such graphic visualizations help disentangle multi-level dynamics, selection rules, and state mixing effects including widespread violation of nuclear spin symmetry species. A review of RES analysis compares it to that of potential energy surfaces (PES) used in Born–Oppenheimer approximations. Both take advantage of adiabatic coupling in order to visualize Hamiltonian eigensolutions. RES of symmetric and D2 asymmetric top rank-2-tensor Hamiltonians are compared with Oh spherical top rank-4-tensor fine-structure clusters of 6-fold and 8-fold tunneling multiplets. Then extreme 12-fold and 24-fold multiplets are analyzed by RES plots of higher rank tensor Hamiltonians. Such extreme clustering is rare in fundamental bands but prevalent in hot bands, and analysis of its superfine structure requires more efficient labeling and a more powerful group theory. This is introduced using elementary examples involving two groups of order-6 (C6 and D3~C3v), then applied to families of Oh clusters in SF6 spectra and to extreme clusters.
Highlights
A key mathematical technique for atomic or molecular physics and quantum chemistry is matrix diagonalization for quantum eigensolution
Before describing tensor eigensolution techniques and rovibronic energy surfaces (RES), a brief review is given of potential energy surface (PES) to put the tensor RES in a historical and methodological context
The latter have only recently been seen in highly excited rovibrational spectra [2] and present challenging problems of symmetry analysis to sort out a plethora of tunneling resonances and parameters for so many resonant states
Summary
A key mathematical technique for atomic or molecular physics and quantum chemistry is matrix diagonalization for quantum eigensolution. We are motivated to seek ways to visualize more of the physics of molecular eigensolutions and their spectra This leads one to explore digital graphical visualization techniques that provide insight as well as increased computational power and thereby complement numerically intensive approaches [1]. Following this is a discussion of mixed-rank tensors that exhibit 12-fold and 24-fold monster-clusters. It uses underlying duality between internal and external symmetry states and their operations. A main idea is that symmetry operators “know” the eigensolutions of their algebra and of all Hamiltonian and evolution operators made of gk’s
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