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Time‐reversal symmetry in molecular rovibronic states and in second‐order processes
Author(s) -
Chiu YingNan
Publication year - 1985
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560280614
Subject(s) - degenerate energy levels , spins , polarizability , degeneracy (biology) , symmetry (geometry) , t symmetry , tensor (intrinsic definition) , physics , quantum mechanics , electron , molecular symmetry , point group , rotation (mathematics) , symmetry operation , jahn–teller effect , condensed matter physics , rotational symmetry , molecule , ion , mathematics , geometry , bioinformatics , superconductivity , mechanics , biology
A unified treatment of time‐reversal symmetry is given for molecular systems. The treatment allows for interconversion of electronic, rotational, and vibrational angular momenta on equal footing because of a coherent phase choice. It also allows for correlation from a continuous group (of spherical or cylindrical symmetry) to lower point groups (such as C 3 , C 4 , C 6 , S 4 , S g , T , etc.). General, many‐electron molecular states that form time‐reversal degenerate components are constructed. Attention is called to the Kramers' doublets as the special odd‐electron case of such double degeneracy. Specific examples of a spiropentane and a 5‐azoniaspiro(4.4) nonane with S 4 symmetry and possible time‐reversal degeneracy are given. The optical rotation due to a time‐odd polarizability tensor in one of the two time‐degenerate components is shown to be of an opposite sign to that in the other component. The above result is from a second ‐ order matrix element (over the polarizability tensor) and is proved to be independent of even‐ or odd‐number of electron spins. It is shown to hold also for Kramers' doubly degenerate components. This result is contrasted with that of a first ‐ order Jahn‐Teller effect which depends on the number of electron spins.