Premium
Optical Rotation of Time‐Reversal Degenerate States
Author(s) -
Chiu YingNan
Publication year - 1985
Publication title -
journal of the chinese chemical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 45
eISSN - 2192-6549
pISSN - 0009-4536
DOI - 10.1002/jccs.198500033
Subject(s) - degenerate energy levels , polarizability , chemistry , optical rotation , dipole , t symmetry , angular momentum , spins , universality (dynamical systems) , rotation (mathematics) , electric dipole moment , symmetry (geometry) , condensed matter physics , quantum mechanics , molecular physics , physics , molecule , geometry , superconductivity , mathematics , organic chemistry
It is shown that time‐reversal (doubly‐) degenerate, many‐electron states in molecules of point‐group symmetry C 3 , C 4 , C 6 , S 4 , and S 6 and T etc., can have non‐vanishing matrix elements over a time‐odd (electric dipole‐electric dipole) polarizability operator contributing to optical rotation. In agreement with well‐known results for Kramers' doublets, the optical rotations of the two separated and oriented states of this doublet have opposite signs in this polarizability mechanism, and they have the same sign in the time‐even pseudoscalar mechanism which is the usual natural optical rotation of chiral molecules. These results are proven, in an alternative formulation using time‐reversal in a second‐order process, to hold regardless of even or odd numbers of spins—in contrast to the first‐order processes such as the Jahn‐Teller effect. The universality of time‐reversal in spin, orbital and rotational angular momentum, in point and continuous groups, is show in a unified treatment with consistent phases. It was shown also how time‐reversal symmetry can resolve the ambiguities in lower point‐groups and determine relationships for which the point‐group symmetry is powerless.