Symmetry eigenvectors pyrocatechin

From this character table, the symmetry eigenvectors for the double internal rotation in planar pyrocatechin are easily deduced on the basis of the double free rotor equation solutions ... 

The non-degenerate symmetry eigenvectors (49) are identical to those of non-planar pyrocatechine(40) except for the threefold multiplicity. The twofold... 

The symmetry eigenvectors of such a group are easily deduced multiplying those of planar pyrocatechin (34) by cos Ma or sin A/a. 

The symmetry eigenvectors may be constructed from those of the former group, by multiplying by cos Ma or sin Ma, and gathering the products by pairs according to their symmetry properties with respect to operations of the subgroup WUy A [ UU y x (Cft/ ) ] of (98), as in the case of non-planar pyrocatechine (89). 

As in the previous case of pyrocatechin, the symmetry eigenvectors of such a group may be deduced from those of the preceding group (98) by taking into account in the present case the products by cos Ma and sin Ma belonging to different irreducible representations. 

In the present paper, symmetry eigenvectors which factorize the Hamiltonian matrix into boxes are given for the single rotation in phenol (24) for double rotations in benzaldehyde (29), pyrocatechin (34) and acetone (44-46), for double rotation and inversion in non-planar pyrocatechin (40) and pyramidal acetone (49-51). In the same way, symmetry eigenvectors deduced in the local approach are deduced for some of these non-rigid systems (79), (83), and (89). Symmetry eigenvectors for the double internal Czv rotation in molecules with frame of any symmetry are given in reference [36]. 

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See also in sourсe #XX -- [ , ]

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