C2h point group

As shown in the Appendix (in Section V), in the C2h point group, the 1Ag - 1Bll (i.e. the monoelectronic r - jr excitation) possesses only an electric dipole moment, while in the C2V structure the electric and magnetic dipole moments, both non-vanishing, are orthogonal. In both cases the product in equation 1 leads to zero rotational strength. 

The molecule tmns-1,2-difluoroethylene, in Figure 4.18(h), belongs to the C2h point group in which none of the translational symmetry species is totally symmetric therefore the molecule has no dipole moment. Arguments using bond moments would reach the same conclusion. 

These two vectors may be used in the description of the stretching vibrations of the molecule. The molecular symmetry is C2h. Figure 4-7 helps to visualize the effects of the symmetry operations of this group on the selected basis. There are four symmetry operations in the C2h point group, E, C2, /, and ah. E leaves the basis unchanged, so the corresponding matrix representation is a unit matrix ... 

Figure 4-7. The four symmetiy operations of the C2h point group applied to the two N-H bond length changes of the HNNH molecule.

Since a representation—reducible or irreducible—is a set of matrices corresponding to all symmetry operations of a group, the representation can be described by the set of characters of all these matrices. For the simple basis of A/t and Ar2 used before for the HNNH molecule in the C2h point group, the representation consisted of four 2x2 matrices ... 

We do not know yet, however, whether this representation is reducible or irreducible. To answer this question, first we have to know the characters of the irreducible representations of the C2h point group. 

Table 4-3. A Preliminary Character Table for the C2h Point Group...

The character tables usually consist of four main areas (sometimes three if the last two are merged), as is seen in Table 4-5 for the C3v and in Table 4-7 for the C2h point group. The first area contains the symbol of the group (in the upper left corner) and the Mulliken symbols referring to the dimensionality of the representations and their relationship to various symmetry operations. The second area contains the classes of symmetry operations (in the upper row) and the characters of the irreducible representations of the group. 

Diimide, HNNH. This molecule belongs to the C2h point group (see Figure 4-7). The number of atoms is 4, so the number of normal vibrations is 3 x 4 — 6 = 6. 

Finally, let us decide which normal modes will be infrared active and which ones will be Raman active. The Cartesian coordinates belong to the Au and Bu irreducible representation of the C2h point group, while their binary products belong to Ag and Bg. Consequently, the selection rules are ... 

RetinalS. The structure and photophysics of rhodopsins are intimately related to the spectroscopic properties of their retiny1-polyene chromophore in its protein-free forms, such as the aldehyde (retinal), the alcohol (retinol or vitamin A), and the corresponding Schiff bases. Since most of the available spectroscopic information refers to retinal isomers (48-55), we shall first center the discussion on the aldehyde derivatives. Three bands, a main one (I) around 380 nm and two weaker transitions at 280 nm and 250 nm (II and III), dominate the spectrum of retinals in the visible and near ultraviolet (Fig. 2). Assignments of these transitions are commonly made in terms of the lowest tt, tt excited states of linear polyenes, the spectroscopic theories of which have been extensively discussed in the past decade (56-60). In terms of the idealized C2h point group of, for example, all-trans butadiene, transitions are expected from the Ta ground state to B , A, and A" excited states... 

The crystal of 23 is orthorhombic, space group Cmca. The molecules possess crystallographic 21m (C2h) point group symmetry, which involves the exact anti bisected form. This is the less stable form in the gas phase, as deduced from their relative abundance The deformation electron-density maps have been determined at 100 K by The... 

Trans-N2p2 has C2h symmetry and its coordinates are taken as those shown below. The character table of the C2h point group is shown below. 

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