Gerade

The cross section for scattering by the gerade potential is then the combination... 

For ungerade potentials, for ieven and j for iodd. For gerade potentials, p = "for ieven and... 

For homonuclear molecules (e.g., O2, N2, etc.) the inversion operator i (where inversion of all electrons now takes place through the center of mass of the nuclei rather than through an individual nucleus as in the atomic case) is also a valid symmetry, so wavefunctions F may also be labeled as even or odd. The former functions are referred to as gerade (g) and the latter as ungerade (u) (derived from the German words for even and odd). The g or u character of a term symbol is straightforward to determine. Again one... 

When this overall sign is positive, the function F is gerade and its term symbol is appended with a "g" subscript (e.g., the level of the O2 molecule, which has 7iu" 7ig 2 occupancy is labeled 2ig) if the sign is negative, F is ungerade and the term symbol is so amended (e.g., the If level of the ItIu configuration of the... 

If a eenter of symmetry is present, all of the states arising from are gerade however, the states arising from 71% ean be gerade if n and 71 are both g or both u or ungerade if n and 71 are of opposite inversion symmetry. 

Fig. 2. Simplified molecular orbital diagram for a low spia octahedral complex, such as [Co(NH3 )g, where A = energy difference a, e, and t may be antisymmetric (subscript ungerade) or centrosymmetric (subscript, gerade) symmetry orbitals. See text.

Figure B A qualitative molecular orbital diagram for ferrocene. The subscripts g and u refer to the parity of the orbitals g (German gerade, even) indicates that the orbital (or orbital combination) is symmetric with respect to inversion, whereas the subscript u (ungerade, odd) indicates that it is antisymmetric with respect to inversion. Only orbitals with the same parity can combine.

Darm, m. gut, intestine. — blinder —, caeeum. — dicker —, colon. — dilnner —, small intestine. — gerader —, rectum- — langer —, ileum. — leerer —, jejunum. 

Modes of flu symmetry are inactive, g = gerade modes are Raman active, u = ungerade modes are IR active... 

The factor group Dzh of orthorhombic Sg includes an inversion operation therefore, the g-u exclusion principle works resulting in modes of either Raman (gerade, g) or infrared activity (ungerade, u). 

One attitude would consist in restoring symmetry by a symmetric superposition of the degenerate and linearly independent but non orthogonal symmetry-broken solutions, considering the gerade and ungerade combinations of the A+A and AA solutions in the... 

In spectroscopic applications the letters g and u (German Gerade, Ungerade) are used to specify the symmetry of the functions under the inversion operation, x — —x. Note that the normalization constant is given by y/TJI, as before. 

Abb. 23. Widerstand R einer bei 90° K entstehenden Kalium-Schicht als Funktion dcr Bcdeckung <3. Eitigezeichoete Gerade nach GI. (14) (nach Nossek). 

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