Symmetry diagram

A symmetry diagram showing a projection of the unit cell and the location of all its symmetry elements. 

Shown below are the symmetry diagrams for C222 and (2222, the only two C-centered orthorhombic space groups. C2,2 2 does not exist because C222 already contains the sets of 2, axes parallel to the a and b axis. (22,2,2, is, in fact, (2222, possibly with a shift of origin. Finally, C2,22 and C22,2 are simply C222, with relabeled axes, while (222,2, and (22,22, are relabeled versions of (22,2,2 (which, as already noted, is (2222). 

There is no space group that could be called Pna2. Show why. (Hint draw the symmetry diagram implied and examine its effect on a general point.)... 

In connection with a-ir exchanges of equations (94) and (96), we noted that certain additions or eliminations were forbidden. A typical orbital symmetry diagram for the forbidden four-center bromine addition to an alkene is given in Fig. 22. Apparently similar concerted additions are allowed, e.g. hydrogen halides in equation (97), because favorable orbital overlap is available. 

In the following discussion, for simplicity we make use of the pair of symmetry diagrams that constitute a representation of space group P2 jc (No. 14) in International Tables for X-Ray Crystallography Volume /, as displayed in Fig. 9.3.4. 

Table 9.3.10. Symmetry diagrams and equivalent positions of some commonly occurring space groups...

Figure 4.32 State symmetry diagram for the protonation of an n,n excited triplet ketone...

A state-symmetry diagram for the Norrish type II reaction (Section 6.3.4) shows that it is allowed only from the n,7t singlet and triplet states to give the covalent biradicals (Section 5.4.4) 1DC7l and 3DC7l, respectively, but not from 7t,7i states (Figure 4.33).331... 

Figure 4.33 State symmetry diagram for intramolecular hydrogen abstraction. The symmetry labels refer to the plane of the carbon chain...

P.W. Atkins, M.S. Child and C.S.G. Philhps (1970) Tables for Group Theory, Oxford University Press, Oxford - A set of character tables with useful additional notes and symmetry diagrams. 

The addition of to a >C=C< system is thermodynamically favorable but generally difficult to achieve. In the laboratory, chemists use catalysts such as platinum black and Rainey nickel to make the reaction proceed at a reasonable rate. The kinetic barrier for this reaction can be understood in terms of simple orbital symmetry diagrams, shown in Figure 5.2. The basic principle is that in the activated state the electrons must flow in such a way as to make and break the appropriate bonds. In the case of hydrogenation, the electron flow must break the H—H o and C—C n bonds and make two C—H bonds. The electrons must flow from an occupied orbital on one molecule to an unoccupied orbital on the other, that is, from the highest occupied molecular orbital, HOMO, on one species to the lowest unoccupied molecular orbital, LUMO, on the other. 

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