Group double groups

The character tables in Appendix A3 include the spinor representations of the common point groups. Double group characters are not given explicitly but, if required, these may be derived very easily. The extra classes in the double group are given by Opechowski s rules. The character of if in these new classes in vector representations is the same as that of R but in spinor representations x(ff) = — (R). The bases of spinor representations will be described in Section 12.8. 

Double group Standard group Double group Standard group... 

When Cj symmetry is present, irreducible representations of the double group (see Table II) so that = 0 by symmetry. In this case, there are only... 

Species of Spin Functions for Some Important Double Groups... 

Case (b). This case includes no single-group representations, and all real one-dimensional, double-group representations. This includes only the following. 

Case (c). This case includes all single- and double-group representations with complex character. 

Dominant-diagonal theorem, 58 Doob, J. L., 171,174,269 Dorodnitzin, A., 388 Double-group representations, 737 Double groups, 727... 

Functional groups are either attached to the carbon backbone of a molecule or form part of that chain. Examples are the chlorine atom in chloroethane, CH3CH2CI, and the OFF group in ethanol, CFF CI OFi. Carbon-carbon multiple bonds, such as the double bond in 2-butene, are also often considered functional groups. Table 19.1 lists the most common functional groups. Double and triple carbon-carbon bonds were considered in Chapter 18. In the following eight... 

Functional group Double bond Triple bond... 

If there is no functional group, double bond, or triple bond, then we should number the chain so that the substituent has the lower number ... 

Recent Advances in the Chemistry of Group 14-Group 16 Double Bond Compounds... 

Second, every compound with a Group 14-Group 16 element double bond corresponds to a minimum on the potential energy surface, as confirmed from all positive eigenvalues of the Hessian matrix. This suggests that all the double bond compounds in Table I are synthetically accessible, if one can find an appropriate synthetic methodology. 

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