Group Correlation Tables

The effect of Eq. 10.52 on the prediction of spectral properties of organic crystals is considerable because the observable k = 0 states of a crystal can thus be extracted from point group correlation tables. The effect is... 

A number of masses in the low mass region (key ions) are considered to be characteristic for certain substructures or classes of compounds. In addition, mass differences (key differences) between the molecular ion and abundant fragment ions or between abundant fragment ions are often related to functional groups. Correlation tables containing such spectral data and the corresponding chemical structures are contained in several textbooks on MS. The use of these tables is widespread and often helpful in MS however, the capability of this approach must not be overestimated. 

Some of these group frequencies are listed in Table 19.1, and amore complete correlation table is provided in Appendix 11. 

What about all the other peaks You can ascribe some sort of meaning to each of them, but it can be very difficult. That s why frequency correlation diagrams, or IR tables, exist (Fig. 120). They identify regions of the IR spectrum where peaks for various functional groups show up. They can get very complicated. Check to see if you can find the C—H stretch and the C—O stretch that are in all four spectra, using the correlation table. It can be fun. 

The examples used above to illustrate the features of the software were kept deliberately simple. The utility of the symbolic software becomes appreciated when larger problems are attacked. For example, the direct product of S3 (order 6) and S4 (isomorphic to the tetrahedral point group) is of order 144, and has 15 classes and representations. The list of classes and the character table each require nearly a full page of lineprinter printout. When asked for, the correlation tables and decomposition of products of representations are evaluated and displayed on the screen within one or two seconds. Table VII shows the results of decomposing the products of two pairs of representations in this product group. 

The various possible site symmetries for the different point groups have been tabulated in several places 3, 19—21). The necessary correlation tables between point and site groups, which are used in discussions of the examples in this text are assembled in the Appendix. 

Table 9.6—Correlation table of organic functional groups in l3C NMR.

In a similar manner, we could determine the splitting of various sets of orbitals in environments of other symmetries which we may encounter in complexes, such as Td, DAtn D2d, and C2l., and indeed for any sort of symmetry we may encounter. An alternative and simpler way of obtaining this information is to use the results we have obtained for the octahedral case in conjunction with the correlation table given in Appendix IIB. In Table 9.3 are the results for a few point groups of particular interest. 

This table shows how the representations of group Oh are changed or decomposed into those of its subgroups when the symmetry is altered or lowered. This table covers only representations of use in dealing with the more common symmetries of complexes. A rather complete collection of correlation tables will be found as Table X-14 in Molecular Vibrations by E. G. Wilson, Jr., J. C. Decius, and P. C. Cross, McGraw-Hill, New York, 1955. 

The correlation tables for alkanes, cycloalkanes and alkyl groups are in Appendix 2, Table A2.1. 

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