Multiple Substituent Shift Additivity

A simple example of how the total effect of more than one substituent can be predicted as the sum of the A8 effects of the individual groups can be seen with the dimethyldecalin shown below. The AS effects of an axial methyl group on C-2 and that of an equatorial methyl group on C-4 are added to the observed shifts for the parent to obtain a predicted spectrum that is quite close to that observed, with an avaage error of 0.4 and with a maximum error of only 1.2. While many of the carbons are not perturbed significantly by either substituent (e.g. C-8 and C-9), large effects for both substituents must be combined for C-3 and C-4, yet, errors here are very small. 

It should be mentioned here parenthetically that the A5 values provided in the tables of monosubstituted systems in this book were derived by comparing the observed shifts with those obtained for the parent that we felt best represented the same experimental conditions. Thus, the A8 values will often not correspond to the difference between the single set of absorption values reported for the parent (usually taken in deuterochloroform). They do reflect as accurately as possible the perturbation expected from a given substituent. 

A somewhat more complex case is rqvesented by the two, stereoisomeric bicyclo[3.3.0]octanes shown below. The AS values for each of the monosubstituted compounds (endo- or exo-2-methyl, endo- or exo-3-hydroxy, and exo-6-methyl) can be added to find a predicted total effect. These values can then be added to the shift values of the parent to arrive at a predicted absorption for each of the framework carbons. In this case the predictions are generally close to the observed spectrum so long as the substituents do not interact with each other either sterically or electronically. 

The observed absorption at 16.6 for the exo, endo, exo isomer fits well only with diastereomers 3 and 7, while the methyl group absorption for the endo, exo, exo isomer is reasonably close to that predicted for isomers 1,4, 6, and 8. When these conclusions are combined with the analysis above of the framework carbon atom absorptions, all but one diastereomer can be excluded for each of the observed compounds, leading to a reliable assignment of st eochemistry. 

In the examples above the assumption was made that the total effect of several groups could be predicted simply as the sum of the individual groiq)s shift effects. While this process resulted in only relatively small errors, there are certain situations where the resulting errors are substantial and it is important to have a clear understanding of when and why shift additivity does not hold. The largest errors are found when groups interact either electronically or sterically and the sections that follow will deal with those situations. 

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Fifolt [ 130] reported this chemical shift additivity method for fluorobenzenes in two deuterated solvents d6 acetone and d6 dimethyl sulfoxide (DMSO) Close correlations between experimental and calculated fluorine chemical shifts were seen for 50 compounds Data presented in Table 18 result from measurements in deuterochloroform as (he solvent [56] Fluorine chemical shifts calculated by this additivity method can be used to predict approximate values for any substituted benzene with one or more fluorines and any combination of the substituents, to differentiate structural isomers of multisubstituted fluorobenzenes [fluoromtrotoluenes (6, 7, and 8) in example 1, Table 19], and to assign chemical shifts of multiple fluorines in the same compound [2,5 difluoroamline (9) in example 2, Table 19] Calculated chemical shifts can be in error by more than 5 ppm (upfield) in some highly fluonnated systems, especially when one fluonne is ortho to two other fluorines Still, the calculated values can be informative even in these cases [2,3,4,6-tetrafluorobromobenzene (10) in example 3, Table 19]... 

A multiple regression analysis is performed on a matrix constructed from a series of chemical shifts values associated with parameters which have the properties of a delta function, i.e. parameters which are equal to 1 or O according as whether a substituent is present or not in the considered position. This treatment, which has been very successful in spectroscopy, leads to additive substituent incre-... 

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