Measuring Coupling Constants from First Order Spectra

5 MEASURING COUPLING CONSTANTS FROM FIRST-ORDER SPECTRA 

When you determine the couphng constants of a compound from an actual spectrum there is always some question of how to go about the task. In this section we wiU attempt to give some guidelines that will help you to approach this problem. The methods given here apply to first-order spectra methods for second-order spectra are given in Section 5.10. Fortunately, most spectra determined at 300 MHz or greater will be first-order spectra. 

First-order resonances have a number of helpful characteristics, some of which are related to the number of individual couplings, n  

symmetry about the midpoint (chemical shift) of the multiplet. Note that a number of second-order patterns are also centrosymmetric, however (Section 7.7)  

the maximum number of lines in the multiplet = 2 the actual number of lines is often less than the maximum number, though, due to overlap of lines arising from coincidental mathematical relationships among the individual / values  

the line intensities of the multiplet correspond to Pascal s triangle (Section 5.16)  

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B 5.5 MEASURING COUPLING CONSTANTS FROM FIRST-ORDER SPECTRA... 

Measuring Coupling Constants From First-Order Spectra 235... 

Measuring Coupling Constants from First-Order Spectra 381... 

More complex spin-spin interactions. As the chemical shift difference becomes similar to the value of the coupling constant, the first-order analysis breaks down completely. It is then not possible to measure either the chemical shift or the coupling constants directly from the spectrum and resort must be made to more rigorous analytical procedures which are beyond the scope of this book. However, there are available a variety of computer programs specifically designed to analyse complex n.m.r. spectra.3 1... 

A) Measure the positions and amplitudes of all the lines in the spectrum and list them in order in a table (a spreadsheet program is convenient for this purpose). A well-defined measure of position in a complex spectrum is the x-axis point halfway between the maximum and minimum of the first-derivative line. The amplitude is the difference in height between the maximum and minimum. If convenient, measure the line positions in gauss if this is inconvenient, use arbitrary units such as inches, centimeters, or recorder chart boxes measured from an arbitrary zero. In your table, also provide headings for the quantum numbers (m1 m2, etc.) for each of the line positions, for the coupling constants (a, a2, etc.), and for the theoretical intensity (degeneracy) of each peak. 

Energy levels and transitions for the proton spin states of formaldehyde. On the left are the levels obtained with neglect of spin-spin interaction, and they are labeled by the ra, quantum numbers of the two protons. The middle level is doubly degenerate. If spin-spin interaction is treated with first-order degenerate perturbation theory, the levels on the right result, with an assumed size of the coupling constant, /. A transition from the 7 = 0 state to an / = 1 state would measure /, but that is a forbidden transition. No splitting of the line in the spectrum occurs. 

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